File:Julia-set z2+c -0.742 0.1 5000.jpg
Original file (2,000 × 1,200 pixels, file size: 327 KB, MIME type: image/jpeg)
Captions
DescriptionJulia-set z2+c -0.742 0.1 5000.jpg |
English: Julia set (in white) and Fatou set (in green and dark violet tones) for with . This value of lies inside the period 1 component (the main cardioid) of , the Mandelbrot set, but near its boundary. The Julia set is connected because . The violet tinted points are attracted by infinity unter the iteration, and for the green points the attractor is the single complex number that satisfies and lies in the main cardioid of . |
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Date | ||||
Source | Own work | |||
Author | Georg-Johann Lay | |||
Permission (Reusing this file) |
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Coloring
[edit]For definition of see Visualising Julia sets and the helper functions.
is sufficient to show the Julia set. stresses the bright parts. serves to shade the Fatou set (green) and is "merged" with to , the brightness. The hue 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;
}
}
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 17:21, 2 April 2008 | 2,000 × 1,200 (327 KB) | Georg-Johann (talk | contribs) | {{PD-self}} |
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