Mandelbrot approximation

[Tugdual]

This is an approximation which uses the triangle_p function to display the Mandelbrot set. This is much faster about 20 secs) than iterating through all pixels but still fairly slow and the resulting image is blur (a bit like over compressed jpeg). It also consumes a fair amount of memory due to usage of very large matrices. In other words, this is not very nice nor practical, just experimental...

Possible improvements:
- is it possible to somehow use the ITERATE function and achieve faster results?
- would be nice to use cursor and zoom (may be with a box?)
- implement better palette

If anybody can think of possible optimizations, please do not hesitate to share ideas.

Code:


grid, color;
func(c);

export Mandel()
begin
local cx:=-0.5, cy:=0, zoom:=80, N:=100;
local minx,miny,dx,dy;

minx:= cx-160/zoom;
miny:=cy-119/zoom;
dx:=320/N/zoom;
dy:=240/N/zoom;

// Create the grid
grid:=makemat(((I-1)*320/N,(J-1)*240/N),N+1,N+1);
color:=makemat(func((minx+I*dx,miny+J*dy)),N+1,N+1);
triangle_p(G0,grid,color);
wait(0);
end;

func(c)
begin
local idxcolor,i:=0, z:=0, max:=50;
while i<max do
   z:=z^2+c;
   if abs(z)>=2 then 
      idxcolor:=2*pi*i/max;
      return RGB(255*(1+sin(idxcolor))/2,0,255*(1+cos(idxcolor))/2); 
   end;
   i:=i+1;
end;
return RGB(0,0,0);
end;