Fun with emergent properties.

[theweaselking]

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 and an ellipse will eventually form!

Comments

[supergee.livejournal.com]

Nifty! Thank you.

[thornae.livejournal.com]

That's a very neat bit of maths, and beautifully demonstrated.


Also, at the linked page, choose 100 vertices and check "Only show alternate frames".
It's oddly relaxing. I've spent rather more time watching random shapes resolve into ellipses than I would have thought likely.

[lafinjack.livejournal.com]

EGG