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Author Topic: atom domain arguments  (Read 1133 times)
Description: save the z_p, it can be useful later
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Fractal Bachius
Posts: 563

« on: May 17, 2017, 02:04:34 PM »

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)


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
   if |z| > escaperadius
      de = exterior distance estimate
// 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:
« Last Edit: May 22, 2017, 01:49:46 PM by claude, Reason: filtered » Logged
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