Joerg's last e-mail reminded me of my first computer graphics experiment (1981), which I since learned that many other people have also tried: ----- Make a color table of N colors (labeled 0 through N-1) representing a discrete circle of hues. (One easy way to do this is to use the circle inscribed in the hexagon cross-section of the RGB cube [0,1]^3 that is halfway between black = (0,0,0) and white = (1,1,1). At that time the maximum I could use was N = 256 colors (equally spaced around the circle of hues). Then for each pixel on the screen, with coordinates given by the integer point (x,y), calculate C(x,y) := x^2 + y^2 (mod N) and then color pixel (x,y) with the color having number C(x,y) in the color table. ----- The effect is an extremely complicated Moire-type pattern. I later used 1024 colors and the effect was even more interesting. I have not seen any good explanation of the very complicated image that this produces. I also tried many other polynomials P(x,y) in lieu of x^2 + y^2, and got some weird results, but nothing was as interesting and I daresay beautiful as x^2 + y^2. —Dan
On Jan 11, 2016, at 2:49 AM, Joerg Arndt <arndt@jjj.de> wrote:
Thanks. My impression is that imposing conditions mod something on x^2 + y^2 would . . . . . . . . .