• January 20, 2022, 12:34:50 AM

Meta Mandelbrot
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Description: Practicing with Meta-Mandelbrot math, slightly altered by changing the power value.

I used Level 2  (control.power set to 3.36)

Level 2 is:
(((z*z+c)*(z*z+c)+(c*c+z)) * ((z*z+c)*(z*z+c)+(c*c+z)) + ((c*c+z)*(c*c+z)+(z*z+c)))
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float2 complexPower(float2 value, float power) {
float rr = value.x * value.x + value.y * value.y; // radius squared
if(rr == 0) return 0.0001;

float p1 = pow(rr, power / 2);
float arg = atan2(value.y, value.x);
float2 p2 = float2( cos(power * arg), sin(power * arg));
return p1 * p2;
}

float2 complexMul(float2 v1, float2 v2) { return float2(v1.x * v2.x - v1.y * v2.y, v1.x * v2.y + v1.y * v2.x); }

float2 q,w;

q = complexPower(z,control.power) + c;           // z raised to power + c
w = complexMul(q,q) + complexMul(c,c) + z;    // (z*z+c)*(z*z+c) + (c*c+z)
w = complexMul(w,w);                                    // w*w
q = complexMul(c,c) + z;                                // c*c + z
z = w + complexMul(q,q) + complexMul(z,z) + c;

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Keywords: alternate Mandelbrot
Posted by: kosalos June 24, 2021, 07:11:55 PM

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