2000x2000 Gibney Fractal Attempt

gistfile1.matlab

## Author:  dmboyd -  Public Domain
## directly derived from descriptions given by http://www.gibney.de/does_anybody_know_this_fractal

xdimension=1000;
ydimension=xdimension;
scale=xdimension;
xoffset=xdimension/2;
yoffset=xoffset;
sensitivity=0.3;
gscale=50;
c=ones(xdimension,ydimension);
xvector=[];
yvector=[];
gdivc=[];
imagex=[];

#load up two vectors to 1..n
[x,y]=meshgrid(0:xdimension,0:ydimension);
x=x/scale;
y=y/scale;
xvector=x(:);
yvector=y(:);
c=complex(xvector,yvector);


g=complex(0:gscale,0:gscale);

#create complex numbers from the two vectors
n=length(c);
c(1)=0.01; #cant divide by zero;

#vectorised loop begin

cmul=1./c;
gdivc=cmul*g;

imagex=((((mod(real(gdivc),1)).*(mod(imag(gdivc),1)))-1).**2);


#end vectorised loop

#shape the vector to 2d

fractal=reshape(sum(imagex'),xdimension+1,ydimension+1);
# convert quadrants back into one big image
fractal=[rot90(fractal,2),flipud(fractal);fliplr(fractal),fractal];
image(fractal);

Could potentially change the code to restrict c to complex numbers a+bi where a>=b as it is symetric accross the diagonal axis. Would mean that you could fit twice the amount of complex numbers in memory.