For some good hands-on intuition of the Sierpinski Triangle check out this tutorial on using some open-source (research) software to build a tile-set which will self-assemble the Sierpinski triangle: http://self-assembly.net/wiki/index.php?title=Sierpinski_tri...

Last summer I received an undergraduate research grant to work on ISU TAS (the above linked software). So I'd love to see more people using it outside of the research community!

For more information on algorithmic self-assembly in general http://self-assembly.net