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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.

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.