Koch Curve    Students use hexagonal graph paper to create a Koch Curve fractal, by repeating a simple substitution process. They fill out a table to discover the pattern relating the number of segments to the total length of the curve. Finally, connections are drawn between this geometric fractal and naturally occurring fractal patterns such as snowflakes and coastlines.

Koch Curve Students use hexagonal graph paper to create a Koch Curve fractal, by…

The Koch snowflake. If you do this forever, you have a simple example of a well defined structure with a finite (and calculable) area, but an infinite perimeter.

The Koch snowflake. If you do this forever, you have a simple example of a well defined structure with a finite (and calculable) area, but an infinite perimeter.

Fractals aren’t just pretty: they’re related to the even-cooler Pascal’s triangle. This triangle is an amazingly simple way to solve about a billion different types of equations, do complex math in your head, and, of course, make some really pretty patterns.

Start with any triangle in a plane (any closed, bounded region in the plane will actually work). The canonical Sierpinski triangle uses an equilateral triangle with a base parallel to the horizontal axis (first image).

Very simple one, was only rotated twice

Fractals- Patterns that go on forever and ever, and get progressively smaller

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