Fun formula

[lycium]

Still quite a lot of exploring to be done with this  

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

[lycium]

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

[mclarekin]

 . I like the maths idea 

[phtolo]

Quaternion version