Fairly amazing video going into the maths of why flowers (and pine-cones, relative leaf positions etc) are so often based fibonacci numbers.
And it’s fairly amazing because I actually understood it. It’s been a loooong time since I tangled with quadratic equations, but (on the 2nd watch) this did actually make sense to me.
I always thought that with seeds and sun-flowers etc, the fibonacci sequence came first (because it (magically) gives the minimal elastic-tension between seeds), and the golden-ratio came as a result of that.
This video gives a fairly cogent explanation as to why it’s actually the golden ratio that comes first… to minimise radial “spoking”… and therefore tension between seeds, or leaves shading each other.
Which is a relief in a way, because I prefer maths to “mystery”… although as far as I am concerned it is still magic. Mathematics is magic that actually works fairly reliably.
I wonder if there’s some similar reason why adjacent finger-joints should approximate to the golden-ratio. I used to think that maybe fibonacci was built into “how DNA does maths” at one point, but maybe it is just natural selection. Billions of years of trial and error.
Anyway – here’s a reassuring video looking at The Rule of Thirds vs The Golden Ratio in photographic composition.