BeschrijvingJulia-set z2+c -0.742 0.1 5000.jpg	English: Julia set (in white) and Fatou set (in green and dark violet tones) for ${\displaystyle z\mapsto z^{2}+c}$ with ${\displaystyle c=-0.742+0.1i}$. This value of ${\displaystyle c}$ lies inside the period 1 component (the main cardioid) of ${\displaystyle M}$, the Mandelbrot set, but near its boundary. The Julia set is connected because ${\displaystyle c\in M}$. The violet tinted points are attracted by infinity unter the iteration, and for the green points the attractor is the single complex number ${\displaystyle z}$ that satisfies ${\displaystyle z=z^{2}+c}$ and lies in the main cardioid of ${\displaystyle M}$.
Datum	2 april 2008
Bron	Eigen werk
Auteur	Georg-Johann Lay
Toestemming (Hergebruik van dit bestand)	Public domainPublic domainfalsefalse Ik, de auteursrechthebbende van dit werk, geef dit werk vrij in het publieke domein. Dit is wereldwijd van toepassing. In sommige landen is dit wettelijk niet mogelijk; in die gevallen geldt: Ik sta iedereen toe dit werk voor eender welk doel te gebruiken, zonder enige voorwaarden, tenzij zulke voorwaarden door de wet worden voorgeschreven.

Coloring

For definition of ${\displaystyle E_{n},\!\,\sigma _{n},\Sigma _{n}(z),h_{a}(x),w_{a}(x)}$ see Visualising Julia sets and the helper functions.

${\displaystyle {\begin{aligned}n&=5000\\K&=E_{n}+2.2\sigma _{n}\\J&=\ln(\delta +\Sigma _{n}(z))-K\\V_{1}&={\begin{cases}h_{0.6}(J)&,{\text{ if }}z\notin A(\infty ){\text{ or }}J>0\\h_{0.09}(J)&,{\text{ else }}\end{cases}}\\V_{2}&=1-(1-V_{1})^{2}\\V_{3}&=0.7(1-w_{7.5}(\Sigma _{n}(z)))\\V&={\begin{cases}1-(1-V_{2})(1-V_{3})&,{\text{ if }}z\notin A(\infty )\\V_{2}&,{\text{ else }}\end{cases}}\\H&={\begin{cases}0.3&,{\text{ if }}z\notin A(\infty )\\0.75&,{\text{ else }}\end{cases}}\\\mathrm {color} &=\operatorname {HSV} (H,1-V,V)\end{aligned}}}$

${\displaystyle V_{1}}$ is sufficient to show the Julia set. ${\displaystyle V_{2}}$ stresses the bright parts. ${\displaystyle V_{3}}$ serves to shade the Fatou set (green) and is "merged" with ${\displaystyle V_{2}}$ to ${\displaystyle V}$, the brightness. The hue ${\displaystyle H}$ is set according to the basin of attraction. There are two basins for this ƒ: one belonging to the attractor ∞.

        int basin = getBasin (z);

        K = EX+2.3*sigma; 
        X = log(ss) - K;

        if (basin == 0 || X > 0)
            v = hfunc(X, .6);
        else
            v = hfunc(X, .09);
        
        v = 1-pow(1-v,2);

        double x;
        if (abstand2 (o, _0) < 10)
        {
            x = (bfunc (15, ss));
            
            x = 0.7*(1-x);
            v = 1-(1-v)*(1-x);
            return hsv2rgb (0.3, 1-v, v);
        }    
        else
        {
            return hsv2rgb (0.75, 1-v, v);
            
            iv = (-.1+JCOLORS) * v;
        }

        color.index = iv;

        return color;
    }
}