Love Sierpinski Triangle

I love Sierpinski Triangle - it is a simple construction, yet gives a lot of insights. For example, it can be constructed both top-down and bottom-up, showing the duality of nature. In the top-down case, you divide space into infinitesimal, while in bottom-up, you count to infinity, adding more and more bits to the triangle. Both figures are the same at infinity.

I'm not familiar with the bottom-up construction. The sierpinski triangle is the result of repeated linear transformations applied to a set (hutchinsons theorem). The cantor set is another example, as is the koch curve & the cayley representation of a free group on two generators. This all sounds freakishly advanced but is extremely easy and approachable even to non-math people.

If you're really interested I can post details.

>>2
No, it only sounds complex to idiots like you.

I'm not familiar with the bottom-up construction.

here are many ways constructing it bottom-up:
http://en.wikipedia.org/wiki/Munching_squares
http://en.wikipedia.org/wiki/Pascal_triangle#Overall_patterns_and_properties

>>3
:-) hows calculus II treating you?

>>4
http://en.wikipedia.org/wiki/Munching_anus

Did /prague/ know that it's possible to type "Satori" in Colemak without moving the fingers from their default position? Forget fucking qwerty and learn Colemak!

>>7
Why don't you just rest your fingers on SATORI on a QWERTY like everybody else does?

>>8
And then I was enlightened.

Basically, this.
S0 = {(0,0), (1/2,1), (1, 0)}
T1 (x,y) = (1/4x, 1/4y)
T2 (x,y) = (1/4x, 1/4y) + (1/2, 0)
T3 (x,y) = (1/4x, 1/4y) + (1/4, 1/2)
S 0 = S0
S n = T1 (S n - 1) U T2 (S n - 1) U T3 (S n - 1)

Where the U symbol means set union and the game means you lost it.

_{(stopping the dubsfaggot from dubsbumping)}