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Author Topic: Fun formula  (Read 1145 times)
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lycium
Fractal Supremo
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Posts: 1158



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« on: February 17, 2016, 05:01:07 AM »

Still quite a lot of exploring to be done with this  afro

Code:
const float2 c = (float2)(1.0f,  sqrt(3.0f)) * -0.4899995f;
const float2 a = (float2)(0.9f, 0.2931446f);

float2 z = p;

const int max_iters = 1 << 10;

int i = 0;
for ( ; i < max_iters; ++i)
{
  const float2 z_num = cmul(z, z) + c;
  const float2 z_den = cmul(z, z) - (float2)(1, 0);
  const float2 m = cdiv(z_num, z_den);

  const float2 n = a + cdiv((float2)(1, 0), cmul(z, z) - cmul(a, a));

  z = cmul(cdiv(m, n), z);

  if (length(z) > 640000) break;
}

// i is bailout iteration

Renders:



Click for 4k resolution image or visit http://lyc.deviantart.com/art/spectral-julia-591316607



Click for 8k resolution image or visit http://lyc.deviantart.com/art/new-formula-8k-render-591318104
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lycium
Fractal Supremo
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Posts: 1158



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« Reply #1 on: February 19, 2016, 04:09:34 AM »

FarDareisMai made a UF formula out of this, with some extra parameters:

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mclarekin
Fractal Senior
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Posts: 1739



« Reply #2 on: February 19, 2016, 08:58:33 AM »

 afro. I like the maths idea  smiley smiley smiley
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phtolo
Navigator
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Posts: 79



« Reply #3 on: April 07, 2016, 07:37:24 PM »

Quaternion version




* lycfunformula.frag (3.41 KB - downloaded 76 times.)
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