Chaos

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5th periods:
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So some of you are thinking uh, it looks like a bunch of dots. But look more closely…there is a faint triangle in the center…squint your eyes a little.

If not, here’s an applet than ran for over an hour … this is, well, kind if cool…
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To create ST, locate midpoints of each side. Connect them. Shade the center triangle to represent we cut it out. Located midpoints of smaller triangles (3 of them), connect, shade out centers. Repeat steps.

HW:
What is a fractal?
What is Pascal’s Triangle, and how is it related to Sierpinskis?
Finally, find a pattern in our triangles we started in class and describe it.

Ex: we started with 1 triangle. When i cut out the center, I have 3 new triangles. When I cut out their centers, I have 9 new triangles. When I cut out those centers, I have 27 new triangles. The pattern is powers of 3…

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