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Manfred Mohr - Celebrating my 50 Year Aniversary (1969 - 2019)


Creating Computer Generated Art by Writing Algorithms

From random walks to algorithmic modulations, my history of writing algorithms

Beta Version 1.1 - September 1, 2019


1938 born on June 8 in Pforzheim, Germany

I lived and worked in:

  • 1962 - 1963, Barcelona
  • 1963 - 1983, Paris
  • 1980 - Present, New York

Early Developments

1950s Kepler-Gymnasium Pforzheim

1956 Interests in my young adulthood

  • Music: Played tenor saxophone and oboe, Jazz and Classical music.
    I was influenced by Mattias Hauer, Anton Webern and Karlheinz Stockhausen in modern music, Stan Getz, John Coltrane, Sunny Rollins and Thelonious Monk in Jazz.
    I played in Jazz clubs in Germany and later in Spain and Paris.
  • High-Frequency Engineering: Built electronic devices; radios and amplifiers
  • Fine Art: Interest in visual arts; Egyptian art, Cycladic art, Catalan Romanic frescos, Jackson Pollack, Henry Moore, Antonio Tapies - to mention a few.

I chose fine art

  • 1957-1961 Art School Pforzheim: Kunst + Werkschule, Pforzheim
    gold and silversmithing, plus studied art history and painting with Prof. Adolf Buchleiter
  • 1961 received school prize in art from the City of Pforzheim for foreign studies. Chose to go to Barcelona
  • 1962-1963 Barcelona: Inscribed in art school, painted in Abstract Expressionist style and joined rock band "Rocky Volcano" with whom I traveled through Spain playing saxophone.
  • 1964-1967 Ecole des Beaux Arts, Paris Inscribed in Lithography, Atelier Clarin

1960 - 1969: Towards the Computer


  • Early 1960s Action Painting: Very influenced by the early work of K.R.H. Sonderborg; his fast gestures and mechanical rhythm.
  • 1961 discovered Max Bense: His rational aesthetics changed my artistic world view completely.
  • 1962 Began the exclusive use of black and white as means of visual and aesthetic expression (binary decisions) Remained black and white until 1999
  • 1963 -1966 Geometry enters my abstract expressionist paintings, in my search for a rational aethetics.
    Influenced by the music of Anton Webern, space and silence.
    Webpage about my early work
  • 1967 - 1968 "Surrealistic Geometry": Geometric experiments led to hard edge painting and and the systematization of the picture content, influenced by electronic signs.
    Webpage about this work

1966 - 1969 Designed and built electronic interactive sound sculptures

  • 1966 - 1967 Lecteur I, a "visual poetry" interactive kinetic / sound machine in collaboration with Jochen Gerz
    I designed and built the music and electronics. Jochen Gerz provided the text.
    It is now considered the first sculpture using ping-pong balls and loud speakers according to Dr. Cathy van Eck
    Webpage about the electronic sculpture Lecteur I
  • 1968 - 1969 built and designed the sound for Ruth Francken's "Egg" sculptures
    Webpage of my collaboration on this

1968 - 1969 My first Visual Poetry Artist Book, "Artificiata I" is published

My first One Person shows (and Catalog):

  • 1968: My First one-person exhibition took place at Daniel Templon Gallery, Paris
    Press including: Catherine Millet in Les Lettres Françaises.
    My first one-person catalog was published
  • 1969: My second one-person show took place at Anne-Marie Verna Gallery, Zurich
  • Both shows exhibited my hard edge geometric paintings, as well as the Lecteur I sculpture.
    My webpage with Catalog, Shows, Press, Invitations ...

Some important Group shows at this time

  • 1965: "Black and White" at Galerie Paul Fachetti, Paris.
    Press New York Times, International Edition called my work "Geometric Hints" and "Frantic Wisps".
  • 1966: DIVERGENZEN 66, Galerie Margarete Lauter Mannheim

1967: Met the composer Pierre Barbaud in Paris, a pioneer of computer music

  • I understood algorithmic procedures from conversations with him. He explained to me how he writes computer music.

1969 - 1973: My Early Computer Drawings

  • 1969: First drawings with a computer
    I was ready and not afraid of creating algorithms and writing computer programs based on my previous experience designing and building electronic devices.
    I chose to write my programs in Fortran IV because I had an visual rapport with it.
    From autumn 1969 until today, all my art work has been created through algorithms and computer programs that I write myself.
  • 1968: After a lecture of Pierre Barbaud, a few of us discussed starting a group at the University of Paris 8, Vincennes (just being established as a results of Mai '68).
  • 1969: This group was created as "Art et Informatique". We started a seminar before we had a computer. We got an old SDS (scientific data systems) computer in the summer and it was installed by mid Fall.
    Some documentation about this time:     Some pages about me from the catalog "Coding the World", Centre Pompidou 2018     Franke article Leonardo, 1971
  • Early October 1969: I met Estarose Wolfson through a friend who brought us together because I was an artist working with computers, and Estarose was a mathematician who had worked in Computer Science in a research lab and was interested in art. We married a few years later.
  • Mid-October 1969, I wrote my first computer program, a random number generator (of course, with an error).
    First computer program I wrote
    My interest in discovering the logic of my work led me to have a very intimate relationship with writing my algorithms and discovering myself through this process. I bought, in early 1969, the only available Fortran book in France and immediately understood that I had to get involved with geometry and logic to understand programming. I later acquired several mathematical handbooks which became my research tools.
    Estarose was involved with her own work, but was always available to answer my questions and share her experience and expertise. For me, this interaction was most valuable. Through her I had contact with the scientific community, which was always intregal to my interests.
  • 1969 Works from this time: Random number collages with vertical lines and reflection, Random number wooden sculpture with vertical lines, P-10 Random Walk drawings with alternating horizontal and vertical lines, P-16 - P-18 Random Walk drawings with horizontal and vertical lines, zig-zags and square waves, culminating in P-21, band-structures (elements as in P-18) in a linear structure from left to right (as in western writing).
    Since in Vincennes we didn't have an output device, I had to plot the lines by hand from the data generated by my computer programs - Thus my hand was the plotter. I made many of these drawings, most of which were made in 1969, some in very early 1970. This procedure was frustrating and time-wise exhausting and with P-21 became infeasible.
    Random number collages,     Wooden sculpture from Random Numbers,     P-10 drawings,     P-18 drawings     P-21 drawings
  • 1969 - first plotting device: Luckily a friend of Estarose ran my program P-18 on the high-resolution light beam plotter at Brookhaven National Laboratory and sent me 30 of these drawings. It was the most overwelming experience that one logic can so easily produce such a variety of visual result.
    Webpage of these drawings.
  • April 1970, The first time my computer generated art is exhibited:
    My random number sculpture and several P-18 drawings were shown at Computer Graphics '70. Some of these works are now in the collection of the Victoria & Albert Museum. (Artifacts from CG '70)
  • Early spring 1970 - first mechanical ink pen plotter drawings (second access to a plotting device): Through the connection of a friend, I got access to a Zuse high-resolution flatbed ink pen plotter and a IBM 7040 computer at the University of Darmstadt, Germany. I plotted P-21. It was a milestone.

  • Spring 1970: Access to Meteorologie Nationale Paris.
    Having previously seen a TV news show, I approached Meteorologie Nationale in Paris, asking to use their Benson high-resolution flatbed ink pen vector plotter, along with their CDC 6400 computer. They granted me access, but I had to officially write a letter and on June 17, 1970, I received the official permission that I could work nights and weekends in their computer center.
    A dream came true, I had the unique access to a technological paradise! I worked there until 1983 when I moved full-time to New York.
    Draft of Letter to Meteorologie Nationale, Paris       Letter of Acceptance from Meteorologie Nationale, Paris       Some photos at Meteo.
  • Facts about this Benson flatbed plotter:
    Size: It had a large plotting area (for the time): In the range of: 1 meter by 1.30 meters.
    Resolution: It was a high-resolution vector plotter with .1 mm step (fast mode .2 mm step), thus it drew very smooth lines.
    Material: Any type of paper and thin smooth canvas could be used with it. I thus used drawing paper, tracing paper, thin canvas, and a treated metal plate. The paper was held down with electrostatics.
  • Spring 1970 - P-21, band-structures (the algorithm I developed in Univ. of Paris - Vincennes, 1969) was the first algorithm I plotted at Meteorologie Nationale: I made many drawings from the algorithm P-21, at that time.
  • 1969 - 1973: It was very easy for me to invent and write another algorithm every day, I had many ideas. For the most part these drawings were logically not connected to each other. I made many of some and few of others at that time.
  • 1969 - 1973: Types of algorithms and methods I invented: Linear Writing, Random Circuits, Path Finding, Linear Transformations, Matrices, Alphabets using the Lines of Squares and Triangles, Division of Space, Shearing, Adding and subtracting of lines, Reflection, Overlaying, Shifting, Superstructures and Substructures, Complimentary elements, Top and bottom of drawing joined as in a torus. Algorithms which kept in memory what was already drawn. I used straight lines, circles, and curves (spline curve fitting). I made short and long series of drawings. I digitized a circuit and made a drawing from it with varying transformations. I made drawings, sculptures, and films (more about this later).
    Webpage with my early algorithms       My webpage about linear transformations in my work
  • 1970 - 1972, Some other experiments I made at that time:
    Room with a continuous random line on randomly generated walls, cardboard model, 1971 (published 1973)
    Random Number book, 1971
    I produced a real printed circuit (on pertinax) from my Random Circuit program P-133, cluster phobia, 1972

Important shows at that time

1971: Historic one-person museum exhibition

  • 1971: First one-person show of digital computer generated art in a Museum, Paris, "Manfred Mohr - Computer Graphics - "Une Esthétique Programmée" ARC, Musée d'Art Moderne de la Ville de Paris
    I showed 20+ drawings, demonstrated some of the drawings on a large Benson high-resolution flatbed plotter (installed by the company), and hung a large white panel, a sort of guest book, asking what the visitors thought about art and the computer. This banner has become a survey of opinions of the time. (Now on permanent loan at ZKM, Karlsruhe)
    Webpage about Show, Catalog, Banner, Photos, Press - le monde etc.

