The image on the left shows a 69 x 69 "still life". That is, a configuration of occupied and unoccupied cells which is a fixed point for Conway's game of life. This was at one time the largest square solution known to be optimal in the sense of maximising the number of occupied cells.
The colours simply represent the numbers of occupied cells adjacent to each one. The solution to the problem was produced by the constraint programming system G12, though the proof of optimality had to be done by conventional mathematics. I hasten to add that I had nothing to do with the research, which was carried out by my colleagues in the Victorian Research Laboratory of NICTA. The eye-jarring colours are, however, all my own work, using the visualisation tools of the same G12 platform. I worked on the visualisation toolset in 2008–2010.
The same research team (notably Geoffrey Chu) later established better results, showing that arbitrarily large solutions exist, but unless you have an infinitely large computer screen, you won't be able to view them all.