• December 06, 2021, 10:40:54 PM

### marcm200

Gallery Name Total Images
Lyapunov images - original algorithm
Images computed by the original algorithm by Mario Markus from 1995.

Images are raw fractals with no post processing. Coloring is done by linear interpolation between two border RGB values for several adjacent intervals of Lyapunov values.
9
Lyapunov images - sectionally defined
The originally defined algorithm was used with sectionally defined functions (also introduced by Mario Markus). The algorithm was modified to allow for different sections to be defined for the initial, non-computing iterations and the following computing ones.
12
Lyapunov images - detached
The original algorithm uses the derivative of the trajectory function f to compute the Lyapunov exponent. The modified algorithm allows to use a second function g, which can be unrealted to f.
15
Lyapunov 3D carved
Computing a three-dimensional Lyapunov space cube with coordinates A, B and C. A smaller object (e.g. a sphere) is inserted into that cube and everything that lies outside of the smaller one is carved off of the cube. The remaining structure is visualized using a moving plane.
19
Julia/Mandelbrot sets w or w/o Lyapunov variations
Using Lyapunov style sequences like e.g. AB, one can use two (or more) c-values to calculate Julia sets with the original formula, using c1 or c2 depending on the sequence position that changes in each iteration, thereb creating a Julia/Lyapunov crossover. Or one could use the orbit to determine which value will be used.

16
Triplex numbers
3D images using trivariate equations to calculate objects under Lyapunov variations.
6