Returning to the Sierpinski Triangle, let's call the next point (X,Y). It will be calculated by one of these equations depending on which colour is chosen: X = (x + 0) / 2    Y = (y + 0) / 2 X = (x + 2) / 2    Y = (y + 0) / 2 X = (x + 1) / 2    Y = (y + 1) / 2 or simply X = .5x + 0    Y = .5y + 0 X = .5x + 1    Y = .5y + 0 X = .5x + .5    Y = .5y + .5

What I'm trying to do is generalise the idea that produced the Sierpinski Triangle.
Retaining the simplicity but generalising as much as possible, I came up with:

• X = ax + by + e    Y = cx + dy +f

So for the Sierpinski Triangle we have:	a .5 .5 .5 b 0 0 0 c 0 0 0 d .5 .5 .5 e 0 1 .5 f 0 0 .5
Finally, we need to state that, each time, there is an equal chance of using column 1, 2 or 3. This is done by adding a probability row to the table thus:	p .33 .33 .34

Putting it all together, I came up with the following turtle project that you may enjoy trying.
You should note that the turtle is really much too slow for this intensive sort of "number crunching" but my intention is to just whet your appetite.

Further information:

• Download this project
• Fractal art by Wolter Schraa