Fractals in 10 minutes No. 5: Sierpinski Chaos Game

A few years back, I was in some course where they also taught me some Matlab. One of the exercises was to draw the Sierpinski triangle using a method of progressing a point randomly. I was quite surprised at the time, because I thought the Sierpinski triangle was more of an analytical thing: you drew it using inverted triangles.

I wanted to check up on it, and it turns out the method has a name: Chaos Game.
To generate a Sierpinski triangle using this method, one starts with a some point inside the triangle. Then, at each step, the next point is half the distance from the current point to one of the corners selected at random. I think this method of generating the Sierpinski triangle is even easier than the analytical one.

A sierpinski triangle generated using a chaos game

I used pylab (matplotlib) to create this image.
As I usually do, I also wanted to draw it using ascii-art. However, I must confess, I am not satisfied with the result:

              %6
             6*%8
            %8  66
           %6%*6%%6
          6%'    '66
         6866'  '6%86
        %6* 86 '%8 *66
       %**%%'***%6***%%
      8'6            6*8
     6%%*8          %*'*6
    6%6'666        86# 86%
   %%*''**%6      %**''*'%6
  *%8'   '6%6    668'   '#%%
 %% '6' '#*'6%  *% %8' '6''6*
%68%#6#*#68*86*%6#%8%8'6%6*6%*

The code isn’t really good, as I didn’t put much thought into it and just hacked it up. Still, I’m putting it up, and I might improve it someday.

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