Print Page - atom domain arguments

A new(?) development, using the argument (phase, angle) of the z_p iterate's value saved when it reaches a minimum in addition to the p value (aka atom domains)

(https://mathr.co.uk/mandelbrot/2017-05-17_atom_domain_quadrants_1.png)
(https://mathr.co.uk/mandelbrot/2017-05-17_atom_domain_quadrants_2.png)

pseudocode:

Code:

C c = pixel
C z = 0
C dzdc = 0  // for exterior de
R mz = infinity
N p = 0
C zp = 0
for (N n = 1; n < maxiters; ++n)
{
  dzdc = 2 * z * dzdc + 1
  z = z * z + c
  if |z| < mz
  {
     mz = |z|
     p = n
     zp = z
     // check if interior to a component of period p, see https://mathr.co.uk/blog/2014-11-02_practical_interior_distance_rendering.html
     if (interior)
     {
        de = interior distance estimate
        break
      }
   }
   if |z| > escaperadius
   {
      de = exterior distance estimate
      break
    }
}
// colouring
use p to adjust hue
use arg zp to adjust saturation and value // this is the new development
use n&1 to darken
use arg z to lighten
multiply by tanh(de / pixel size) for black boundary

EDIT: I developed this after thinking about locating periodic points, this method should scale more readily to deeper zooms than the periodicity scan using the box period Jordan curve method.... https://mathr.co.uk/blog/2017-05-17_periodicity_scan.html

EDIT: I wrote another blog post about a modification of atom domains:
https://mathr.co.uk/blog/2017-05-22_filtered_atom_domains.html
(https://mathr.co.uk/blog/2017-05-22_filtered_atom_domains_2.jpg)

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Fractal Math, Chaos Theory & Research => Mandelbrot & Julia Set => Topic started by: claude on May 17, 2017, 02:04:34 PM