Stuff like this is so cool. The golden ratio is really neat too, it works out to the longest period between overlaps for leaves and petals, which maximizes ene

Stuff like this is so cool. The golden ratio is really neat too, it works out to the longest period between overlaps for leaves and petals, which maximizes energy per cost. An interesting aspect of that is that phi =1+1/phi, which if you expand that fraction it becomes 1+1/(1+1/(1+1/(...))), so it's actually the irrational number least approximatable by rationals. All repeating rotations are rational ratios, and so phi, being the least appriximable gives the angle with the least overlap for leaves over any number of leaves.