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]