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Visualising Julia sets

Hi, Thx for great images and article.

What means

in

Also I can't find explanation of Dn, DX and EX. Best regards --Adam majewski (talk) 19:13, 31 October 2009 (UTC)[reply]

Hi E is "Erwartungswert" resp. Expected Value of a set and the variance D is where X² is the set of squares of X. See Computational formula for the variance and de:Benutzer:Georg-Johann/Mathematik#Stability of Orbits. --Georg-Johann (talk) 15:06, 6 November 2009 (UTC)[reply]
So one have to compute :
  • expected value
  • variance
  • standard deviation

Am I wrong ? --Adam majewski (talk) 17:18, 8 November 2009 (UTC)[reply]

It's some time ago I implemented the coloring... E and D should suffice. Note that you likely will need to play around with the parameters to get a satisfying result. AFAIR the result depends on the number of pixels and therefore scaling is not as easy as with other algorithms. --Georg-Johann (talk) 13:56, 10 November 2009 (UTC)00[reply]
Your method is very intresting because it :
  • distinguish between Julia and Fatou set ( and maybe can be used for parabolic Julia sets
  • allows drawing interior of filled Julia set without knowing finite attractore
  • gives beatifull pictures

I will try to explore it futher. First steps are here. Can you put a code to your images ? --Adam majewski (talk) 11:30, 11 November 2009 (UTC)[reply]

Sorry, I just kept the parameters and the formulas. The code was throw-away-code. I thought describing the way to get a coloring is more enlighting than an encoding in some programming language (which is not as easy to grasp, IMHO). --Georg-Johann (talk) 11:38, 12 November 2009 (UTC)[reply]