1972 - 1974: Other one-person exhibitions showing this work

  • 1972: Galerie Hendrike Swart, Amsterdam
  • 1973: Galerie Edith Wahlandt, Schwäbisch Gmünd
  • 1974: Galerie Pierre Weiller, Paris
  • 1974: Galerie Gilles Gheerbrant, Montreal

1973: Group Show

  • 1973: New Tendancies 5, Zagreb, Croatia/Yugoslavia.
    I was in this important group show see: About / Artists and the excellent book by Margit Rosen, ZKM.

1972: Sold my first computer drawing:

  • Artist and Collector Gottfried Honnegger bought a drawing from the algorithm P-48, "UHF 81", 1970 which is now one of my artworks in the collection of the museum EAC, Espace de l'Art Concret, Mouans-Sartoux, France

1971 and 1974: One-person catalogs covering this work

Computer generated 16mm algorithmic films

  • 1972-1974: In 1972, the CEO of a company specializing in micro film (who saw my 1971 show at ARC) invited me to use his company's machines to make 16mm films. I made 3 short film between 1972 - 1973 (and another 2 in 1973 - 1974, talked about later). I made long series of drawings on cellulite for the films (which were transfered onto 16mm film). I also made long series of drawings on paper from my algorithms.
  • See my webpage about the films


1973 - to the present: Visual Instruments / Algorithmic Systems

  • I had been inventing, writing, and plotting algorithmic artworks since 1969. It was easy for me to create a new algorithm daily. In 1973, I felt I had to search for a more global concept. Since an instrument in music has its unique sound, one recognizes the instrument. I felt that I could invent a "Visual" Instrument with my algorithms which expresses a graphic system. This I found in the cube and hypercube.
  • All my algorithms from this time forward use fixed structures, the 3-D cube or n-D hypercube.
    The cube and hypercube are structures having fixed relationships between vertices, edges, and planes.
  • In all algorithmic systems, I find and create new and different relationships that are inherent in the structure.

  • A word about computer generated art and dates:
    With algorithmic computer art there are two dates associated with an artwork. The first date is the year of the finished algorithm written as a computer program (which is also the date of the first artwork generated from this program). The second date reflects when a particular artwork is rendered at a later date, since once an algorithm is written many unique artworks can be generated from it.
    Since I didn't realize the importance of signing my artworks with the two dates until late 1977, my algorithmic artworks from 1969 to late 1977 are single dated with the date of their actual physical realization. From late 1977 to the present my artworks are double dated - Algorithm/Rendering - unless these two dates are the same.
  • My artworks were realized within a short time-frame after their generating algorithm was written, but some were realized again later for special reasons.

  • Selection of aspects of the complete system:
    In the western alphabet there are 26 letters: We would not use them all together. One chooses single letters to create a word. The same in music, there are 12 half-tones in an octave, no one would play them all at the same time. One would choose single tones to create a melody. I do the same thing in fixed systems of cubes and hypercubes. I choose subsets from this structure to create my visual instrument with which I work. I was never interested in showing the complete system but only aspects of it, thus visually fracturing the symmetry and at the same time creating an ambiguity in the sign.

1973 - 1975 and 1976: Cubic Limit I

  • 1973: First use of the cube as a fixed system, a generator of my artworks: The 12 edges of the cube became my alphabet to which I apply algorithms.
  • 1970-1973, Earlier use of a structures's lines as an alphabet : I used the lines of squares and triangles as an alphabet, 1972 and 1973, created cubes 1971 from linear transformations, and added and subtracted lines 1970 to form structures. These were unrelated individual drawings. All methods were published at the time.
    Webpage for these earlier examples       My webpage for geometric objects used as alphabets
  • 1973 - 1976, Methods and Algorithms I created and used: Rotational, Statistical, Combinatorial, Complementary objects, Arithmetic and Logical operations on lines, Adding and subtracting of lines, Summing of lines (the width of a line equals its multiple use), Overlaying structures, Extension of the 2-D projection of the cube to a circumscribed circle. I created long series, Introduced a visual formula of the process.
  • I showed all combinations of n-lines of cube at time in series of 13 drawings, 1975, and also in my 16mm films 1973 - 1974,
    Webpage of Cubic Limit I       Webpage about combinatorics in my work
  • 1973: I made drawings studying the cube for my 16mm films Some of these drawings
  • 1973 - 1974: I made the computer generated algorithmic 16mm short films "Cubic Limit" and "Complementrary Cubes". 16mm Film Webpage

Shows, Catalogs, Press

  • 1975: This work was first shown in my one person show at Galerie Weiller, Paris: They were Also shown in one person shows in Amsterdam, 1975 and in Neuchatel, Stuttgart, Montreal, Hamburg 1976.
  • 1975: The art critic of Le Monde, Michel Conil Lacoste writes positively about my show in Paris: Article, Other press about the shows
  • 1975: Cubic Limit catalog with work 1973 - 1975: Webpage of Shows, Catalog, Invitations, Press ...
  • 1977: Cubic Limit II, contains two parts, showing Cubic Limit I from 1975 - 1976 : Webpage of Catalog, etc

Some experiments at this time

  • 1974, Hybrid drawings - sewing plus computer drawing: Webpage
  • 1975, Computer generated and plotted etchings: I replaced the pen on the plotter with a steel needle and drew on a treated copper plate. A numbered etching was included in first 100 1975 catalogs. Webpage
  • 1975, I participated in an early teleconference between Paris and Geneva (long before the WWW was invented): Webpage.
  • 1976, I created vertical artworks of transformation of images and text on continuous sprocketed computer printer paper for the group show Contrastes at the Centre Culturel du Marais, Paris: Webpage
  • 1976, I wrote programs for Anamorphoses (cylindrical-, pyramidal- and conical-projections) for a group show Anamorphoses at the Museum of Decorative Arts, Paris: My Cube anamorphose is in the Paris catalog of the exhibition. Webpage
  • 1971 and 1973, Twice I was invited to write about computer art in the journal Humidité Nr.5, 1971 (I was guest editor) and Nr.14/15, 1973. Info
  • 1973, I was invited to be guest editor of Page 28, of the Computer Arts Society, CAS. A survey of computer art in Paris.

1973: Awards

  • World Print Competition-73, San Francisco
  • 10th Biennial in Ljubljana

1976 - 1977: Cubic Limit II


  • Cubic Limit II uses Windowing and Clipping of the 3-D cube to generate the artworks of this visual algorithmic system.
  • 3-D Cubes are divided into two parts by one of the Cartesian planes. For each image, the two partitions contain independent rotations of a cube. They are projected into two dimensions and clipped by a square window (the projection of a cube at 0,0,0 degrees). Furthermore this clipping forms an inside and an outside. By rotating both parts of these cubes in small but different increments, long sequences of images are developed.

Websites, Catalogs

Some added information on this work

  • 1977: Re-started making paintings, this time with a ink pen plotter on Canvas
  • 1977: Overlay and Tranparency: In my drawings, I overlayed 2 sheets of drawing paper, with the top one slightly transparent, to create a gray surface.

1977, IBM Film Interview

  • 1977: "Ideas, Experiments, Results" 1979 film interview: IBM Germany and Condor-films Zurich made film with 7 artists from 5 countries working with a computer (Art, Music, Poetry). My interview was conducted in 1977 at both Meteorologie Nationale and my apartment in Paris.
    The interview gives an overview of how I was working at the time. I speak about programming among other things.
    My excerpt, English version, Webpage of this excerpt

Some one-person shows in galleries

  • 1977: Weiller, Paris;   Wahlandt, Schwäbisch Gemünd
  • 1978: S:t Petri, Lund;   Teufel, Cologne

Interesting Group show

  • WORLD PRINT COMPETITION 77, Museum of Modern Art, San Francisco, USA

1977 - 1978: Dimensions I

About this algorithmic system

  • 1977: I began to work with the 4-D hypercube and graph-theory.
  • 1978: I first introduced "Diagonal-Paths" on an n-dimensional hypercube in my work.

Explanation of the concepts

  • In search for a more complex structure than the 3-D cube, I logically embraced the 4-D hypercube with its richer structure of lines and relationships. This beccame my basic generator of signs.
  • In this workphase, the fixed structure of a 4-D hypercube is used as a graph: A two-dimensional representation of the hypercube indicating relationships between points, lines, squares and cubes, inherent in this structure.
  • A visual structure is generated either by combinatorially selecting lines from the cube or by showing connecting paths between 2 given diagonally opposite points on the graph (diagonals). A 4-d hypercube has 8 pairs of diagonally opposite points. A "diagonal-path" is the connection of 2 such diametric points through the network of edges of this complex structure (there are 24 "diagonal-paths" for each of the 8 diagonals).

