Hi,
Back in the nineties I wrote a fractal generator program called Minifrac, written in Delphi which I never finished and never released. The program was unremarkable except that it had two fractal variations (Crystal 1 and Crystal 2) that I found myself, and also a nice palette generator. Below is the Pascal code for the two Crystal fractals for anyone who is interested. For the Mandelbrot version the initial values are x = 0 and y = 0, with the point on the screen assigned to (a, b). Whereas the Julia sets for these fractals have parameters (a, b) and the point on the screen assigned to (x, y). For iterations that do not escape, I used the minimum of the norm squared (e.g. x*x + y*y) to colour the interior points. Attached is a nice zoom of one of these fractals, sorry I forget which one it is, although I remember that it is a Mandelbrot.
{ CRYSTAL 1 - Barnsley fish variant }
c := 0;
d := 0;
nz2_min := LARGE;
nz2 := 0;
while (nz2 < nz2_max) and (iters < term_iters) do begin
e := x;
f := y;
if x >= 0 then begin
p := x*c - y*d - a;
y := y*c + x*d - b;
x := p;
end else begin
p := x*c - y*d + a;
y := y*c + x*d + b;
x := p;
end;
c := e;
d := f;
nz2 := sqr(x) + sqr(y);
if nz2 < nz2_min then nz2_min := nz2;
inc(iters);
end;
{ CRYSTAL2 - Another sort of barnsley fish variant }
c := 0;
d := 0;
nz2_min := LARGE;
nz2 := 0;
while (nz2 < nz2_max) and (iters < term_iters) do begin
e := x;
f := y;
if x >= 0 then begin
p := x - c;
y := y - d;
x := a*p - b*y + 1;
y := a*y + b*p;
end else begin
p := x + c;
y := y + d;
x := a*p - b*y - 1;
y := a*y + b*p;
end;
c := e;
d := f;
nz2 := sqr(x) + sqr(y);
if nz2 < nz2_min then nz2_min := nz2;
inc(iters);
end;
August 31, 2013, 06:56:00 PM
Variations VI
2d Art
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