nmmmnu
Forums Freshman
Posts: 15


« on: June 14, 2015, 05:48:32 PM » 

Hi I need help / opinions in fractal formula summations.
Are following names correct? Is there anything "famous" I am missing (beside Mandelbar / Tricorn / Conjugated)
Here is the list "collected" for the moment:
Mandelbrot Its formula is Z = Z^2 + C here is simple code:
static color Z_mandelbrot(float x, float y, color it){ float zx = 0; float zy = 0;
color i; for(i = 0; i < it; ++i){ float zx2 = zx * zx; float zy2 = zy * zy;
if (zx2 + zy2 > ESCAPE2) return i;
// z = z*z + c
zy = 2 * zx * zy + y; zx = zx2  zy2 + x; }
return i; }
Burning Ship
same as Mandelbrot, but get ABS of zx and zy:
static color Z_burningship(float x, float y, color it){ //... for(i = 0; i < it; ++i){ zx = ABS(zx); zy = ABS(zy); //...
Perpendicular Burning Ship
same as Mandelbrot, but get ABS only on zy (imaginary)
static color Z_perpendicularburningship(float x, float y, color it){ //... for(i = 0; i < it; ++i){ zy = ABS(zy); //...
Perpendicular Mandelbrot
same as Mandelbrot, but get ABS only on zx (real) and we do it with negative sign
static color Z_perpendicularburningship(float x, float y, color it){ //... for(i = 0; i < it; ++i){ zx =  ABS(zx); //...
Buffalo
Its formula is Z = Z^2  Z + C
static color Z_buffalo_original(float x, float y, color it){ float zx = 0; float zy = 0;
color i; for(i = 0; i < it; ++i){ zx = ABS(zx); zy = ABS(zy);
float zx2 = zx * zx; float zy2 = zy * zy;
if (zx2 + zy2 > ESCAPE2) return i;
// z = z*z  z + c
zy = 2 * zx * zy  zy + y; zx = zx2  zy2  zx + x; }
return i; }
Question  how is called same fractal without ABS() ? It looks interesting enough to have name?
Celtic
For these I do not know the complex number formula. It looks like Mandelbrot formula, but have ABS "inside".
static color Z_celtic(float x, float y, color it){ float zx = 0; float zy = 0;
color i; for(i = 0; i < it; ++i){ float zx2 = zx * zx; float zy2 = zy * zy;
if (zx2 + zy2 > ESCAPE2) return i;
// z = z*z + c
zy =  2 * zx * zy + y; zx = ABS(zx2  zy2) + x; }
return i; }
Perpendicular Celtic
same formula as Celtic, but ABS(zx), with negative sign.
static color Z_perpendicularceltic(float x, float y, color it){ //... for(i = 0; i < it; ++i){ zx =  ABS(zx); //...
and we have another Celtic variation called Perpendicular Buffalo same formula as Celtic, but ABS(zy).
static color Z_perpendicularbuffalo(float x, float y, color it){ //... for(i = 0; i < it; ++i){ zy = ABS(zy); //...
Question  Is this correct name? Its formula have noting to do with Buffalo?
I will edit the question and add pictures tomorrow