    Methods applied to this structure

    • 1977: Divide the 32 lines of the 4-D hypercube into 4 random groups of 8 lines each
    • 1977: Superstructures (squares) over the chosen lines
    • 1978: Recombining the 4 parts in a magic square to form paintings and drawings
    • 1978: Combinatorial use of diagonal paths
    • 1978: Construction of a multi-piece wooden wall structure from one combinatorial set of diagonal paths.
    • 1978: All possible maximal planar graphs of diagonal paths between 2 points.
      The width of the line represents the number of paths passing through an edge (as in P-181 1976).
    • 1977 - 1978: create drawings with diagrams of the process

    Webpages for this workphase

    One person shows

    • 1979: Mueller-Roth, Stuttgart;     Gheerbrant, Montreal;     Weiller, Paris
    • 1980: Teufel, Cologne

    Important group shows:

    • 1978 Centre Pompidou: RECHERCHE et CREATION, Centre Pompidou - Musée National de l'Art Moderne, Paris
    • 1978 NUMERALS 1924-1977: Leo Castelli Gallery, New York;     Yale University Art Center, New Haven;     Dartmouth College Museum, New Hampshire

  • 1980 - 1984: Divisibility I

    1980: I introduced the "4-cut" which generates "out-lines" and "in-lines"

    • I return to the 3-D cube used as a fixed structure to generate signs. The cube is divided into four sections by a horizontal and a vertical cut. The "4-cut" is the basic structure where the "out-lines" form shapes and the "in-lines" form signs.
    • In addition, the 4-cut is used together with clipping by the frontal window (as in Cubic Limit II) with the "in-lines" in black (the lines inside the window) and the "out-lines" in gray (the lines outside the window).

    Methods applied to this structure

    • 1980 4-cuts as a 4 piece structure: Shape of canvas is out-lines, Drawings on each section are in-lines
    • 1980 A sequence of two drawings with matrix of rotating cubes as 4-cuts, showing in-lines as surface and out-lines as form:
      Achieved by overlaying drawings to create surface (as in P-196 1977) and creating surface / form with 4-cut in black ink.
    • 1980 matrix of out-lines also constructed as a cardboard, then wooden, relief with 144 pieces
    • 1980 series of five 4-cuts where the cut rotates (not the cube) to create 4-cuts: drawn and constructed in both in-line and out-line version
    • 1980 4-cut together with frontal window (as in Cubic Limit II) creating in-lines (black lines) and out-lines (gray lines)
    • 1980 series of 5 paintings using frontal window and 4-cut: Each subsequent painting is overlayed by a quarter of the width (alternating horizontally and vertically)
    • 1980 - 1985 First time I show all possible 2-D projections of a higher dimensional object: Projections of 4-cut of 3-D cube onto XY, YZ, and XZ planes.

    Webpages for this workphase

    One person shows

    • 1981: Gheerbrant, Montreal
    • 1982: Mueller-Roth, Stuttgart;     Weiller, Paris

    Important group shows:

    • 1980: IMAGES, ART ET ORDINATEUR, Palais de la Découverte, Paris
    • 1981: ARS + MACHINA I, Institut Franco-Americain, Maison de la Culture de Rennes
    • 1982: DIE HANDZEICHNUNG DER GEGENWART II, Staatsgalerie Stuttgart
    • 1983: ELECTRA 83, Musée d'Art Moderne de la Ville de Paris
    • 1983: ZEICHNEN KONKRET, Pfalzgalerie, Kaiserslautern
    • 1984: DIE SPRACHE DER GEOMETRIE, Kunstmuseum Bern
    • 1979 - 1984: McCrory Collection Travelling Exhibition: CONSTRUCTIVISM AND THE GEOMETRIC TRADITION
            - Museums in the USA and Japan: Buffalo, Dallas, San Fransisco, Seattle, La Jolla, Pittsburg, Kansas City, Detroit, Milwaukee, Denver, San Antonio, New Orleans, Toledo, Indianapolis, Ithaca, Tokyo, Sapporo
    • 1982 - 1984: DEUTSCHE ZEICHNUNGEN DER GEGENWART, World travelling Exhibition:
            - Museums in Cologne, Sydney, Brisbane, Zagreb, Ljubljana, Belgrad, Oslo, Trondheim, Buenos Aires, San Paolo

    1983: My first home computer center

    • 1983: I established my first home computer center when I moved full-time to New York
      Since Meteorologie Nationale announced it was planning to move to Toulouse, I had to find another solution.
      I lived in both Paris and New York between 1980 - 1983, but found I was often in the wrong place at the wrong time, and not going anywhere else.
    • 1983 Computer: I bought a DEC LSI 11-23 computer constructed by Charles River Data, Boston
      A computer which many scientific research groups were using (including the research lab at NYU Medical School where Estarose worked).
      This was one of the first affordable mini-computers and didn't need air-conditioning.
    • 1983 Plotter: I went to SIGGRAPH '83 to find an affordable plotter. In a journal handed out, I found an advertisement from a newly formed company for an Alpha Merics plotter.
      I contacted them, I bought the plotter in a special deal by accepting to become their beta-site.
    • About this plotter:
      Resolution: It was a high-resolution flatbed ink pen vector plotter ( .1 mm plotting step, as I had before).
      It was bottomless: It was just a rectangular frame without a bottom.
    • 1983: The first drawing I plotted at my new computer center: My algorithm from 1970 P-21, band-structures.
    • 1983 The bottomless plotter allowed me to make very large paintings: I plotted P-21 and a few of my other early algorithms directly on canvas. I did this by calculating the cuts and carefully moving the machine to juxapose these parts on canvas.
      Photos of this plotter and the process

    1984 - 1986: Divisibility II & Divisibility III

    For this time-line, Divisibility II & III are grouped together because they are complementary

    • 1984: Divisibility II: A molecular-like growth is created with the 4-cut as its seed. Growth results from algorithms of graph patterns deciding which out-lines of the quadrants created in the preceding generation is used to produce the 4-cut of the next (non-overlapping) generation.
    • 1986: Divisibility III: The contours of the 4-cut is seen as a "shadow-form", a two dimensional visual history of the cube-growth. The connecting path between the center point of one 4-cut and the center point of the next 4-cut is shown as a black line, the growth-line. Similar to the spine in a body, the growth-line is embedded in the shadow-form.

    About the workphase

    • Divisibility II was realized as drawings, paintings, and eventually multipart structures
    • Divisibility III was realized as drawings, paintings, and structures with gray cardboard as the out-lines and a black wooden continuous multi-sectioned line as the spine.
    • Multi-part installations were made from Divisibility II
    • Multi-part series: All possible growth patterns after four generations from the same initial 4-cut

    Links for this workphase

    One person shows

    • 1985: Teufel, Cologne;     Gheerbrant, Montreal
    • 1986: Weiller / Chevalier, Paris;     Buytaert, Antwerp;     Mueller-Roth, Stuttgart

    Important group shows

    • 1985: VOM KLANG DER BILDER, Staatsgalerie Stuttgart
    • 1985: EMERGING EXPRESSION - COMPUTER GENERATED IMAGERY, The Bronx Museum of the Arts, New York
      Installation photo of my 16 part art piece from Divisibility II       New York Times article
    • 1985: LES VINGT ANS DU MUSEE A TRAVERS SA COLLECTION, Musée d'Art Contemporain de Montreal
    • 1986: VON ZWEI QUADRATEN, Wilhelm-Hack-Museum, Ludwigshafen
    • 1986: IMAGES DU FUTUR, Vieux Port, Montreal
    • 1986: EIN ZEITDOKUMENT, Sammlung Etzold, Städt. Museum Mönchengladbach
    • 1986: TRENDS IN GEOMETRIC ABSTRACT ART, Tel Aviv Museum of Art
    • 1986: KONKRET VI, Kunsthaus Nürnberg

    1987 - 1989: Dimensions II

    1987: Return to the 4-D Hypercube, Rotation in 4-D space is projected onto a 2-D plane

    • A 4-D hypercube can be seen as a structural relationship of eight interconnected cubes. Each of these eight cubes are looked at through a square frontal window (the 0,0,0 rotation of each cube). Four of the cubes are represented in their clipped window in black and four in their clipped window in gray. This partitioning of black or grey is a combinatorial element in the algorithm of this work.
    • This work demonstrates how rotation in 4-D will change shape in 2-D.

    About the workphase

    • 1987 Shaped Canvases: The rotation and clipping result in shaped canvases.
    • 1987 Multi-layered drawings: As before, I overlay 2 sheets of paper (the top slightly transparent), to obtain the surface and the black / gray paradigm.
    • 1988 Drawings of all combinations of the 4 gray / 4 black paradigm of the 8 inherent cubes, at a given rotation.
    • 1988 Multi-part drawings of 4-D rotations projected in 2-D: Shape and content changes become visible.

