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From Random Polygon to ????

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Take a polygon with random vertices, find the mid-points of its sides, and use these to create a new polygon, replacing the original. Do this repeatedly. What happens? Inspiration: https://www.jasondavies.com/random-polygon-ellipse/
Click mouse to restart with a new set of random points. Up key on keyboard will double the number of starting points. Down key will halve the starting points.
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