Fractals/Lyapunov fractal

Lyapunov fractal in wikipedia

Lyapunov fractal in Mathematica and C console program

images of Lyapunov fractrals in commons


   "The "problem" with pretty much all fractal-type systems, is, that, what happens at the beginning of an actually infinite iterational scheme, is often not descriptive of the long-time limit behaviour. And that's happening with the perturbed Lyapunov exponent from Mario Markus' algorithm as well. If I recall correctly, he states in his 90's article something like "let the x-value settle in". It's similar to the statement "for sufficiently large N" in math papers or in general with convergent series.
   The actual value of how many skipping iterations one performs, is, however, (at least afaik) just a guess till you're satisfied with the quality of the image. In my images, I could not get rid of those artifacts in full, one example being the UFO image, where vasyan did a great job removing those spots:
   my version (with spots):;sa=view;id=1960" marcm200[1]


  1. : what-could-these-artifacts-be-on-my-lyapunov-fractal-renders