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61 lines
2.0 KiB
61 lines
2.0 KiB
#version 100
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#define PI 3.1415926535897932384626433832795
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precision highp float;
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// Input vertex attributes (from vertex shader)
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varying vec2 fragTexCoord;
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varying vec4 fragColor;
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uniform vec2 offset; // Offset of the scale
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uniform float zoom; // Zoom of the scale
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// NOTE: Maximum number of shader for-loop iterations depend on GPU,
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// For example, on RasperryPi for this examply only supports up to 60
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uniform int maxIterations; // Max iterations per pixel
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const float max = 4.0; // We consider infinite as 4.0: if a point reaches a distance of 4.0 it will escape to infinity
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const float max2 = max*max; // Square of max to avoid computing square root
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void main()
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{
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// The pixel coordinates are scaled so they are on the mandelbrot scale
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// NOTE: fragTexCoord already comes as normalized screen coordinates but offset must be normalized before scaling and zoom
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vec2 c = vec2((fragTexCoord.x - 0.5)*2.5, (fragTexCoord.y - 0.5)*1.5)/zoom;
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c.x += offset.x;
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c.y += offset.y;
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float a = 0.0;
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float b = 0.0;
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// The Mandelbrot set is a two-dimensional set defined in the complex plane on which the iteration of the function
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// Fc(z) = z^2 + c on the complex numbers c from the plane does not diverge to infinity starting at z = 0
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// Here: z = a + bi. Iterations: z -> z^2 + c = (a + bi)^2 + (c.x + c.yi) = (a^2 - b^2 + c.x) + (2ab + c.y)i
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int iter = 0;
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while (iter < maxIterations)
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{
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float aa = a*a;
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float bb = b*b;
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if (aa + bb > max2)
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break;
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float twoab = 2.0*a*b;
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a = aa - bb + c.x;
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b = twoab + c.y;
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++iter;
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}
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if (iter >= maxIterations)
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{
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gl_FragColor = vec4(0.0, 0.0, 0.0, 1.0);
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}
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else
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{
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float normR = float(iter - (iter/55)*55)/55.0;
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float normG = float(iter - (iter/69)*69)/69.0;
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float normB = float(iter - (iter/40)*40)/40.0;
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gl_FragColor = vec4(sin(normR*PI), sin(normG*PI), sin(normB*PI), 1.0);
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}
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}
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