    Webpage for this workphase

    Retrospective Museum Exhibitions

    • 1987, My First Retrospective Exhibition: Manfred Mohr | Fractured Symmetry | Algorithmic Works 1967 - 1987
      Wilhelm-Hack-Museum, Ludwigshafen, Germany
      Photos, Invitation, Press from the Retrospective, 120 of my works were in the show.
    • 1988, My Second Retrospective Exhibition: Manfred Mohr | Retrospective 1960-87
      Kunstverein Pforzheim im Reuchlinhaus Museum, Pforzheim

    Catalogs of the Retrospectives

    • 1987 Manfred Mohr | Fractured Symmetry: Algorithmic Works 1967-1987, Wilhelm-Hack-Museum, Ludwigshafen, 120 pages
    • 1988 Manfred Mohr | Arbeiten 1960-1988: Reuchlinhaus, Pforzheim, 120 pages
    • Both catalogs contain images from this workphase

    One-person show in Gallery

    • 1988: Teufel, Cologne

    Important group shows

    • 1987: 2nd EMERGING EXPRESSION BIENNALE, The Artist and The Computer, The Bronx Museum of the Arts, New York
      Photo of my 2 works from Divisibility III       New York Times article about show
    • 1987: DIGITAL VISION, Everson Museum of Art, Syracuse
    • 1987: Von der Magischen Zahl, MATHEMATIK IN DER KUNST DER LETZTEN 30 JAHRE, Wilhem-Hack-Museum, Ludwigshafen
    • 1987: ARTISTS IN THE COMPUTER AGE, MIT List Visual Arts Center, Cambridge, Mass.
    • 1988: COMPUTERS and ART, IBM Gallery, New York
    • 1988: KUNST IN DER PROVINZ, Städt. Museum Schwäbish Gmünd

    1989 - 1990: Line Cluster I & II

    Use of 5-D hypercube and 6-D hypercube, with rotation in n-D, to generate more complex graphics signs

    • 1989 I used a 5-D hypercube:, A structure build from a set of eighty lines
      A subset of twenty lines, containing four lines from each dimensional direction, are chosen from this structure.
      Therefore, each dimensional direction consists of four parallel lines, represented by three thin lines and one thick line.
    • 1989 First work with 6-D hypercube: Using similar algorithms as with the 5-D hypercube,
      but with black and gray lines of equal width (with a square frontal window as support).

    About this workphase

    • 1989 - 1990: Paintings and drawings were made from Line Cluster I & II
    • 1989, Again (as in Divisibility I) showing all possible 2-D projections of an n-Dimensional space:
      Series of 10 plotter drawings of each of the 2-D projections for the 5-D hypercube (with a given set of lines and a given rotation)
    • Again, I used overlaying and tranparent paper to make the drawings

    Links and Catalog for this workphase


    One-person shows in Galleries

    • 1989: Prakapas, New York;     Weiller / Chevalier, Paris;     Buytaert, Antwerpen
    • 1990: Durhammer, Frankfurt
    • 1991: ACP, Zurich;     Teufel, Mahlberg

    Important group shows

    • 1989 AUS DEM WÜRFEL MUSEUM, Karl-Ernst-Osthaus Museum, Hagen
    • 1989 NULL DIMENSION I, Hipp-Halle, Gmünden
    • 1989 SIMPOSIUM DE ARTE SISTEMATICA Y CONSTRUCTIVA, Centro Cultural de la Villa, Madrid
    • 1990 MATHEMATICS AND MODERN ART, University of Leicester

    1991 - 1993: Laserglyphs

    6-D hypercube: diagonal-paths, computer generated laser-cut metal reliefs, rotation, projection and combinatorics

    • 1991: The 6-dimensional hypercube has 32 diagonals. The two endpoints of each diagonal lie diametrically opposite in the structure. Each of these 32 diagonals have 720 different diagonal-paths (the connection of two such diametric points through the network of edges of this complex structure, introduced in Dimensions I 1978).

    About this workphase

    • 1991: Metal reliefs created by randomly choosing four diagonal-paths from the repertoire of 23040 (32x720) possible paths in a 6-D hypercube (rotated in 6-D space and projected on a 2-D plane).
      The 2-D dimensional projection of such groups of four are cut out of a metal plate by a computer-controlled laser to form a relief which I call a Laserglyph.
    • 1992 Combinatorial drawing series: A series of 32 drawings each showing the 720 diagonal-paths between two of the diagonally opposite points in the 6-D structure.
    • 1993 15-part combinatorial computer generated Laser-cut steel relief: The 15 possible 2-D projections of a diagonal-path through a 6-D hypercube (at a given rotation).

    Webpage and catalog for this workphase

    One-person show in Gallery

    • 1992: Weiller / Chevalier, Paris;     Mueller-Roth. Stuttgart;     ACP, Zurich

    Important group shows

    • 1991: 3rd EMERGING EXPRESSION BIENNALE, The Bronx Museum of the Arts, New York
    • 1992: REGARD MULTIPLE, Centre Pompidou - Musée National de l'Art Moderne, Paris
      Showing new works in their collection - My painting is from a 5-D cube
    • 1992: ZUFALL ALS PRINZIP, Wilhelm-Hack-Museum, Ludwigshafen
    • 1992: NEW REALITIES, Museum für Gestaltung, Zurich
    • 1993: INTERFACE II, Die präziesen Vergnügen, Hommage an Max Bense
      Galerie Meissner, Hamburg, Germany; Living Galerie, Braunschweig; Kunstraum Universität Lüneburg
    • 1993: FORUM KONKRETE KUNST ERFURT, Museum der Künstler, Erfurt
    • 1993: STREIFZUG DURCHS DEPOT, Wilhelm-Hack-Museum, Ludwigshafen
    • 1993: KONSTRUIERTE UNREGELMÄSSIGKEIT, Galerie Schoeller, Düsseldorf

    1993 - 1995: Counterpoint

    Two diagonal-paths from a 6-D hypercube are used in relationship to one another to create a visual counterpoint

    • 1993: One diagonal-path is drawn as a thin black line and the other diagonal-path is drawn as a thick grey line.
      The line width is inversely proportional to the decrease in color intensity from black to grey.
    • To visually maintain the inherent connectivity, only such diagonal-paths can be chosen which have at least one common point in the structure.
    • Both diagonal-path lines have a visual relationship comparable to the counterpoint of a succession of sounds in music.

    About the work, Webpage

    First Monograph on Manfred Mohr

    • 1994: Manfred Mohr, Waser Verlag Zurich
      Work from 1961 - 1993, 28 x 24 cm, 230 pages


    • 1993: Freimann - M.Mohr, Galerie Teufel Mahlberg

    Two-person Museum Exhibition and Catalog

    • 1994 Manfred Mohr & Christoph Freimann: Galerie der Stadt Stuttgart
    • 1994 Catalog: Christoph Freimann - Manfred Mohr, Galerie der Stadt Stuttgart

    One-person shows in Galleries

    • 1993: Teufel, Mahlberg (2 person show with Christoph Freimann)
    • 1994: Teufel-Holze, Dresden;     Dürhammer, Frankfurt;     ACP, Zurich
    • 1995: Weiller / Chevalier, Paris;     Buytaert, Antwerp

    Important group shows

    • 1994: VUE DU COLLECTIONNEUR, L'Espace de l'Art Concret, Mouans-Sartoux
    • 1994: PROJECT 30x30, KONKRETE KUNST INTERNATIONAL, Wilhelm-Hack-Museum, Ludwigshafen
    • 1994: KONSTRUKTIV-KONKRET, Kunstverein Wolfsburg
    • 1995: IN TEILEN, Stiftung für Konkrete Kunst, Reutlingen
    • 1995: LASZLO MOHOLY-NAGY: IDEE UND WIRKUNG, Kunsthalle Bielefeld
    • 1995: THIRD ANNUAL NEW YORK DIGITAL SALON, School of Visual Arts, New York
    • 1995: L'ART CONCRET AUJOURD'HUI, L'Espace de l'Art Concret, Mouans-Sartoux

    1995 - 1998: Half-Planes

    Shaped structures are created from two diagonal-paths of a 6-D hypercube together with vectors connecting their corresponding vertices

    • 1995 A 6-D hypercube has 23040 diagonal-paths which can be calculated combinatorially. A random selection of two diagonal-paths from this complex alphabet of signs are used as the basis of this work. A 6-D diagonal-path is built from 6 consecutive connected vectors, each having a different but distinct direction (representing one of the 6 mathematical dimensions). All 6 vectors of one diagonal-path are matched with their corresponding vector on the other diagonal-path, resulting in six vector pairs. Each vector pair is oriented to form a non-intersecting planar quadrilateral (at a given rotation), and then is completed visually with thin lines. Thus, 6 joining quadrilaterals are created, describe a contour form, resulting in the most surprising shapes.

    About this work and Webpage

    • 1995 - 1996 Shaped gray paintings with white and black lines: The diagonal-paths are represented by thick white lines. The vector pairs are represented by thin black lines. The 6 joined quadrilaterals are colored grey to create the shape of the painting.
    • 1995 Drawings: The diagonal-paths are represented by thick black lines and the vector pairs are represented by thin black lines.
    • 1997 Computer generated metal reliefs: The artwork is composed of 3 bent flat metal strips. The strip representing the contour is painted white, and the 2 strips representing the diagonal-paths are painted grey and black.
    • Webpage for this work

    Started my Website - manfred mohr

    • 1997     website created: I wrote my first html webpages (with images).
      It was alot of hard work representing the first 40 years of my artistic career on the world wide web.
    • Discovering the World Wide Web in its beginnings, I became fascinated and immediately learned HTML and started writing my own website (including images of my artwork). This webpage,, has become very diverse. In 2011, starting with the 40th anniversary of my historic exhibition in Paris at ARC, I decided to extend my webpage into a historical direction. Estarose volunteered to help with the research for a first draft, which we then together developed into the final version of this historic show. In the same way, Estarose continues to research the historic part of my work for my website, while I continue to write and develop the webpages for each new workphase with all its programming and graphic decisions.

