0xDE (11011110) wrote,

A multicolored checkerboard

After giving my last two lectures of the school year today, I'm not up for much more than posting pretty pictures, so:

This diagram is a visualization of the partition of matrix data among 18 different processors in a distributed algorithm. The connections between data elements A[x,y] and their transposes A[y,x] is stronger than the connections between adjacent elements, so many subsets of the partition are disconnected, consisting of two pieces symmetrically placed across the main diagonal of the matrix from each other.

The part I'm interested in here is the choice of color for the visualization. We would like colors that are all distinguishable from each other, so that even when subsets are disconnected we can tell which pieces belong to which subset; this figure is a little defective in this regard, with two similar pinks. We would also like to make the partition boundaries visible by choosing especially distinct colors for pairs of sets that share a boundary. Mike Dillencourt, Mike Goodrich, and I have been working on the problem of automatically choosing colors by embedding a graph representing adjacency of partition sets into a three-dimensional space representing the possible colors; it turns out that the choice of three-dimensional color space coordinates is important as some color spaces correspond better than others to human perception. The diagram above was colored automatically by our algorithm, using a color gamut in Lab color space formed by the convex hull of the eight corners of the sRGB gamut.
Tags: color, graph drawing, information visualization
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