Direct colouring exponent smoothing? 2D

[Alef]

Looking at direct colouring orbit traps and helpfiles about direct colouring in mind came an idea, that exponent smoothing algorithm could be made as direct colouring algorithm.

summ=summ+e^(-cabs(z))
If exponent smoothing uses eulers number as base and -|z| as exponent, then red blue and green chanells having different bases would generate some sort of colour information.

It worked especialy when bases are enought different, real, imaginary and negative. Not shure how would look graph of y=-1.5^(-|x|) or y=1.5i^(-|x|), but wikipedia claims that exponent function is periodic on imaginary argument.

This generated very poisonous colours  emo magenta, cyanide and radioactive yellow. This mandelbulbs looks like of toxic waste after nuclear accident and unmodified were yellow, not great. Looking at brots I expected more, probably just all surface is like inside with similar values of |z|. But mandelbrots are quite a nice;) I 'm just thinking, that exponent smoothing of CMYB colours would result of more natural red green and blue.

[Alef]

Looked throught all aviable formula database and found just a few direct colouring algorithms and even fewer not relying on pallette. Still, no a clue, how y=(-2)^x would look like, some growing 3D periodic curve, dissapearing curve in just XY. Wikipedia sayes it is not an exponent.
x   y=(-2)^x

1/3   =-1,26
1/2   =i
1   =-2
2   =4
3   = -8

Rotated mandelbrot is very coloured. Some details were revealed just by antialiasing. Burning ship is pretty interesting one. Of coarse this could be any other colour, but i think inside being in hott colours and outside being cold is pretty logical.

[Alef]

I just remembered a switch to use RGB light instead of HSL and now it looks much better;)

Colours are distributed as in 2D. Basic mandelbulb is golden yellow but any modifications are more colourfull.

With few changes of exponents or adding some number to z (changing orbits) colours become more interesting. The inverted bulb with some +2 orbits probably have every toxic colour possible;) Plain directly smoothed modified bulb is green and violet. A bitt ugly mandelbox is somewhat dark, like 2D fractal far outsides, but pallete colours wouldn't created such colour diversity. Forth is Chaos pro mandelbulb example coloured by direct exponent smoothing, very smooth gradient. (With few additions released this method publicly under the name TwinLamps direct colouring, this realy is not the easy to control colouring.)

Generaly speaking colours very much depends on fractal formula, even starting z, but it works the best with DE.

I think, this method can be used to colour many other massivs of data.

[tit_toinou]

"Still, no a clue, how y=(-2)^x would look like,"
Euler's magic formulae : e^{i*pi}+1=0
So for t negative, t^x = (-t)^x = (-1)^x * t^x = e^{i*pi*x} * t^x = e^{x*( i*pi + ln(t))} ( complex number of argument pi*x and of abs value (-t)^x ).

[Alef]

I mean't a graphic. I think that would look like graph of exponent multiplied with oscillating sine function, but with certain features if x<1.