This new coloring method (calculating 1 more iteration past max iteration, then using the magnitude of all values to assign color) really makes some interesting patterns, especially for good old z^2! Using an additional iteration in other fractal types will probably be equally as awesome. Anyways...
Code for calculating fractal (which is also used to calculate the color) is posted after images (although it is a totally standard 3d bulb, although it is the faster complex triplex variety (instead of trig)).
seahorse valley:
elephant valley
1 more iteration:
17 iteration deep zoom into above 8 or 9 iteration image:
zoom on top part:
side view straight on:
side view top down:
Anyways, here is the code (from another thread). It's simply the Mandelbulb formula I prefer due to its simplicity, the fact that it's faster than the trig versions, and the it is an obvious extension of complex numbers.
r1=sqrt(sqr(sy)+sqr(sz));
r3=r1^(-n); // take it to the -n so you don't have to divide by r3, as it can equal zero for the first iteration
victor=complex(sx,r1);
bravo=complex(sy,sz);
victor=victor^n; // for higher powers, set up a script if n= integer powers for each n so
bravo=bravo^n; // for n=4 bravo^4 = sqr(sqr(bravo)) || for n=6 bravo^6 = sqr(bravo)*sqr(sqr(bravo))
nx=real(victor);
ny=imag(victor)*real(bravo)*r3; // since r3=r1^-n you don't have to divide here.. good if r3=0
nz=imag(victor)*imag(bravo)*r3;
if (juliaMode) {
sx=nx+cr;
sy=ny+ci;
sz=nz+cj;
} else {
sx=nx+(pixelr);
sy=ny+(pixeli); // take the abs(pixeli) for a more uniform fractal, although the distortion of the even n
sz=nz+(pixelj); // z^2,4,6.... is to be expected considering the asymmetry of the 2d set for even n
}
z=quaternion(sx,sy,sz,0); //this feeds information to ChaosPro's orbital color scheme
// it sends the x, y, and z values to the coloring calculation which simply repeats the above
// calculation one (or more) time
bail=abs(sx)+abs(sy)+abs(sz);
March 30, 2010, 02:45:18 PM
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