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Author Topic: Period 17 Minibrot  (Read 1035 times)
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David Makin
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« on: March 15, 2009, 04:35:59 PM »

Period 17 Minibrot



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=499

Just a quick example from the standard z^2+c Mandelbrot that I created when testing my new periodic bailout formula, rendered exactly as seen (i.e. at 640*480) with the divergent area in black and max. iterations set to 10000.
The divergent bailout was 65536, the convergent bailout was 1e-8, the centre is:
-0.7325973162545/-0.216460853226
with magnification:
2018.8244
The coloured areas are periods 17,34,51,68,85,102 and 119 simply coloured using smooth iterations with the ArcTan transfer function.
The render took around 2mins 50 secs using just one thread on my 3GHz P4HT - one thread as I'm still using the "DEBUG" option occaissionally and using more than one thread produces confusing compiler message output.
You can see slight errors for instance where the higher periodic areas attach to the main period 17 cardoid - the formula does allow the option of increasing the accuracy to almost completely avoid this but at the cost of using much higher iterations internally.
Unfortunately I haven't had as much time to work on the formula and special colourings for it as I hoped so it may be another few days before I finally upload to the UF database.
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cKleinhuis
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« Reply #1 on: March 15, 2009, 06:31:39 PM »

hi, nice , just for clarification: is this a special method to achieve smooth "inside" gradients ??!  huh?
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David Makin
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Makin' Magic Fractals
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« Reply #2 on: March 15, 2009, 07:01:55 PM »

hi, nice , just for clarification: is this a special method to achieve smooth "inside" gradients ??!  huh?

Well, yes I guess, except that the area ends up coloured as "outside" because a bailout based on detecting the period is occurring.
It's basically using the same method that Paul's been using.

Getting smooth iteration colouring for periodic bailout turns out to be quite simple - I've only checked for a given period "n" on every nth iteration and the smooth iteration calculation is based on the z values from the last iteration i, iteration i-n and iteration i-2*n otherwise it's exactly the same as normal convergent bailout.
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The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
David Makin
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Posts: 2286



Makin' Magic Fractals
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« Reply #3 on: March 15, 2009, 09:06:57 PM »

hi, nice , just for clarification: is this a special method to achieve smooth "inside" gradients ??!  huh?

Well, yes I guess, except that the area ends up coloured as "outside" because a bailout based on detecting the period is occurring.
It's basically using the same method that Paul's been using.

Getting smooth iteration colouring for periodic bailout turns out to be quite simple - I've only checked for a given period "n" on every nth iteration and the smooth iteration calculation is based on the z values from the last iteration i, iteration i-n and iteration i-2*n otherwise it's exactly the same as normal convergent bailout.


I should have said also the iteration count value used in the smooth colouring is last iteration i divided by the period i.e. the complete iteration is effectively reduced to the nth iterations only.

Also when using higher max. iteration counts having bailout testing for such areas actually reduces rendering times because some areas normally "inside" that reach max iterations bailout at a lesser iteration count.

I'm working on doing some colourings specifically designed for this sort of bailout and another main fornula that's designed specifically for bailouts on periodic areas in Julia Sets - in such cases that formula will render faster and more accurately than the generic one I've done that produced the minibrot example.
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