Direct logarithmic colouring

[Alef]

Once there were Fractal Explorer, and I think, it's log count was one of the best ever colour methods.

After I got Fractal Explorer colour methods codes I realised that they are much simmilar to exponent smoothing, they uses summs of inversed logarithms of each z, and negative exponent is the same as inversed exponent. Having different logarithms appears different stalks, so maybe this could be used to generate all 3 Red, Green and Blue channell information.

The same principle used in buddhabrot method, and how NASA colours space photos.

I had in mind 3D, so used just modulus of z values insted of FE x*y*+sin(x*y). Insides required normalisation for iterations. Alsou added 1.0E-15 to z or else sometimes it generated dots, and magnet fractal was all white.

Finnaly I got this:

And rotated M-brot.

I think, these stalks must mean something, they curves around zeros, but alsou they freely go inside and outside of mandelbrot set.



* * * * * * * * * * * * *
As uploaded to EM.ucl and Chaos pro database.

Code:

Fractal1 {
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  uf/FfotL3A==
}

New.ucl:LogTrichrome {

; Direct colour method based on Fractal Explorer and NASA
; colour techniques. Summs of inveversed multiple log,
; algorithm by Arthur Sirotinsky and Olga Federenko.
; Colour information is generated by each channel having
; different logarithm bases.

; + post functions for greater variety.
; + switch to use gradient, index is green channel.

; by Edgar Malinovsky 16.04.2012.
; You may redistribute this algorithm, modify, derivate or use comercialy as you wish as long as you give proper credits.
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  agx/BQAliCD=
}

[Alef]

This works quite an interestingly with kalisets / ducks. Here I used simplest possible z=abs(z)/c+c. Around this it often generates bifucation patterns, but just not here.






Tried with Fractmonk's multipowerbrot, it it looks to have too much powers just for 4 consecutive logarithms, hence just few stalks and dots in insides.


Alsou with some 3D, but this works the best with mandelbrot and kalisets.



Here is my bug filled code with kaliset:

Code:

Fractal1 {
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}

Pablo2.ufm:kaleidopatterns {
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}

New.ucl:LogTrichrome {

; Direct colour method based on Fractal Explorer and NASA
; colour techniques. Summs of inveversed multiple log,
; algorithm by Arthur Sirotinsky and Olga Federenko.
; Colour information is generated by each channel having
; different logarithm bases.

; + post functions for greater variety.
; + switch to use gradient, index is green channel.

; by Edgar Malinovsky 16.04.2012.
; You may redistribute this algorithm, modify, derivate or use comercialy as you wish as long as you give proper credits.
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  agx/BQAliCD=
}

p.s.
Could not find the name for it, but I think log trichrome is good enought, it is pretty self explanatory, name have 12 letters and sounds as google chrome or trichomes;)

[Alef]

More and larger examples.
Here in 3D:


And Mandelbrot set in 2D: