This was unexpected (bit of a technicolor headache there, sorry, but I'll explain)→[More:]I will avoid too-technical details, but that came out of some research I'd been working on with a student. Each row represents the expansion of a positive numer in an exotic 'fractional base' system - in this case, instead of good old decimal digits, we have a 'base 63/64' system, with 'digits' from 0 to 62. The first row of pixels is a color-coded sequence of digits that represents '1', the second row is a sequence that represents '2', and so on.

We studied these arrays of digits and proved a lot of good (and, above all, neat) theorems - but for some reason, I'd never thought to make an image out of the array. Today, after almost two years away from the problem I came back to it and decided to try plotting things. The results for "base 3/4" or "base n/(n+1)" when n is fairly small were just a jumbled mess - these were the cases we'd spent the most time on. But when I pushed n up to moderate sizes I suddenly got these amazing cascading pools and spirals. Each row can be continued indefinitely to the right, and if I extended it enough you'd see them all fall into chaos (it's beginning to happen in the upper right corner already). I have no idea what to make of this unexpected structure - which I never would have noticed from looking at small tables of digits - or if the striking visual patterns have any useful meaning whatsoever. Still, I thought it was a vibrant reminder that there's always another view to be had, on any vexing problem.