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)
pseudocode:
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
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March 18, 2011, 09:35:50 AM
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