Hey there, That's a very nice mandelbox there.
I had something similar when i tried to rewrite the mandelbox function in mandelbulber source one time, to find some new mathematics. I only changed 2-3 of the functions to arcsin/atan/ any random function that i could figure out... most of them had an infinity in them, but at some stage i found a fractal similar to the one you have above, except that the voids also contained gothic arch topology rather than mostly cubic, they went straight for a long time and at the top they had gothic arches everywhere. It was the only mandelbox var that worked nicely, i think perhaps it was arcsin added somewhere, i can't recall it. Darkbeams fractal looks very cool, it's good to not rely on sin in the mandelbox and to use periodic functions that are weird, perhaps inspired by audio synthesizer design... in synthesizers, we have frequency modulation, additive and sampling mostly as sources for complicating linear periodic functions, most simply mathematically and minimum computationally intensive.
In synthesizers, one of the best easy tricks that i know to mutate a single periodic function is "filter feedback loop" where the output of N wave iterations/periods, passes through a frequency filter which takes out some of the frequencies and changes the wave, and feed the output of that filter back into the frequency of the original oscillator using a time delay of at least one period.
That means it is self modulating it's own frequency with a delay of at least one period with a periodically semi consonant sound wave, and it's perhaps useable in fractals, i.e. copy a simple lowpass/highpass/bandpass filter code, use it to modulate the sine function through multiple iterations. That shouldn't be attempted without first trying simple additive/rectifying(abs value)/Frequency Modulation of the same wave, where the effect changes over time, as it's more difficult.
When doing Frequency modulation for example of a sine wave, Three important factors count to have very nice forms computationally cheaply and with much varietly without the sine degenerating into noise:...
A/ control of an ampltude varliabe on the amplitude of the frequency modulating sine wave into the frequency input of the main sine wave,
and then two controls to mutate the frequency modulating signal very subtly using two independent variables:
B/ in steps consonant with the period (.25/.5/2/4/8/16)
C/ in dissonant increments of 1-100th of the period of the main sine wave... it means that the signal never repeats once, and 100 periods or "recursions" later the measures of the sine wave (that makes a sphere for example in 3d) would have changed slowly from the first with a periodicity of perhaps 500 recursions.
I don't know totally how that works out in a recursion, else an ISO surface sense, because every sine function mutation used for the next recursion, would be best to not have any jagged moments caused by aperiodicity form being slightly mutated away from a normal sine. In synthesizers, the FM sine is a perfectly rounded aperiodic sine wave, i am not sure if that can even translate into a recursive function... if it is possible, it would perhaps mean that every next SIN function used in for example a mandelbox, was had it's freqency changed by another SIN of frequency .5 /.25 + 0.001, and of amplitude exponantially variable from 0.01 to 1.
I often program graphically and the fractals are higher than my normal maths level because the recursion spins me out and i didn't learn that in programming, but i believe that synthesizer periodic wave tricks can be applied to fractals. I may be completely wrong that synthesizer FM, which made a revolution in digital synths in the 80's and is still used in most synths today, can be applied to fractals, but if it can, that above ABC guide is the way to get the most out of it using very simple maths
Sorry about that synthesizers theory there, perhaps designing synthesizer wave generating central engines and writing recursive maths are not the same?!?! perhaps synthesizer wave folding (serge wave multiplier) and audio FM maths can be applied to give as much variety in fractals as they did in Yamaha's line of DX syths that changed music some time ago. FM can be very challenging mathematically to use it as advancedly as it's used in today's expensive synths because they manage to use totally random freqencies to produce unchaotic sounds using the FM index which is too complex for ordinary synth programmers and requires very advanced mathematicians.
perhaps someone else can tell me if synthesizer tricks can be used on fractal mathematics?!?
Changing the frequency of one periodic function using another atuned one is much more powerful than multiplying or adding them, and a lot more chaotic and less predictable.
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May 14, 2015, 06:40:57 PM
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