Exhaustive Variation

From jazz and painting to programs

Manfred Mohr (b. 1938) was born in Pforzheim and trained as a gold and silversmith. He played tenor saxophone and oboe as a working jazz musician and painted gesturally into the 1960s. In Paris in the early 1960s he read Max Bense's information aesthetics and turned to rational, rule-based art. He later said in an interview:

"It was only when I got into the philosophy of Max Bense in the early 1960s that I understood that 'rational' thinking in art, as Bense proposed, could solve that problem." — Manfred Mohr, interview, Right Click Save

The composer Pierre Barbaud showed him how to think in algorithmic procedures. Mohr wrote his first programs, in FORTRAN IV, in 1967, and his first computer drawings date to 1969. From 1970 he drew on a Benson flatbed plotter (sources differ on the exact model, 1284 or 1286) at the Météorologie Nationale computer center in Paris.

1971: a solo show at the Musée d'Art Moderne

In 1968 Mohr co-founded the Art et Informatique seminar at the University of Vincennes and showed at Cybernetic Serendipity in London alongside Georg Nees and Frieder Nake. Then, from 11 May to 6 June 1971, the ARC gallery at the Musée d'Art Moderne de la Ville de Paris mounted Une Esthétique Programmée: twenty-eight framed drawings, a Benson plotter running live in the museum, and a panel for visitor comments. Mohr and the Digital Art Museum both describe it as the first solo museum exhibition of works entirely calculated and drawn by a digital computer.

The cube as an alphabet

In 1973 Mohr adopted the cube, generating signs from its twelve edges with combinatorial, logical, and additive operators. The idea grew out of an earlier work, Sphereless (P-128, 1972), which used a square's four sides plus its two diagonals. He later described the choice:

"I came to the idea of the cube and decided that it could be my instrument. Out of this, I developed a whole graphical alphabet which replaced the linearity of my earlier algorithms." — Manfred Mohr, interview, Right Click Save

Mohr developed the Cubic Limit algorithm from 1973 to 1977 (Cubic Limit I, 1973 to 1976; Cubic Limit II, 1976 to 1977). Each of the twelve edges is either drawn or not, which gives two to the twelfth, or 4096, possible edge subsets. Mohr did not draw all of them; he applied his operators to the alphabet and chose among the results. The tool on this page draws a grid of cubes, each cell a different selection from the same twelve edges.

Hypercubes and color

From 1978 Mohr moved to the four-dimensional hypercube, the tesseract. Dimensions I (1978 to 1980) introduced his "diagonal path" device. space.color (around 1999 to 2003) brought his first color after roughly three decades of black and white. It is built on the six-dimensional hypercube, with 720 possible diagonal paths, four selected algorithmically, drawn as thick lines threaded by thin connecting vectors. Mohr used the color to clarify spatial ambiguity rather than to decorate. klangfarben (2006 to 2007) took its name from Klangfarbenmelodie and drew the diagonal paths of an eleven-dimensional hypercube, high-chroma color on black, with a logic borrowed from the rules of serial music.

Mohr on his aims

In his own words:

"My artistic goal is reached when a finished work can visually dissociate itself from its logical content and convincingly stand as an independent abstract entity." — Manfred Mohr (Digital Art Museum; ACM SIGGRAPH History Archives)

His honors include a 1990 Golden Nica at Prix Ars Electronica and the 2013 ACM SIGGRAPH Distinguished Artist Award for Lifetime Achievement in Digital Art.

The Sol LeWitt lesson and the Vera Molnár lesson cover related work. LeWitt handed a single instruction to many drafters, and Molnár worked a matrix of forms from order into disorder. Mohr spent decades on the variations of one shape and its higher-dimensional relatives.

In the tool, pick a Preset based on one phase of Mohr's work, then set Grid size, the Min and Max number of edges drawn, and the Rotation range. Every cell is computed from the seed, so the same settings and seed always return the identical grid, and a saved plate is the seed and settings that reproduce it.