DE calculation for "compound" fractals ?

[David Makin]

Hi all,

Here's a compound fractal, (on each iteration) the standard Mandelbox (without constant) followed by standard ^8 -sine White/Nylander Mandelbulb:



This was rendered with correct scaling of the running derivative in the Mandelbox calculation and correct adjustment of it in the Mandelbulb calculations with the final DE value calculated based on the normal Mandelbulb method.

My question is - what should have been done as the final DE calculation ? Should it actually be different due to the use of the Mandelbox ?
If the Mandelbulb had been done first followed by the Mandelbox then should the DE calculation use the Mandelbox DE calculation insted of the Mandelbulb one ?

[reesej2]

The use of the Mandelbox should change it somehow, but I haven't a clue how to work it out... I'd be fascinated to see it.

[Jesse]

That is very promising, good work.
Just wonder if there is already a common way to calculate the derivative and a DE based on it for general formulas?

[David Makin]

That is very promising, good work.
Just wonder if there is already a common way to calculate the derivative and a DE based on it for general formulas?

Well there is, in that in this case any of the delta DE methods should work OK, it's just that in my experience so far the analytical method produces the best results when you consider quality of image and render speed together so I was hoping if maybe someone had ideas on how to turn the running derivative and final z into a DE value correctly for compound fractals like this one.
The method I have used here, simply using the DE formula for the Mandelbulb, works OK but I'm sure (based on the render speed) that it's not producing very linear distance estimation i.e. its a lot slower at rendering to a given quality than using the analytical method for either a pure Mandelbox or a pure Mandelbulb.

[knighty]

Honeslty, I don't know but I suspect it is related to the asymptotic behaviour of the orbits, the phi function and the fact that the DE formula for the mandelbox doesn't involve log(r). If I remember well, phi(z)=z when z->infinity. for the mandelbox we should have something like phi(z)=z/scale^i (which gives DE=|z|/|dz|).

[knighty]

I have given it a try with DE=0.5*r*log(r)/dr/DEfactor. It works very well and is near optimal when not adding 1 to DEfactor. If not, it is up to 3 times smaller.

[David Makin]

I have given it a try with DE=0.5*r*log(r)/dr/DEfactor. It works very well and is near optimal when not adding 1 to DEfactor. If not, it is up to 3 times smaller.

Do you mean the same thing I did, i.e. Mandelbox(without constant) followed by Mandelbulb, or did you actually try Mandelbulb(without constant) followed by Mandelbox ?

[knighty]

I did Mandelbox without constant followed by mandelbulb this way:
DEfactor=1.
dr=1.
iterate begin:
box fold.
sphere fold (including update ofEfactor).
scale without adding constant and including update of DEfactor without adding 1.
Mandelbulb including update of dr.
iteration end.
DE=0.5*r*log(r)/dr/DEfactor.

(I have separated DEfacor and dr just for convenience)
Haven't yet tried the other case.

[visual.bermarte]

compound fractals: tests
super.fatty


land.of.confusion

[visual.bermarte]

K.tests

[matsoljare]

Can we have some higher resolution versions of those?