### Genetic algorithms to search the Lyapunov space

• 0 Replies
• 156 Views

0 Members and 1 Guest are viewing this topic.

#### marcm200

• Fractal Freak
• Posts: 682

#### Genetic algorithms to search the Lyapunov space

« on: July 04, 2019, 12:14:55 PM »
I tried the genetic algorithm approach by Ashlock (see fractalforum-link) with Lyapunov exponents. I started with the b*sin²(x+r) formula and sequence AAAAAABBBBBB.

The "chromosome" for one individual consists of the parameter b, the position (x0,y0) and a size. I used the tournament-7-rule: In each round, pick 7 individuals randomly, assess their fitness and breed the two best: now the two children replace the two least fit individuals of that seven (after some cross-over mutations with swapping b between children or x,y). Afterwards a mutational round for all 7 starts with slight changes to the parameters in decreasing maximal amount as the population ages.

I ran the program 15 times, took the fittest and displayed it below. Also included is the palette (upper row) and the fitness function (upper left black/white image), which works as a 20x20 grid imposed on the rectangle of each individual and calculates the square distance to a pre-defined "target" 20x20 grid of Lyapunov exponents between -1 and +1.

It proved very difficult to find any fitness function that produces some kind of convergent behaviour in the sense that the best indivuduals of separate runs share some similarity. The current function likes a big ordered corner region (silver) going into more or less smooth chaos (red).

Current observation is, when using Lyapunov exponent as target value, that using a highly volatile fitness function like a forest with high trees (the first I started with), it always "converges" to more or less a featureless order region instead of what I expected to see: a chaos/order spot pattern.

Currently it looks like the grid fitness function does not work well with Lyapunov exponent images. Maybe a more statistical approach on the image itself (like spyke did, see above link) would be better suited.

### Similar Topics

###### Genetic algorithms to search the Mandelbrot set

Started by marcm200 on Fractal Mathematics And New Theories

12 Replies
576 Views
July 02, 2019, 10:27:17 AM
by claude
###### Evolving 3d Fractals with Genetic Algorithms

Started by ansr23 on Other Artforms

3 Replies
877 Views
January 29, 2019, 11:57:11 AM
by mrrudewords
###### Three dimensional Lyapunov space

Started by marcm200 on Image Threads

31 Replies
1299 Views
March 21, 2019, 11:05:42 AM
by marcm200
###### Space Station Space-Rock--"Premonition"--(Railboard, Dubstep & Fractals)

Started by Paigan0 on Fractal movie gallery

2 Replies
241 Views
November 06, 2018, 11:42:29 PM
by Tas_mania
###### No search engine?

Started by AnJo888 on Off Topic

4 Replies
371 Views
June 04, 2018, 04:03:49 PM
by Caleidoscope