# Fractals/Lyapunov fractal

< Fractals

Lyapunov fractal in wikipedia

## algorithms

edit"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: vasyan's: https://fractalforums.org/index.php?action=gallery;sa=view;id=2388 my version (with spots): https://fractalforums.org/index.php?action=gallery;sa=view;id=1960" marcm200^{[1]}

## images

edit## Video

edit## Programs

edit- creating Lyapunov images based on Mario Markus' algorithm from 1995 in the german science magazine Spektrum der Wissenschaft by Marc Meidlinger, July 2019
- lyapunov – a 2D/3D Lyapunov fractal generator in C++ by Lars H. Rohwedder RokerHRO
- haxe-shaderfun by Sylvio Sell (maitag) using HaxeUI ( free, open-source user interface toolkit)
- fractalforums.org : minuscule-source-code-for-lyapunov-images-ascii-style by marcm200
- Lyapunov fractal in Mathematica and C console program