Wallpaper

Written by Paul Bourke
January 1991
Images updated January 2018


The wallpaper fractal is an illustration of all the points in the following series with seeds x0,y0 on the plane. There are three parameters a, b, c with values supplied for the examples presented here.

xn+1 = yn - sign(xn) | b xn - c |1/2
yn+1 = a - xn



a = 1, b = 4, c = 60



a = 2, b = -1, c = 200



a = 10, b = -10, c = 0.01



a = 31, b = 12, c = 0.5



a = 0.1, b = 0.1, c = 10



a = 10, b = 1, c = 60



a = 474.12, b = 28.43, c = 17.03



a = 8.39, b = 90.96, c = 0.25



a = 0, b = 8.01, c = 115.63



a = 0, b = 20.62, c = 362



a = 63.79, b = 0.60, c = 0.38