P-231a, plotter drawing / ink on paper, 1978, 52cm x 82cm,

© 1978 by Manfred Mohr

The "dimensions" work-phase is based on the graph of a 4-Dimensional hyper-cube. The graph is a two-dimensional representation of the hyper-cube, indicating relationships between points, lines, squares and cubes inherent in this structure. In the algorithm for this drawing, diagonal paths along the edges of the structure between two diagonally opposite points (here 0000 - 1111) are chosen so that the edges do not cross except along the structure (along edges or at vertices). Each element in this drawing represents a maximally planar graph using this procedure - that is, the maximum number of such diagonal paths which can be combined along the structure between the diagonally opposite points, such that there are no intersections outside of the structure. Taking combinatorially from the alphabet of 24 such diagonal paths between a set of diagonally opposite points, one obtains the 112 maximal planar graphs, as shown here. In this drawing, P231, the width of a line represents the number of diagonal paths that pass through this line. Another drawing, P230, in the work-phase is similar except that the lines are not additive, they are all equally unit width.

Manfred Mohr, "Dimensions", Galerie Mueller-Roth, Stuttgart 1979

The explicative diagram above, and the 2 drawings P230 and P231 are represented in the catalog

A work from this program was shown in the historic show:

KONSTRUKCJA W PROCESIE/ Construction in Process, Lodz, Poland in 1981

- List and images of what I sent to Lodz in 1981

The work also was shown again in the 30th anniversary of this show

- CONSTRUCTION IN PROCESS 1981 - THE COMMUNITY THAT CAME?, Muzeum Sztuki Lodz, Poland, 2011

- Video of the show

The work is in the collection of the Muzeum Sztuki Lodz, Poland