|Sierpinski Triangle, rendered in red Lego roof-bricks (angle view)|
The Sierpinki Triangle, rendered in Lego. The basic building-unit used here (to get proportions that look like an equilateral triangle) consists of four bricks: a 1×1×4 base strip, two 1×2×1 slanted roof pieces and a 1×1×2 top strip.
|The Sierpinski Triangle model, in the "Lego Digital Designer" ("LDD") program|
This model has 64 of these units per side. In theory, it should take 4*3^6 = 2,916 bricks to build it, but in practice, if you were building a real one and having it standing vertical, you'd want to replace a lot of the little adjacent base strips with longer strips for reinforcement, and maybe also stagger them for extra strength (which is why Digital Designer's showing a reduced brick-count in the screenshot that's closer to ~2700).
A "World's Biggest Lego Sierpinski Triangle" competition might be entertaining. You can imagine kids building little sections of these at educational fairs, and then getting to watch them being assembled into bigger and bigger versions. Fun.