Logo by Fiery - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Visit the official fractalforums.com Youtube Channel
 
*
Welcome, Guest. Please login or register. December 16, 2018, 08:16:51 AM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Pages: [1]   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: atom domain arguments  (Read 508 times)
Description: save the z_p, it can be useful later
0 Members and 1 Guest are viewing this topic.
claude
Fractal Bachius
*
Posts: 563



WWW
« 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)




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
« Last Edit: May 22, 2017, 01:49:46 PM by claude, Reason: filtered » Logged
Pages: [1]   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
The Overseer's Domain Mandelbulb3D Gallery Don Whitaker 0 267 Last post March 18, 2011, 09:35:50 AM
by Don Whitaker
Atom in a Fractal Universe Images Showcase (Rate My Fractal) Fractal Ken 0 1854 Last post July 09, 2011, 06:40:43 AM
by Fractal Ken
looking for art to add to the Public-Domain Let's collaborate on something! matty686 3 890 Last post July 25, 2012, 05:02:09 PM
by matty686
Di-abolical Di-atom-ic Diatoms! Images Showcase (Rate My Fractal) reactorman 0 248 Last post December 29, 2014, 06:30:58 PM
by reactorman
Quasi-Structured Domain Images Showcase (Rate My Fractal) JoeFRAQ 0 270 Last post August 15, 2015, 02:01:12 PM
by JoeFRAQ

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.103 seconds with 27 queries. (Pretty URLs adds 0.005s, 2q)