    Retrospective Museum Exhibitions

    • 1998 My Third Museum Retrospective Exhibition: Manfred Mohr, Algorithmic Works (1968 - 1998) Quadrat Bottrop, Josef Albers Museum, Bottrop
    • 1998 My Fourth Museum Retrospective Exhibition: Manfred Mohr, Retrospective 1968-98, Museum Pforzheim Galerie, Pforzheim

    Catalog of Retrospective

    • 1998 Algorithmische Arbeiten / Algorithmic Works, Quadrat Bottrop, Josef Albers Museum, Bottrop, 66 pages
      The museum produced three silk screens of my work for this exhibition

    Awards and Honors

    • 1997 Receives an Artists' Fellowship from New York Foundation for the Arts
    • 1997 Elected a member of the American Abstract Artists
    • 1998 Invited to sign the Golden Book of Pforzheim
    • 1998 Selected for Pioneering Artists exhibition, SIGGRAPH Orlando

    One-person shows in Galleries

    • 1996: Weiller / Chevalier, Paris
    • 1997: Wack, Kaiserslautern;     ACP, Zurich;     Mueller-Roth, Stuttgart;     Mathieu, Lyon
    • 1998: SPACE 504 (with Charles Hineman), New York;     Lahumière (with Vera Molnar), Paris;     Teufel - European Art Concrete, Berlin

    Important group shows

    • 1997: COMPAREZ POUR VOIR, L'Espace de l'Art Concret, Mouans-Sartoux
    • 1997: MAGIE DER ZAHL, Staatsgalerie Stuttgart
    • 1997: GEOMETRIC ABSTRACTION 1937-1997, Snyder Fine Art, New York
    • 1998: IMMERZEIT II, Forum Konkreter Kunst, Erfurt
    • 1998: LE DROIT DE RÈVER, L'Espace de l'Art Concret, Mouans-Sartoux


    1999 - to the present:     Use of Color;     Ink Jet Raster Graphics;     Non-Repetitive Real-Time Screen-Based Computer Animations

    • 1999 I re-introduce Color into my work:
      In order to find a more adequate visual expression, the steady increase of complexity in my work forced me to reconsider the use of my 36 year adherence to a Black / White binary system. Adding colors to my work describe spatial relationships which are not based on color theory. The colors should be seen as random elements, showing through their differentiation the complexity and spatial ambiguity essential to my work.
    • 1999 Introduction of Ink Jet Raster paintings and drawings into my work:
      Having used vector plotters for 30 years, I introduce paintings and drawings executed with inkjet raster plotters to realize my algorithmic systems.
    • 2002 Construction of non-repetitive real-time screen based computer animations:
      From 2002 and in all my subsequent algorithmic systems, the screen-based computer work uses my program from the same workphase as my paintings and drawings. Each installation of an animation has a unique set of parameters and each time the animation starts a non-repetitive continuous flow of images appear (since the starting point of the program is related to the present time and date). It took me several years to build the screen-based animation as an artwork because I was using Sun Microsystem computers which I could not modify. Only when I got access to Microsoft and Apple PCs was I able to build the machines, in 2002.
    • Animations, Paintings, and Drawings as Instances of my algorithmic program: In this and in all my subsequent algorithmic systems, the animations became, like my paintings and drawings before, instances of my algorithmic system.
    • 2002 Self-designed and self-built computer introduced into my artwork: Until there existed commercial computers that satisfied my needs, I designed and built the computers myself. My interest in electronics in my youth and early artwork, once again entered my artistic domain physically.
      My design for building a computer, 2002     Image of my self-built computers, gallerists Mueller-Roth and me, 2003
    • 2002: When I started building my screen-based works, the environment became more complex. After I developed the program for a workphase, the physical building of the machines and the software interface (between program and machine) created problems which had to be solved. Having the expertise and being interested, Estarose volunteered to assist me with the program / hardware interface. She helped prepare the modules for the automated running of the screen-based works, and I faced the hardware problems.

    1999 - 2004:   space.color   &   space.color.motion

    • 1999 space.color (Ink-jet raster paintings and drawings) and 2002 space.color.motion (non-repetitive screen-based real-time animation) use the same algorithm, thus they are grouped together.
    • The basis of the algorithm is similar to my previous workphase Half-Planes where 2 diagonal-paths were deconstructed into 6 quadrilaterals.
    • 1998 - 1999, The algorithm: Four diagonal-paths are randomly chosen (thick black lines) and are ordered from 1 to 4 and the corresponding vectors are connected with thin black lines. Thus vector pairs are created and together with the thin lines form planar quadrilaterals, or color fields.
      The two outer diagonal-paths (1 and 4) are connected in the same way but without the thin lines, wrapping the image around the outside of the bounding rectangle (The flat plane is transformed into a torus, as in my 1973 drawing P-148). The hypercube, is rotated in 6-dimensional space and then projected into 2-dimensional space. The resulting image overlays the color fields from front to back. Together with the diagonal-paths, the resulting image creates unimaginable constellations.
    • The 24 color fields thus created, each with a random color (2 of which are always white, to create a visual balance), are used as distinctions to indicate the complexity of the structure and its rotation.
    • 2002 space.color.motion using the same algorithms as space.color, was updated to run on all computer platforms, including PCs. I designed and built PCs to execute the 6-D animation program, where each installation used a unique set of parameters to generate the sub-structure and color set. Each time the program is restarted it picks a new set of 6-D random angles and increments (based on the present time and date). This results in unique images which don't repeat and are always surprising.
    • 2001: space.color also included long (over 16 foot) large series composed of five juxaposed paintings.
    • 2002: space.color.motion was first exhibited at the Wihelm-Hack-Museum in Ludwigshafen and at the Schoeller Galerie in Dusseldorf using a Windows XP PC and at bitforms gallery in New York with 3 self designed and built PCs.

    Webpages for this workphase

    Exhibitions in Museums

    • 2001: Manfred Mohr, space.color, Museum für Konkrete Kunst, Ingolstadt
    • 2002: Manfred Mohr, space.color, Wilhelm-Hack-Museum, Ludwigshafen
      The second one-person exhibition I had in this museum, covering my workphases since my 1987 retrospective.


    • 2001, space.color;     Museum für Konkrete Kunst, Ingolstadt;       Wilhelm-Hack-Museum, Ludwigshafen, 78 pages
    • 2005, space.color.motion: Selected installation views of P777 (2002-2005), Stuttgart, Madrid, Basel, Berlin, Würzburg etc

    One Person Shows in Galleries

    • 1999: Schoeller, Dusseldorf
    • 2001: Wack, Kaiserslautern
    • 2002: Schoeller, Dusseldorf     bitforms gallery, New York
    • 2003: Mueller-Roth, Stuttgart
    • 2004: DAM, Berlin

    Important group exhibitions

    • 1999: GEOMETRIE ALS GESTALT / GEOMETRY AS FORM, Sammlung Daimler Chrysler, Neue Nationalgalerie, Berlin,
    • 1999: PURE ABSTRACT ART, Mondriaanhuis, Amersfoort
    • 1999: LA NATURE IMITE L'ART, L'Espace de l'Art Concret, Mouans-Sartoux
    • 1999: HOMMAGE à VORDEMBERGE-GILDEWART, Kunsthalle Dominikanerkirche, Osnabrück
    • 2000: LIGNE(S) DE CONDUITE, L'Espace de l'Art Concret, Mouans-Sartoux
    • 2000: 8th ANNUAL DIGITAL SALON, School of Visual Arts, New York
    • 2000: VON ALBERS BIS PAIK, Sammlung Daimler Chrysler, Haus für Konstruktive und Konkrete Kunst, Zurich
    • 2000: 30 JAHRE SAMMLUNG ETZOLD, Stadt. Museum Abteiberg, Mönchengladbach,
    • 2001: KONSTRUKTIV-KONKRETE KUNST, Josef Albers Museum - Quadrat, Bottrop
    • 2002: 15 variations sur un mème thème, L'Espace de l'Art Concret, Mouans-Sartoux
    • 2003: Wege zur Abstraktion II, FORM + STRUKTUR, Kunstverein Schloss Plön
    • 2003: László Vass Collection, Gallery of Modern Art, Veszprém
    • 2003: Sammlung Holze - Konkrete Kunst, Von Der Heydt-Museum, Wuppertal

    2003 - 2005:   subsets   &   subsets.motion

    • 2003 subsets (Ink-jet raster paintings and drawings) and 2003 space.color.motion (non-repetitive screen-based real-time animation) use the same algorithm, thus they are grouped together.
    • 2003 subsets is a work phase based on the 11-D hypercube. The algorithm I wrote selects a subset of cubes from a repertoire of 42240 cubes inherent to the 11-D hypercube and decides which sides shall be black or white. Clipped by a defined window, this structure rotates in front of a green background. Since the above mentioned subset is by definition incomplete, the green background occasionally becomes visible, as the structure is rotating in 11-dimensions and projected in 2-D. Based on these algorithms and without losing the geometric and systematic content of my work, I approach through logic a seemingly chaotic visual system, which I refer to as visual music. It is symbolic of action painting and free jazz, the things which were very important to me as a young artist in the early 60's.
    • 2003 subsets.motion uses the same computer program as subsets. It runs on all computer platforms, including PCs. Self-built PCs execute the 11-D animation program with each installation using a unique set of parameters which determines the sub-structure. Each time the program is restarted it picks a new set of 11-D random angles and increments (based on the present time and date). This results in unique images which don't repeat and are always surprising.
    • The black and white sides of the selected cubes overlay to form supersurfaces which, similar to the leaves of a tree on a sunny day, combine to cast a patterned shadow on the ground.

