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Fractal Math, Chaos Theory & Research => Mandelbrot & Julia Set => Topic started by: Alef on April 17, 2013, 02:59:27 PM




Title: Iterating Random Powers
Post by: Alef on April 17, 2013, 02:59:27 PM
I had an idea to try to iterate random powers. Such as z=z^random +c.
At first it generated almoust nothing, as positive and negative numbers nullify each other. Then z=z^abs(random) +c generated something. Then with limiting random range it generated pretty interesting fractals, especialy julias of a burning ship version. Each random seed then generates different fractal. Something like:

int RRandpower = seed = random(seed)
int IRandpower = seed = random(seed)

Randpower=( abs (RRandpower) /(#randomrange/5)) + flip(abs (IRandpower) /(#randomrange/5))

z=abs(z)^Randpower+c

Probably a simmilar to burning ships with imaginary powers, never tried. With maximum iterations = 100, there must be 100 different fractional powers. Countrary to this, this formula works best with plain smoothed iterations colouring.

(http://www.ljplus.ru/img4/a/s/asdam/untitled4.jpg)
(http://www.ljplus.ru/img4/a/s/asdam/untitled5.jpg)
(http://www.ljplus.ru/img4/a/s/asdam/untitled6.jpg)
(http://www.ljplus.ru/img4/a/s/asdam/untitled7.jpg)

In Chaos Pro this generate something simmilar, jet different. Random numbers in each programm are different.


Title: Re: Iterating Random Powers
Post by: Dinkydau on April 18, 2013, 02:51:17 AM
Interesting


Title: Re: Iterating Random Powers
Post by: KRAFTWERK on April 18, 2013, 11:39:23 AM
Cool idea and images Alef... And now... Can you port it to 3D?  O0


Title: Re: Iterating Random Powers
Post by: Alef on April 18, 2013, 06:20:13 PM
Quote
Interesting
Thanks.
Quote
Cool idea and images Alef... And now... Can you port it to 3D?
Thet would be beyond my skills.




Here is random complex Burning Ship.
(http://www.ljplus.ru/img4/a/s/asdam/random_complex_burningship.jpg)

Looks noisy, but it could be good start for exploration of julia sets as I just uploaded formula to UF database. Nice julia sets are in area around left bottom white spot. Some mexican or Marrakech ornaments here:
Code:
Fractal1 {
::xohURgn29J1yutNMQw7Gw/DE6etJttsVbAP0UgeoAFoo+DIghal0mwXgkq2+vvLlkTCQBqOR
  NzOzu7Q2FV6sy8l1rYsMmNgs67zQiK2FsNPIPegzGAsfILP0wZG1NImkiiCdEaxcSW91Ury+
  whtimt74i9VrXNV2ktaVIjens6Rl+1+of01Wx8BlGz3kCOf9KrKEQX/c1gLDRJfLnZV9uSf6
  8R7oRNRbVXxCPpjzCQUPA6Xl+uOWHaAnySLAY3M2ZrYkTxbyqfrcte7v8XgYVxiwTPrQjfML
  Pd6E/9PiI6aDl6kfzbDG4KBN//Epy1Dy6ZLWmJ5jjRHN6nHwAhmgc+WAk/kaJYeO6zFwLYWP
  cn6HjGUN7xLljyPJ2UvlvRQAo7PQMDtSnv0CMNkyRwVSeBr7puRnmmnUWit0uNbSJNoJJjBD
  eX5dMJfDnmX0lIBzXx0Sk6oFy5dw6VUI8vUG0Bq4HyzzZadUx2Njazbp6Zr3nHqeLh2vd//J
  cXvqPqaRS7UvSTil3gEDpk6KlvavxHlNnEH310sgSXyL4ijidim66FidFHZLcHOW/ZxCx+3V
  Ufk2v5XZfsnUAdvl3fDurmCp/OgG7/I=
}


Title: Re: Iterating Random Powers
Post by: Alef on September 16, 2013, 06:07:20 PM
Tested alternating random formulas. Well, the result looks very simmilar (throught i think boring). This should be solely property of random numbers, with large enought max iterations orbits escapes whenever it's possible, and instead of line art creates escaping regions.

Well, this should be pretty possible in 3D, random number mandelbulb woun't require great programming skills, but here main interest are complex power, and so far haven't seen complex power mandelbulb but that's possible.


Title: Re: Iterating Random Powers
Post by: Rychveldir on November 19, 2013, 05:28:45 PM
Out of curiosity, when do you randomize the powers?

once at the beginning of the calculation or every iteration but then use the same for all pixels?