walking the color cube
TODO: like most everything on this blog, this post is half finished. But I have other things to do, like my research and getting a submission to Electrofringe ready
What can you do with a color circle?
1. Generate labels!
[image of a color circle with N points selected, evenly spaced]
The outer ring of most color wheels varies one dimension at a time, crossing through the primaries, secondaries, and greys. This kind of color circle can be easily generated by taking a Hamming walk along the edges of the color cube:
[image of trivial color circle]
What would a color circle look like that also includes the inside of the color wheel? The root of this question is how to walk through the color cube in a way that doesn’t pass through the same colors twice. If you partition the color cube as a graph, you can start to think about circuits. In particular, an Eulerian circuit through the color cube that looks good (not a Hamiltonian circuit, which is a more complex beast).
Above left is a cube I’ve partitioned so that it’s an Eulerian graph (all nodes are even degree). Of course, if you brush up on Eulerian graphs, you’ll know that if you start walking, never crossing the same edge twice, you are guaranteed to come back to where you started, forming a circuit. So if we record a color for each edge we pass in the graph, it’s given that we’re going to generate some color circle for any walk we take.
I was interested to explore the walks that generated nice color circles, where the colors are compact in some way.
Here are some ways to walk:
1. Principal Directions
[image of color circle]
References:
1. http://www.colourlovers.com/forums/1,3,1087/how_do_you_compare_two_colors
2. z-sorting uses some tricks from stereopsis … I’ve wanted to publish a JNI wrapper for parallel list sorting for a long time
Notes:
Eulerian cube generator breaks down for three or more subdivisions. This doesn’t make sense mathematically. I’ll have to check out my implementation later.
svn: http://resisttheb.org/rtb/colorcircles