The Sierpinski triangle page to end most Sierpinski triangle pages

>>pr_fan+(OP)
For those who happen to have Mathematica, try this to get a smooth, high-resolution interactive fractal explorer (make sure you have a C compiler installed):

  JuliaFP = Compile[
    {{const,_Complex}, {init,_Complex}}, 
    Module[{val=init,n=0},
      While[Abs[val] < 5 && n < 25, val = val^2 + const; n++];
      {Mod[Arg[val]/(2*3.14159), 1], 1 - Abs[val]/5, 1 - Abs[val]/100}
    ],
    CompilationTarget -> "C", 
    RuntimeAttributes -> Listable, 
    RuntimeOptions -> "Speed"
  ];
  
  {fine, coarse} = Table[Complex[j,i], 
    {dx, {0.008, 0.002}}, {i,-1.5,1.5,dx}, {j,-1.5,1.5,dx}
  ];

  pt = {0.0,0.0};
  Graphics[{
    Raster[
      JuliaFP[Complex @@ pt/2, If[ControlActive[], fine, coarse]], 
      {{-2.0,-2.0}, {2.0,2.0}}, 
      ColorFunction-> Hue
    ],
    Locator[Dynamic[pt]]},
    ImageSize -> 800
  ] // Dynamic

P.S. Original post is awesome. I love the cow!

>>talies+3z
Thank you for this. I tried looking around for the "best fit" for a Mathematica work-alike that is Free software, but came up somewhat short. The closest I could find was Gnu mathics, but it doesn't appear to be very complete (ie: many Mathematica examples won't work). Other alternatives are SAGE and of course Julia -- and I guess SAGE would be the best for "playing" or "live coding"?

Anyone have any insights?

I'll also note that Mathematica looks quite awesome indeed.

>>e12e+pn1
One of the Julia creators did a fractal demo [1] recently, including the Sierpinski triangle. Julia is now quite nice for interactive work via the IJulia notebook (IPython kernel for Julia). As a bonus, it does not require a C compiler to get good performance.

[1] http://nbviewer.ipython.org/url/beowulf.csail.mit.edu/18.337...

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