Turing's sunflower

Vi Hart made an excellent series of videos related to plants and Fibonacci numbers. Here is the first one: <a href="https://www.youtube.com/watch?v=ahXIMUkSXX0" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=ahXIMUkSXX0</a>. Links to the other ones can be found in the description.

I made another toy like this: <a href="http://wry.me/hacking/powersp.html" rel="nofollow">http:&#x2F;&#x2F;wry.me&#x2F;hacking&#x2F;powersp.html</a><p><a href="https://en.wikipedia.org/wiki/Phyllotaxis#Phyllotaxis_and_mathematics" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Phyllotaxis#Phyllotaxis_and_ma...</a> for links to more of the math.

Looks like this is what Nest Protect uses for its mesh design: <a href="https://nest.com/smoke-co-alarm/life-with-nest-protect/" rel="nofollow">https:&#x2F;&#x2F;nest.com&#x2F;smoke-co-alarm&#x2F;life-with-nest-protect&#x2F;</a>

Fascinating stuff, thanks for sharing!

z_{n+1} = (1 - 1&#x2F;q^2)z_n where z_n are the continued fraction approximations of the square of the Golden ratio phi^-2