Zio Chris' Wall Drawing 256

Chris Culy, 2015-2016

License: Creative Commons License
Zio Chris' Wall Drawing 256 by Chris Culy is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Thanks to "Superstar" KB for the original impetus.

The instructions for Sol Lewitt's Wall Drawing 358 say to fill a grid with arcs drawn from one corner, and

"[T]he direction of the arcs and their placement are determined by the draftsman."

Letting the computer be our "draftsman", we can in principle draw all the possible combinations of arcs for a grid of given size. "In principle", because the number of combinations grows exponentially: since there are 4 arcs (one for each starting corner), if there are n cells in the grid, there are 4n combinations. To give you an idea, the version of Wall Drawing #358 linked to above has 15 rows and 24 columns for 360 cells, giving 4360 combinations, which is more than 10216 combinations. If we looked at one example per second, it would take over 10209 years to view them all, about 92 times the estimated age of the universe!

While that is a bit much, we can scale things back a bit: if we have a 2x2 grid, then there are only 44 = 256 combinations, which we can easily visualize all at once. By clicking on the "Visualize!" button, you can see all those combinations, themselves laid out randomly in a grid, in the spirit of Sol Lewitt. Or go here to get a new combination each time.

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