User talk:Georg-Johann

Visualising Julia sets

Hi, Thx for great images and article.

What means

$$ E \left\{ \right\}_{\!z\,\in\,\Gamma} $$

in

$$ E_n = E \left\{\log (\delta +\Sigma_n (z, \varepsilon) )\right\}_{\!z\,\in\,\Gamma} $$

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


 * Hi E is "Erwartungswert" resp. Expected Value of a set and the variance D is $$DX=EX^2-(EX)^2$$ where X² is the set of squares of X. See Computational formula for the variance and de:Benutzer:Georg-Johann/Mathematik. --Georg-Johann (talk) 15:06, 6 November 2009 (UTC)


 * So one have to compute :


 * expected value $$E (X) \,$$
 * variance $$D (X) =\operatorname{E}(X^2) - (\operatorname{E}(X))^2$$
 * standard deviation $$\sigma(X)= \sqrt{D(X)}$$

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


 * 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


 * 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)
 * 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)