News: Support us via Flattr FLATTR Link
 
*
Welcome, Guest. Please login or register. November 01, 2014, 04:53:08 AM


Login with username, password and session length



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: Relationship between bailout and accuracy of analytical DE  (Read 784 times)
0 Members and 1 Guest are viewing this topic.
David Makin
Global Moderator
Fractal Senior
******
Posts: 2269



Makin' Magic Fractals
WWW
« on: April 05, 2010, 04:27:31 PM »

Hi all,

Since <see subject> is pretty fundamental to most 3D rendering I decided to investigate the relationship in more detail and wrote the following in UF:

Code:
init:
  z = @start
  complex dz = (0,0)
  float d = 0.0
  float dold = 0.0
  float m = 0.0
  bool bail = true
loop:
  dold = d
  dz = @power*dz*z^(@power-1.0) + 1.0
  z = z^@power + #pixel
  m = |z|
  d = 0.25*log(m)*sqrt(m)/cabs(dz)
  if |(d-dold)/d|<@smallbail
    bail = false
  endif
bailout:
  bail

And then created a normal layer of the standard Mandelbrot and adjusted the smallbail on this layer and then adjusted the bailout on the normal layer until the iteration bands matched as closely as possible.
I found the result very significant, at least for 2D complex fractals - I'm hoping the result extends to 3D+ smiley

Basically if your bailout is 10000 i.e. you're testing magnitude squared against 10000 then your DE estimates are accurate to just two decimal figures i.e. if your DE is 0.01 then it's only accurate to +/-0.0001, if you're using a bailout of 1000000 then your DE is accurate to 3 decimal figures etc.
This result was confirmed for all powers I tried on the standard z^p+c Mandelbrot.
Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
reesej2
Guest
« Reply #1 on: April 08, 2010, 02:56:03 AM »

Oh, that's interesting. It makes a lot of sense, though. I'd think it would hold for the Mandelbulb and similar, too.
Logged
Pages: [1]   Go Down
  Print  
 
Jump to:  


Related Topics
Subject Started by Replies Views Last post
Dynamic Bailout General Discussion jgabase 4 1444 Last post April 21, 2012, 05:37:06 PM
by Alef
numerical problem with bailout test Programming Adam Majewski 12 855 Last post May 12, 2012, 05:15:50 PM
by Adam Majewski
Etymological Relationship Images Showcase (Rate My Fractal) thom 0 134 Last post May 21, 2012, 01:45:27 AM
by thom
Different Bailout Conditions FractInt simon.snake 0 171 Last post October 04, 2013, 11:15:25 PM
by simon.snake
A relationship between Riemann Hypothesis and rolling fractals New Theories & Research hgjf2 0 91 Last post April 13, 2014, 06:53:44 PM
by hgjf2

Powered by MySQL Powered by PHP Powered by SMF 1.1.20 | SMF © 2013, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.2 seconds with 29 queries. (Pretty URLs adds 0.014s, 2q)