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Vi Hart made an excellent series of videos related to plants and Fibonacci numbers. Here is the first one: https://www.youtube.com/watch?v=ahXIMUkSXX0. Links to the other ones can be found in the description.

Another excellent source on this topic is a book I cited in the code comments called "The Algorithmic Beauty of Plants" by Prusinkiewicz and Lindenmayer, available online here: http://algorithmicbotany.org/papers/#abop

I absolutely love Hart's presentation style in that video. It's so refreshing to see maths presented at a decent pace but still be easy to follow. And the quirkiness of the delivery only serves to make those videos more watchable.

Thank you for the recommendation. I'll definitely be subscribing to her channel :)

This kids, is what happens when you recursively ask the question, "Why?" and and answer it seriously. Made my day.

I made another toy like this: http://wry.me/hacking/powersp.html

https://en.wikipedia.org/wiki/Phyllotaxis#Phyllotaxis_and_ma... for links to more of the math.

Looks like this is what Nest Protect uses for its mesh design: https://nest.com/smoke-co-alarm/life-with-nest-protect/

Fascinating stuff, thanks for sharing!

z_{n+1} = (1 - 1/q^2)z_n where z_n are the continued fraction approximations of the square of the Golden ratio phi^-2

Turing's sunflower