    Webpages and Catalog for this work

    Museum Exhibition

    • 2005: Manfred Mohr | Zeichnungen aus 30 Jahren, Museum im Kulturspeicher, Würzburg
      The museum mounted an informal retrospective of around 30 of my computer generated drawings from 1969 - 2005

    One-person Exhibitions in Galleries

    • 2005: Wack, Kaiserslautern
    • 2006: bitforms, New York

    Important Group Shows

    • 2004: DIGITAL SELECTIONS, Millennium Museum in Beijin
    • 2004: Klassische Moderne bis Neo Geo, SAMMLUNG DAIMLER CHRYSLER, Galerie der Stadt Sindelfingen
    • 2004: Les systèmes de l'art concret, L'Espace de l'Art Concret, Mouans-Sartoux
    • 2004: Hubertus Schoeller Stiftung "...stets konkret", Leopold Hoesch-Museum, Düren
    • 2004: 25 Jahre Wilhelm-Hack-Museum -- 25 Jahre Sammeln, Ludwigshafen
    • 2005: The ALGORITHMIC REVOLUTION, Zur Geschichte der interaktiven Kunst, ZKM, Karlsruhe
    • 2005: ANGEKOMMEN im eigenen Haus, Kunstmuseum Stuttgart
    • 2005: KONKRETE KUNST IN EUROPA, Sammlung Ruppert, Museum Art Speicher, Würzburg
    • 2005: ERÖFFNUNGS AUSSTELLUNG der Sammlung Marli Hoppe Ritter, Museum Ritter, Waldenbuch
    • 2005: EXPERIMENT KONKRET, Museum für Konkrete Kunst, Ingolstadt

    2006 - 2008: klangfarben

    • 2006 - 2008 klangfarben, diagonal-paths from the 11-D hypercube: This workphase consists of two square LCD screens, a computer and my own custom software.
    • 2006 11-D hypercube and diagonal-paths: The 11-D hypercube contains a graphic repertoire of an unimaginable 40 billion possible diagonal-paths. From this repertoire four sets of eleven diagonal-paths with three distinct line widths are chosen as basic elements for each work. Every time this screen work is switched on, one out of the four sets is randomly chosen.
    • 2006 Two square screens constructed from 2 rectangular screens, each fitted with frames whose shape reveals a square viewing area.
    • The right square screen, Motion: shows a graphic construct consisting of 2 to 10 diagonal paths rotating in slow motion, and all colors change randomly every 10 seconds. Single diagonal-paths fade in or out during the color changes in a cyclic but random order so that the back most diagonal-path always moves to the front.
    • The left square screen, Still: Before each color change, the last image is sent from the right screen to the left screen and remains there until the following image is received 10 seconds later.
    • Motion / Still paradigm: The moving image on the right screen shows the making of a sign and the receiving left screen shows a fixed and therefore contemplative sign. Both screen-images should not be seen simultaneously but observed independently. The screens are therefore presented in a 90 degree angle to each other, so that the observer is encouraged to choose one or the other event.
    • Like serial music: The underlying logic of this work is similar to the rules of serial music in which each element of a series of elements has to appear at least once before the series can be repeated.
    • klangfarben, sound modulation, and frequencies: klangfarben refers to a compositional technic of playing one musical note but constantly changing the instrument which plays that note. A subtle sound modulation or "klangfarbemelodie" appears because of the inherent differences in upper and lower frequencies which create the character of each musical instrument. The random modulation of colors on each diagonal-path render exactly that subtle quality to my work.

    Webpage and Catalog

    Award, Museum Retrospective Exhibition, Auxilary Exhibition, Catalog, Webpage with photos of shows

    • 2006 Award: d.velop digital art award [ddaa] for digital pioneering, Cologne / Bremen / Berlin
    • 2007 Retrospective Museum Exhibition: Manfred Mohr, broken symmetry, [ddaa] Award, Computer works 1969-2007, Kunsthalle Bremen
    • 2007 Second exhibition associated with the [ddaa] award: Manfred Mohr, [ddaa] Award, Landesvertretung Bremen in Berlin
    • 2007 Catalog; broken symmetry, Kunsthalle Bremen, Bremen
    • Webpage with Photos of the two shows, Press, Invitation...

    Another Museum Restrospective and a Foundation Show

    • 2008 Manfred Mohr, Visuell Zuhören, Retrospective 1963-2008, Kunstverein Pforzheim im Reuchlinhaus Museum, Pforzheim
    • 2008 Manfred Mohr, ART STATIONS PREVIEW - IT FROM BIT, Grazyna Kulczyk Foundation, Poznan

    One-person Exhibitions in Galleries

    • 2007: Mueller-Roth, Stuttgart
    • 2008: bitforms, New York;   DAM, Berlin;   Lahumière, Paris;  La Ligne, Zurich

    Important Group shows

    • 2006: CYBERNETIC SENSIBILITY, Daelim Contemporary Art Museum/bitforms gallery, Seoul
    • 2006: 20th CENTURY COMPUTER ART, Beginnings + Developments, Tama Art University Museum, Tokyo
    • 2006: BEWEGUNG IM QUADRAT, Museum Ritter, Waldenbuch
    • 2006: DIE NEUEN TENDENZEN, Museum für Konkrete Kunst, Ingolstadt
    • 2006: STRICTLY GEOMETRICAL, Wilhelm-Hack-Museum, Ludwigshafen
    • 2006: ANFÄNGE DER COMPUTERGRAFIK, Aus der Sammlung Etzold, Städt. Museum Abteiberg
    • 2006: SONIC ACTS XI, International Arts Festival + Conference, Amsterdam
    • 2007: SAMMLUNG GUTMANN, Stiftung für konstruktive und konkrete Kunst, Zurich
    • 2007: 15 JAHRE MKK, Neuhängung im Museum für Konkrete Kunst Ingolstadt
    • 2007: Ex Machina - Frühe Computergrafik bis 1979, Kunsthalle Bremen
    • 2007: DER ZWEITE BLICK, Stiftung für Konkrete Kunst, Reutlingen
    • 2007: WHITE & BLACK, Vasarely Museum, Budapest,
    • 2007: Painting Painting, the Vass Collection, Modern Gallery, Arthouse, Veszprém
    • 2007: BIT-International, Neue Galerie Graz
    • 2007: FEEDBACK, Laboral Centro de Arte, Gijon
    • 2007: DIE NEUEN TENDENZEN, Leopold-Hoesch-Museum, Düren
    • 2007: AUSGERECHNET... Mathematik und Konkrete Kunst, Museum im Kulturspeicher, Würzburg
    • 2008: MINUS SPACE, P.S.1 Contemporary Art Center / MoMA, Long Island City, New York
    • 2008: BILDERTAUSCH 3, Museum Ritter, Waldenbuch
    • 2008: TO INFINITY AND BEYOND: Mathematics in Contemporary Art, Heckscher Museum, Huntington
    • 2008: bit international. [Nove] tendencije, Computer und visuelle Forschung, Zagreb 1961-1973, ZKM, Karlsruhe, Germany
    • 2008: KUNST WERK, Sammlung Alison und Peter Klein, Hängung #2, Eberdingen-Nussdorf
    • 2008: IMAGING BY NUMBERS, Block Museum of Art, Evanston
    • 2008: SPACE, COLOR, AND MOTION, Block Museum, Northwestern University, Evanston

    2009-2011: parallelResonance

    • 2009: Two rotating overlayed 11-D diagonal-paths are rendered as wide bands and together create a mutual relationship, between form and tension field.
    • Return to use of a tension field: The theory of abstract composition in art states that any form is embedded in a visual tension field (Paul Klee). Thus with the movement of a set of forms into different positions, one can explore complex relationships between forms and tension fields.
    • In the 1960s, I used these ideas in my own way to create a geometry. Seen from today with my experience creating algorithms, I consider this work a "surrealistic geometry".
      Now, in this workphase, I am once again engaged in systematically investigating the idea of tension fields.
    • 2009 Mutual relationships between form and tension fields: Tension fields appear as the two diagonal-paths expand in width.
      What particularly interested me, in this workphase, was the creation of forms and tension fields which, so to speak, generate each other mutually. Forms and tension fields are produced simultaneously and become one and the same thing. The tension field around the line becomes the form and the form is at the same time visually the tension field.
    • More details of my ideas at the time, from my website

    • Algorithm details: Two randomly selected 11-D diagonal-paths are superimposed. Both diagonal-paths have a very thick line width (line expansion) with their edges running parallel on both sides of the original diagonal-path. The top line expansion is always white, describing a white form. The bottom line expansion is black, describing a black form. Both forms are projected on a colored background. In random intervals, the black form interchanges with the colored background so that the background becomes black and the previously black form assumes a color. These exchanges create continuously new visual relations in form and tension fields. The clearly visible thin black/white lines in the image show the original diagonal-paths.
    • In the first part of parallelResonance the above described visual action encloses the original diagonal-paths (thin lines) whereas their expansions (forms) are clipped by a square window and are realized in both still images (inkJet on canvas) and in the slow motion realtime non-repeating square screen-based computer works.
    • In the second part of this work, the visual action is not clipped by the square window. Since the 1970s, I have intermittently superimposed computer drawings on translucent paper to achieve grey levels and/or forms. In this work, both diagonal-paths (forms) are white and each is placed on a grey background drawn on the translucent paper. The superimposition of the two diagonal paths create two different grey levels and where they overlap they create a white field. This procedure evokes ambiguity of the forms which is an integral element of my work.

