Title: More natural Mandelbulb surfaces Post by: Alef on December 18, 2011, 05:09:19 PM Mandelbulbs are marvelous things, but their surfaces still could be somewhat are unnaturaly perfect.
With another formula I found that surfaces could be manipulated with iteration equations. http://www.fractalforums.com/3d-fractal-generation/gilgamesh-head-the-3d-mandelbulb-like-fractal/msg38938/ (http://www.fractalforums.com/3d-fractal-generation/gilgamesh-head-the-3d-mandelbulb-like-fractal/msg38938/) In mandelbulb formula at the end of iteration adding z=(cabs(z)+ 0.1 )*z/cabs(z); a bitt increased mandelbulb colour density. The more interesting gets at the end of iteration adding some number. Code: z=quaternion(sx,sy,sz,0); [it was very late] Title: Re: More natural Mandelbulb surfaces Post by: Alef on December 18, 2011, 05:21:58 PM [next day]
It realy does. Certain level of natural imperfection do makes result more realistic, but at the expense of increased of changing colour;) Since mandelbulb algorithm iterates sx, sy, sz, only final z is affected. Or more likely it just affects final solutions of equation. Code: ... The depends mostly on bailout value, so single flag;) Replacing this with z=z*z+pixel; colour density is increased, but crack and wear pattern changes no more than changing bailout value. This thing should work on all triplex formulas, as all iterate sx, sy, sz instead o z. Testing on (julia) underwater terrain and (julia) coral. Even Both have a bitt of more natural feel as crack pattern unlike of adding some texture depends on fractal geometry. Decreased colour density so fractal have colours of unmodified version. Title: Re: More natural Mandelbulb surfaces Post by: Alef on December 18, 2011, 05:26:15 PM Testing on (mandel) cave. The second picture are with bailout maybe 100 or 1024, last picture are with bailout increased to 10000000000. Didn't changed colours. It don't looks more aesthetic, but it do looks more natural, like some ordinary sandstone cave.
Title: Re: More natural Mandelbulb surfaces Post by: Alef on December 25, 2011, 04:49:58 PM Well, maybe this could be implemented in colour algorithm. Colour methods use modulus of z, so colours do not depend on positive or negative values. Adding 2 before calculcating modulus diferentiates positive and negative orbit value mandelbulb sides. If z=-n; |z+n|=0, so all respective negative orbit values are marked with dots.
(http://www.ljplus.ru/img4/a/s/asdam/Number_mandelbulb_negative.jpg) I put this into exponential smoothing colour technique (maybe the best so far), added simple cabs(z) colouring (sometimes exponential smoothing just don't work), and to decrease noise added iteration counter. (http://www.ljplus.ru/img4/a/s/asdam/Nemo_numbersseeker.jpg) Code: NumberSeeker {Title: Re: More natural Mandelbulb surfaces Post by: Alef on December 25, 2011, 04:56:17 PM Nothing exeptional, but usable. Much interesting result are in 2D. Mandelbrots looks like fake buddhabrots, z^3 mandelbrots have morning dew with dipping out numbers. I think, I had seen the same fractal generated with some fake buddhabrot algorithm, but it just generated z*z mandelbrots. (http://www.ljplus.ru/img4/a/s/asdam/Number_mandelbrot_negative.jpg) This is nicer. power 3 do not lose positive and negative real value signs. (http://www.ljplus.ru/img4/a/s/asdam/Number_mandelbrot3_negative.jpg) |