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Move the cursor over the line in the top left. When you're over a corner, it will be highlighted and you can drag it with the left button or delete it with the right. If you're over the half-way point. If you're halfway between two points, a green circle will appear meaning you can click to add a new point. Hold down the button and you'll be dragging it.

Left and right click the shape in the bottom-left to change the underlying polygon.

This page creates a Koch Snowflake from a triangle. To do this, it replaces each side of the triangle with the shape in the top left of the screen, and then it replaces each side of *that* with the shape in the top left of the screen, and it does that infinite times. Although for the sake of computation, we approximate "infinite" to "five".

If we really kept going for infinite steps, we'd get a shape with finite area but infinite perimeter. It can have these properties because it is a fractal: you can keep zooming in on it and it will not change. To explore this side of fractals, visit my Mandelbrot Set demonstration.

This demonstration lets you tinker with both the starting shape and the shape each side is replaced by. See what you can make.

The default curve, at five iterations, has over three thousand sides. If you add a couple more corners to the line segment it goes up to 23,328. What I'm saying is, think about reducing the number of iterations before you start adding corners.