    Webpage and Catalog for this workphase

    Retrospective Exhibition in Gallery, Webpages, Press, Invitations

    Feature Film: DIALOGE: Manfred Mohr, 1 hour 10 minutes

    • 2011 Manfred Mohr interviewed by Annett Zinsmeister. in German
      Kunst + Technik/ Art + Technology - Interview takes place in New York, September 2011
      On vimeo - Hi-Res;     On youTube

    One-Person Exhibitions in Galleries

    • 2009: Lausberg, Düsseldorf
    • 2011: DAM Berlin   Wack, Kaiserslautern   DAM Cologne   Hollinger {2 person show with Jan van Munster), Ladenburg

    Important Group Exhibitions

    • 2009: DIGITAL PIONEERS, V & A, Victoria and Albert Museum, London
    • 2009: RECONNAITRE, Museum Paksi Keptar, Paks
    • 2009: KONKRET, Sammlung Heinz und Anette Teufel, Kunstmuseum Stuttgart
    • 2009: REGARD 6: Quand la géométrie devient Art, L'Espace de l'Art Concret, Mouans-Sartoux
    • 2009: DAS QUADRAT IN DER SAMMLUNG, Stiftung für konkrete Kunst, Reutlingen
    • 2009: ALLES, Wilhelm-Hack-Museum, Ludwigshafen
    • 2010 BENSE UND DIE KÜNSTE, ZKM, Karlsruhe
    • 2010 100 JAHRE KONKRETE KUNST, Kunsthalle Rehau-Art, Rehau
    • 2011 SPOT-ON, Segment #1A, Borusan Contemporary Art Collection, Perili Kösk Museum, Istanbul
    • 2011: KONKRET, Sammlung Heinz und Anette Teufel, Panstwowa Galeria Sztuki, Sopot
    • 2011: Works from the Borusan Contemporary Art Collection, Perili Kösk Museum, Istanbul
    • 2011: RAM, Rethinking Art and the Machine, 7 pioneering artists, THEMUSEUM, Kitchener/Waterloo
      Installation photos - my works 1964 - 2008
      Video - 30th Anniversary of the "solidarity" show
    • 2011: QUADRATISCH-PRAKTISCH-KUNST, Sammlung Marli Hoppe-Ritter, Museum im Prediger, Schwäbisch Gmünd
    • 2011: TRANSPARENCY - LOOKING THROUGH, Vasarely Museum, Budapest
    • 2011: Art, Image and Science, Kavli Institute for Theoretical Physics (KITP), Santa Barbara
    • 2011: DRAWING WITH CODE: Works from the Anne and Michael Spalter Collection, deCordova Museum, Lincoln, Massachusetts
    • 2011 - 2013: AUFBRUCH, MALEREI UND REALER RAUM / Awakening, Painting and Real Space: Travelling Exhibition and Catalog
      Situation Kunst Bochum; Museum Pfalzgalerie Kaiserslautern; Akademie der Künste Berlin; Museum Kulturspeicher Würzburg; Kunsthalle Rostock

    2012 - 2016: Artificiata II, a workphase in four parts: baseline, projections and dimensions, parity, traces


    • 1969, 2012: In 1969, I published my first visual artist book "Artificiata" with Edition Agentzia in Paris. It was a visual-poetry book and also my last art work drawn by hand (ie not calculated by machine). At the time, I envisioned to create a second Artificiata book based on algorithms, calculated and drawn by computer. Since my visual research around 2012 developed a strong relationship to visual-music in a music score-like flow, similar to Artificiata of 1969, I decided to call this work Artificiata II and at the same time created a visual-book with the same name. I finally published the book Artificiata II in 2014. In 2017, I created a third book Artificiata III, but because of problems with the printing it was delayed. It is once again in preparation.

    2012 The General Algorithm:

    • In this work, a diagonal-path from a hypercube, randomly chosen between 11 and 15 dimensions, is drawn. A diagonal-path is a multiple-segmented line where each change of direction indicates the passage through a single dimension (diagonal paths were introduced into my work in Dimensions I, 1978). Horizontal lines are attached to the line at each change of dimension, i.e. the horizontal lines are drawn through the y-value of each vertex of the diagonal path when it is projected into 2-D. The spaces between the horizontal lines on either side (left/right) of the diagonal-path are filled with distinct sets of randomly chosen colors. The same procedure also calculates lines and colors in the vertical direction through the x-value of each vertex. The vertical lines are not drawn, but the resulting color sets are retained. This procedure creates four color sets from which three are randomly chosen to construct the resulting image. By overlaying the color sets successively, unpredictable constellations appear. The color spaces and horizontal lines move with the structure when the diagonal path (white line) is in slow motion (rotating in hyper-dimensional space and then projected into 2-D), and can be observed in my real-time computer animation works. These horizontal lines can be compared to the lines in music scores; Musical notes without these lines have no meanings, adding the lines makes the score. My horizontal lines, in a similar way, give structure and sense to the work. The lines, with or without the color fields, show the dynamics of the rotation.

    The four parts of this workphase

    • 2012 Baseline:
      The algorithm of the screen-based animation contains random variations of speed and suites of stills, adding a musical rhythm to this work. The works on canvas and the screen-based works are, as always, instances of the algorithm, as described above. This part of Artificiata II was first published in a fold-out catalog in 2013.
    • 2013 Projections and Dimensions:
      The screen-based works show all the 2-D projections of a randomly chosen n-dimensional diagonal path between 2-D and 13-D in a cyclic sequence. Similar to the rules in 12-tone music, each dimension has to be selected once before the same dimension can appear again. The colors and rotations are chosen randomly.
      2014 I also show this work as a series of 12 drawings, one for each dimension between 2-D and 13-D, where each drawing depicts all the 2-D projections of a chosen n-dimensional diagonal-path. The algorithm of each individual projection in an image is described above.
      In 2012, I previously made individual drawings with all the 55 2-D projections of a 11-D hypercube (as part of Artificiata II). In 2014 I made very large drawings.
      As mentioned before, my use of showing all the possible 2-D projections of of a higher dimensional hypercube began in 1980 - 1985 with Dimensions I. My use of combinatorics on the cube began in 1975.
    • 2014 Parity - Fracturing n-dimensional diagonal paths:
      In this workphase, I show the fracturing of a diagonal-path into even and odd numbered lines. An n-dimensional diagonal-path is shown with its even numbered lines in the left part and its odd numbered lines in the right part of each image. Furthermore, the respectively missing lines are shown as compressed vertical lines along the sides of each part. The horizontally attached lines hold the image together and enhance the movement, they show the dynamics of the rotation. The animation chooses between 20 and 100 dimensions, in intervals of 10.
    • 2014 Traces - Capturing the history of n-dimensional rotations:
      This fourth part of Artificiata II shows a rotating diagonal-path of an n-dimensional hypercube (between eleven and fifteen dimensions) and the visual rendering of the history of that rotation. The thick white line shows a rotated n-dimensional diagonal-path projected into 2-D and the color lines (the traces) show the history of that movement restricted to the 2-D rectangular space.
      The animation switches between multicolor and monocolor lines, thus creating different visual experiences which could be compared in the sound spectrum to polyphony and unison. This duality can also be compared to hearing the sounds of a orchestra or the sounds of a soloist. The animation shows mainly a series of stills which are the history of previously calculated movement and occasionally shows the rotating white diagonal path. Each time the rotation stops the color lines switch between multicolor and monocolor. This paradigm of random variations of speed and suites of stills add a musical rhythm to this work.
      As before, the horizontal lines show the dynamics of the rotation. I also made drawings and paintings with both monocolored and multicolored traces.

