Adam Campbell's Website
tic-tac fractal

  • This is an example of a simple substitution fractal that I had first seen in Stephen Wolfram's book "A New Kind of Science" on pages 187-188
  • The fractal begins as one large square containing only the third (blue) color from above. This large, blue square is then broken up into nine square like a tic-tac-toe board, and those nine squares are colored based on the replacement rule for the third color (the 3x3 grid to the right of the blue square). This process then repeats on each of those smaller 9 squares, and then on the resulting 81 squares, and so on. Ideally, this recursive process would be repeated infinitely, but this is obviously not practical, so here the process is repeated 5 times. Even though the depth of this recursive process is only 5, we still have to compute the color of (3*3*3*3*3)^2 = (3^5)^2 = 59,049 pixels. If we were to allow one more level of recursion, 531,441 pixel colors would be computed!
  • To change any of the three colors, simply click on one of the three colored boxes to the right of the fractal drawing space. Doing this will bring up an RGB slider that will allow you to specify each of the colors. Simply click on one of the three ^ and drag the arrow to where you want the color. The color of the fractal will update automatically.
  • In order to change the actual fractal that is drawn, click on one of the 9 boxes to the right of any one of the colors. Doing this will change the replacement rule and automatically redraw the fractal.
Additional Information:
  • Check out Wolfram's aforementioned book if you want to get more information on fractals, cellular automata, etc. and the beauty of simple, self replicating programs
  • E-mail me at if you have any questions