Every Combination of an Incomplete Cube + 1 (after Sol Lewitt)

Date: 2014
Size: 4m x 1m
Materials: Watercolor Paper and Ink
Tools: Rhino, Grasshopper, Python, Hal, ABB Robot, Ink Brush
Location: Abedian School of Architecture, Bond University, Australia
Description: In 1973, the artist Sol Lewitt began exploring variations on an incomplete cube as the generator for a series of drawings and sculptures. Like many of his works, this project was governed by the following three rules:

  • Each incomplete cube had to have at least one edge from each axis
  • The remaining edges of each incomplete cube had to be joined
  • Each incomplete cube had to be rotationally unique

Based on these rules, Lewitt found that there were 122 variations on a incomplete cube which he then documented in his drawing “Variations of Incomplete Cubes” as well as through numerous sculptures.

Inspired by this project, I was interested in discovering other incomplete cubes by removing Lewitt’s rules. That is, how many incomplete cubes are there with a total number of edges between 1 and 11? Using a parametric model to iterate through a project axonometric of a cube, it was determined that there are 4094 incomplete cubes. When a completed cube is also included, the total number is 4095.

One of Lewitt’s other areas of interest was the nature of concept versus artifact in art. That is, is art simply the physical drawing or object or is it the idea that generates it? He clearly came down on the side of the concept being the art and often created a set of procedures for others to follow in the production of the artifacts (wall drawings, sculptures, etc.). For him, the script was art.

Following this line of investigation, a robot, following a set of instructions that I wrote, physically drew my expanded set of all possible incomplete cubes. There is a gap between the concept and its physical manifestation that is essential to this understanding of the nature of the art. Each physical iteration is simply a visualization of the concept, but is not the concept itself.

One of the largest gaps between concept and artifact is due to the nature of the robot’s “natural” movement. Although the robot can be programmed to move linearly from point to point, this is not the most efficient robot movement. Instead, the robot was programmed to move from point to point quickly but with a constant velocity of joint rotations. This interpolation of the target points appears more gestural, almost calligraphic, however, it is actually what could be called the robot’s innate drawing style.

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