    Webpages, Catalogs, Artist Books associated with this workphase

    • My webpage about this work
    • 1969 Artificiata I, preface by Pierre Barbaud, Edition Agentzia Paris     My webpage about this book
    • 2014 Artificiata II, Artist book, afterword by Margit Rosen, OEI Editor Stockholm     My webpage about this book
    • 2013 Fold-out Catalog of first part of this workphase, Manfred Mohr: Artificiata II, Mueller-Roth Stuttgart, [DAM] Berlin
    • 2015 Catalog of the four parts of this workphase, Manfred Mohr: Artificiata II, works from 2012-2015, bitforms New York

    Museum Retrospective, ZKM

    One Person show in ArtBasel, Featured Artist


    • 2013 ACM SIGGRAPH Lifetime Achievement Award in Digital Art
      for pioneering achievements in creating art through algorithmic geometry
    • Citation
    • 2013 Manfred Mohr, Award Talk, ACM SIGGRAPH, Anaheim, Calif., July 22, 2013
    • 2013 ACM SIGGRAPH Distinguished Artist Award for Lifetime Achievement in Digital Art: Manfred Mohr
      Leonardo Vol. 46, No.4, pp 320-321, MIT Press, 2013
      Leonardo, Vol. 46, No. 4 at MIT press

    Other One-Person Shows in Public Spaces

    • 2014 Manfred Mohr | Evolving Geometries: Line, Form, and Color
      Center for the Arts at Virginia Tech, Blacksburg, Virginia
      Three artists, 3 one-person shows in seperate spaces under a common theme     Brochure
      Parts of Manfred Mohr's talk

    • 2015 Manfred Mohr | Pioneer of Algorithmic Art,   Simons Center Gallery, Simons Center for Geometry and Physics (SCGP)
      Stony Brook University, New York     SCGP Webpage of show
      2015 OnLine video of artist talk: From Rhythm to Algorithm - Manfred Mohr     SCGP Video of Manfred Mohr Talk
      2015 Catalog Manfred Mohr: Pioneer of Algorithmic Art, SCGP, 20 pages

    Fold-out visual document

    • 2014 Manfred Mohr: Künstler, Kritisches Lexicon der Gegenwartkunst, Dr. Annette Doms
      Der Kunsthandel Verlag, Ausgabe 108/ Heft 25/ 4. Quartal, Neu-Isenburg, 18 pages

    One-Person Shows in Galleries

    Important groups shows in Museums and Foundations

    • 2012 Rasterfahndung. Das Raster in der Kunst nach 1945, Kunstmuseum Stuttgart
    • 2013 On Abstraction III, At the Same Time, Elsewhere ..., Musée d'Art Contemporain de Montréal (MACM), Montréal
      Website of show   Photos of show
    • 2013 Light. Art. Kinetics., Museum Ritter, Waldenbuch
    • 2014 Grazyna Kulczyk Collection. Everybody is nobody for somebody, Fundacion Banco Santander, Madrid
      Installation photo of work in show
    • 2014 Luminous Flux, Digital and Geometric Art from the Thoma Foundation, Art House, Santa Fe, New Mexico
    • 2014 //the_ART_of_DATA, Boulder Museum of Comtemporary Art (BMoCA), Colorado
    • 2015 I Got Rhythm. Kunst und Jazz seit 1920, KunstMuseum Stuttgart
    • 2015 Rendezvous der Länder, Neuhängung der Sammlung Peter C. Ruppert - Konkrete Kunst in Europa nach 1945
      Museum im Kulturspeicher, Würzburg
    • 2015 RAM II, Rethinking Art & Machine, Marla Wasser Curator, Art Gallery of Nova Scotia, Halifax, Nova Scotia
      A group show with 5 artists, Each artist had their own rooms.
      My webpage of photos of my work in the show
    • 2015 Ein Quadrat ist ein Quadrat ist ein Quadrat, Museum Ritter, Waldenbuch
    • 2015 Short Cuts, Centre PasquArt, Kunsthaus Centre d'art, Biel
    • 2016 [UN]expected: The Art of Chance, KunstMuseum Stuttgart
      Installation Photos
    • 2016 Shadow & Space, Thoma Art Foundation, Orange Door, Chicago
      Installation photos, courtesy of the Thoma Foundation
    • 2016 The Thinking Machine. Ramon Llull and the ars combinatoria
      CCCB - Centre de Cultura Contemporània de Barcelona
    • 2016 Electronic Superhighway (2016 - 1966), Whitechapel Gallery, London
      Installation photo

    • 2012 Vasarely, Budapest;   Haus Konstruktiv, Zurich
      L'Espace de l'Art Concret, Mouans-Sartoux;   Musée d'Art Moderne et Contemporain, Strasbourg
    • 2013 Vasarely Museum, Budapest
    • 2014 Borusan | Contempory, Istanbul;   Museum für zeitgenössische Kunst, Chemnitz
    • 2015 Thoma Foundation, Art House, Santa Fe, New Mexico
    • 2016 Borusan Contemporary, Istanbul;   Stiftung für Konkrete Kunst, Reutlingen;   Shirley Fiterman Art Center, New York

    2017 - 2018: Transit-Code

    • Transit-Code refers to my many years of writing code in search of visualizing my artistic ideas. Of all the algorithms I wrote, not all of them were successful and often had to be rewritten or sometimes abandoned because I could not find a satisfying visual solution. I rarely deleted my code. I sometimes go back to algorithms I had given up and give them a second look. My artistic experience is the guide in finding new solutions for those originally unclear ideas. But once in a while, I am tempted to try to get from a perfectly accepted solution more than one answer.
    • 2017 P2300 is based on the same algorithm as in the workphase Artificiata II - parity from 2014
      In the 2014 workphase, an n-dimensional diagonal-path is divided into its even and odd segments and the respectively missing lines are shown as compressed vertical lines along the sides of each part.
      These compressed fragmented lines fascinated me. They had a musical character. I envisioned bringing them together, to see how the two fragmented lines would visually work together.
      Thus in the P2300 series, each square is bent 180 degrees around it's center point and then moved and rotated placing the two fragmented lines into the horizontal position, with one common center point. The original compressed vertical side lines become thick horizontal lines, creating a rhythm.
      In the P-2300 series, the circular form is the generated content of the work; As opposed to some of my earlier circular drawings such as P-38 (Rotor, 1970) and P-154 (Cubic Limit I, 1974) where the circular form is a container for the placement of the graphic signs.
    • 2017 The P2400 series is based on my 1978 algorithm from the workphase Dimensions I
      In P226 the graph of a 4-D hypercube is divided in four parts of 8 lines each, adding up to the complete structure of 32 lines.
      The first version of the algorithm from 1978 did not include the possibility of rotating the 4-D hypecube. Years later in 1987, I wrote another version of this code by introducing the 4-D rotation of the hypercube which generated a successful workphase Dimensions II. In 2017, out of curiosity, I took a new look at the first version of my code from 1978 and suddenly became interested in persuing this handicap of "no-rotation" again. I used the original code with its rigid position of 45-degrees in all angles and directed the algorithm into a different visual solution. Again, the basic 32 lines which constitute the hypecube are divided into 4 sets, but this time the elements are called randomly and placed in a linear visual 4/4 rhythm.
      In 2018, I used the thicknesses of the lines and generated a new set of drawings which shows the four sets of 32 lines as rectangular outlines or with one randomly colored section. The global visual effect of these drawings remind me of free jazz.
    • 2018 The P2500 series is based on my 2014 algorithm from workphase Artificiata II, traces.
      Each drawing, in a series of 9, shows only the traces (not the generating diagonal-path).



    • 2018 Elected to the SIGGRAPH Academy "for pioneering achievements in creating art through algorithmic geometry", ACM SIGGRAPH
      Photo of award

    Museum Retrospective, Catalog, Webpage

    One-person Shows in Galleries

    • 2017, Charlot, Paris (2 person with Eric Vernes)
    • 2018, Mueller-Roth, Stuttgart;   DAM, Berlin

    Important Groups shows in Museums and Foundations

    2019: algorithmic modulations

    • 2019: One randomly chosen diagonal path through a 12-D hypercube is selected and placed in three different angular positions. This diagonal path in three positions represents the initial graphic constellation as the inherent generator of the images.
    • After being rotated in 12-D and projected into 2-D, the diagonal-paths become visible as transparent color bands. A thin horizontal black line is drawn starting from each vertex (of all three diagonal-paths), crossing the vertical center of the image and continuing to the opposite side. In addition, for each vertex a slightly thicker horizontal black line is drawn starting from the vertical center of the image and continuing to the negative x-value of the respective vertex (reflection from the vertical center).
      The rotation in 12-D horizontally modulates the black line construct, whereas its symmetric aspect creates a graphic counterpoint to the visually floating transparent color bands.
    • In the screen-based work the algorithm randomly changes the colors of the 3 transparent bands and occasionally switches completely to white bands on a grey background. On other occasions the 3 bands transform to full color and while returning to their transparency they are overlayed with a shrinking and slowly fading structure, revealing the generating diagonal-paths.
    • The music related horizontal lines were initially used in Artificiata I, 1969 and then again on numerous occasions, including Artificiata II.

    Webpage for this workphase

    One-Person shows in a Gallery and Art Fair

    Important Group Exhibitions in Museums and Foundations

    Some of the Museums and other Public Collections in which I am represented

    • Centre Pompidou, Paris; ZKM | Center for Art and Media, Karlsruhe; Joseph Albers Museum, Bottrop; Mary and Leigh Block Museum of Art, Chicago; Victoria and Albert Museum, London; Ludwig Museum, Cologne; Wilhelm-Hack-Museum, Ludwigshafen; Kunstmuseum Stuttgart, Stuttgart; Stedelijk Museum, Amsterdam; Museum im Kulturspeicher, Würzburg; Kunsthalle Bremen, Bremen; Musée d'Art Moderne et Contemporain, Strasbourg; Daimler Art Collection, Berlin / Stuttgart; Musée d'Art Contemporain, Montreal; The Tel Aviv Museum of Art, Tel Aviv; Espace D'Art Concret (EAC), Mouans- Sartoux; Museum für Angewandte Kunst, Cologne; Borusan Art Collection, Istanbul; McCrory Collection, New York; Esther Grether Collection, Basel; Thoma Art Foundation, Chicago.

    List of important publications in which I am represented

    To come ....

    For more information see: