Hi, so I might have found an alternative way to draw the Sierpinski triangle without using the chaos game.

As the chaos game is actually just an algorithm used to plot an IFS a different algorithm could also be used. Quote from wiki:

"An alternative algorithm is to generate each possible sequence of functions up to a given maximum length, and then to plot the results of applying each of these sequences of functions to an initial point or shape."

I know this could be done with recursive programming in an ordinary programming language. But wouldn't it also be possible to make a program on the TI that would do something similar?

I have a couple of ideas but im having a hard time structuring them. Since the functions in the IFS are all linear (simply distance function divided by two every time) it should be possible to calculate a point at a given level without doing all the iterations.

Any ideas are welcome and please ask if theres something cryptic in my text :p