Ultimate Anti-Buddhagram

  • 0 Replies
  • 181 Views

0 Members and 1 Guest are viewing this topic.

Offline claude

  • *
  • 3f
  • ******
  • Posts: 1593
    • mathr.co.uk
« on: November 21, 2019, 02:09:43 PM »
blog post: https://mathr.co.uk/blog/2019-11-20_ultimate_anti-buddhagram.html

implicit surface (4D) approximate distance estimate (no proof this is correct, but it seems to work)

Code: [Select]
float DE(vec2 c, vec2 z0)
{
  vec2 z = z0;
  vec2 dz = vec2(1.0, 0.0);
  float de = 1.0 / 0.0;
  for (int p = 1; p <= MaxPeriod; ++p)
  {
    dz = 2.0 * cMul(dz, z);
    z = cSqr(z) + c;
    de = min(de, max(length(z - z0), length(dz) - 1.0));
  }
  return 0.25 * de - Thickness;
}

I think the 4D normal is \[ \left( \frac{\partial F}{\partial c} ; \frac{\partial F}{\partial z} \right) \] where \[ F(c, z) = f_c^p(z) - z \], choose the period p that minimizes the DE.


Linkback: https://fractalforums.org/fractal-mathematics-and-new-theories/28/ultimate-anti-buddhagram/3200/


xx
Mandelbulber 2.14 - Anti-Aliasing

Started by stilikon on Mandelbulber

11 Replies
674 Views
Last post November 22, 2018, 03:54:30 PM
by stilikon
xx
How can I zoom fractal so they will look smooth / with anti-aliasing ?

Started by fdps20_ on Noob's Corner

0 Replies
106 Views
Last post June 01, 2020, 11:28:20 PM
by fdps20_
clip
anti-Buddhabrot with partial orbits - behaviour at infinity?

Started by marcm200 on Fractal Mathematics And New Theories

6 Replies
406 Views
Last post March 19, 2019, 09:22:34 AM
by marcm200