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#Stability of Orbits. --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)