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Author Topic: Maybe more colour algorithms  (Read 1676 times)
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Alef
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Posts: 1174



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« on: August 26, 2012, 04:55:38 PM »

Maybe more colour algorithms? Colour methods for 3D fractals realy is pretty unresearched territory. It's not 2D where colouring is everything, but coulouring could retrieve more from Abox.


Orbital colouring (colour map on output vector?) with iteration counter in Chaos Pro  works pretty nicely on all the 3D fractals. (Colour by modulus of z of xxx iteration) Iteration number is pretty powerfull tool, colour density strongly depends on iteration number. Maybe "colour map on output vector" could have iteration counter.


Exponent smoothing (iterated sum=sum+ exp( -|z| ) ) + limited iteration number. Exponent smoothing alsou are too dense, but of first 5 - 30 iterations goes well. For visual effects one can change normal e exponent with negative base, (-e)^( -|z| ), this would involve math of complex numbers but then it would be more different, and there is no point of having bunch of similar colouring methods.

I have 2 pics, negative base exp smoothing,

and exp smoothing divided by (1+zmax-zmin) where zmax and zmin are maximal and minimal exp( - |z| ).


Then I had Log Trichrome in NumberSeekerColouring.ccl (Chaos Pro) (and in in EM.ucl of Ultra Fractal but without 3D) which generate colour lines, which are something like z value isogradients, throught method works better with smoother surfaces;) Like Exponent Smoothing, but it uses summ of inversed multiple logarithms, a bitt more complex method derived from Fractal Explorer where similar colour method was known as Log Counting. This was intended as direct (without colour map) colouring method but goes with colour map, too. In Fractal Explorer "Log Counting" was one of the best colourings, but it calculated red, green and blue values seperately.



Code:
//simpliefied, during iteration loop:
cabsz= cabs(z + 1.0E-15);
cnt=cnt+1;
normaliter =sqr(cnt );
dataG=  abs( log (  log ( log (cabsz)  )  ) );
sumG= recip(dataG*normaliter +  1) + sumG;

//after iterations:
colour index=sumG;


p.s.
One can download Chaos Pro, and all the Ultra Fractal formula database. Since Chaos pro have native 3D, one can use whatever mandelbulb / mandelbox to test how UF colour methods would work in 3D. Throught 50% don't (some functions are incompatible with quaternion math, some use unsupported plugin feature), and many are just versions of the same, but UF database is gargantuan. (Some non native Ultra Fractal implementation of 3D do work with colour methods, but in native 3D this works much smoother.)
Star of David trap of PWC.ucl seems to work as do Aleph One (needs some normalisation) or Perlin Noise 3D. Bof60 works with brots, but it requires to multiply colour maping value by ~5. It seems, that colour methods intended for fractal insides works better with 3D fractals.  

Perlin Noise 3D:


Aleph One



Star of David trap


Chaos Pro savefiles of these pic included, all would working with outside formula files downloaded.

* Test_box.par (14.03 KB - downloaded 105 times.)
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Alef
Fractal Supremo
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Posts: 1174



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« Reply #1 on: August 26, 2012, 05:00:58 PM »

The first fractal is something like julia set of amazing surface rotbox with _asdam transfrom, then there are the same julia set of amazing surface without rotations, then there is another box and finnaly are pretty ugly plain abox.
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