http://www.geocities.com/rlbagulatftn/chaotic_steptonoise.gif Two new types of chaotic sequence plotted against each other. Mathematica: Clear[a, f, b, c, g] (* fractal noise chaotic sequence*) f[0] = 1; f[1] = 0; f[1] = 1; f[n_] := f[n] = f[n - f[n - 1]] + f[Floor[2*n/3]] (* Cantor like fractal stair step chaotic sequence*) g[0] = 1; g[1] = 0; g[1] = 1; g[n_] := g[n] = g[Floor[2*n/3]] + g[Floor[n/3]] ListPlot[Table[{f[n], g[n]}, {n, 0, 200}], PlotJoined -> True]