Absolutely computer graphics. It’s not about generating beautiful abstract images, but realistic and not repeating landscapes. Read about Fractal Landscapes. Perlin Noise, which might be considered a simple fractal is used in computer graphics everywhere. The author joked around that if he would patent it, he’d be a millionare now. Fractals are also used in … Read more
This is the smooth color algorithm: Lets say you start with the complex number z0 and iterate n times until it escapes. Let the end point be zn. A smooth value would be nsmooth := n + 1 – Math.log(Math.log(zn.abs()))/Math.log(2) This only works for mandelbrot, if you want to compute a smooth function for julia … Read more
There was a perl solution already some years ago posted in perlmonks, it reads: #!/usr/bin/perl $r=25; $c=80; $xr=6;$yr=3;$xc=-0.5;$dw=$z=-4/ 100;local$”;while($q=$dr=rand() /7){$w+=$dw;$_=join$/,map{$Y=$_* $yr/$r; join”” ,map{$ x=$_*$ xr/$c;($ x,$y)= ($xc+$x *cos($ w)-$Y* sin$w,$yc+ $x*sin ($w)+$Y*cos $w);$ e=-1;$ a=$b=0 ;($a,$b) =($u-$v+$x,2*$a* $b+$y) while( $ u=$a*$ a)+($v=$b*$b)<4.5 &&++$e <15;if (($e>$ q&&$e< 15)||($e==$q and rand() <$dr)) {$q=$e;($d0,$d1) =($x,$ y); } chr(+( … Read more
I’m not clear why you can’t use the product of the bounds and do for x in range(y exp n) where n is the # of loops…. You say y exp n will be huge, but I’m sure python can handle it. However, that being said, what about some sort of recursive algorithm? def loop_rec(y, … Read more
Programming the Mandelbrot is easy. My quick-n-dirty code is below (not guaranteed to be bug-free, but a good outline). Here’s the outline: The Mandelbrot-set lies in the Complex-grid completely within a circle with radius 2. So, start by scanning every point in that rectangular area. Each point represents a Complex number (x + yi). Iterate … Read more