Mathematical Biology

Mathematical biology! After having read about mathematical biology in a Wikipedia article, I couldn't sleep last night. I kept thinking about how you might model plant growth or how plant photosynthesis could be used to generate energy.

I was googling for a free text book on the subject to sate my curiosity when I found this link: http://spot.colorado.edu/~dubin/bookmarks/b/1240.html

There was a textbook there from the Hong Kong University of Science and Technology. The author goes through many mathematical derivations, but he takes the time to apply it to living things.

He wrote about Phi, the golden ratio and how it could be seen in a sunflower. phi is the ratio between consecutive Fibonacci numbers as n goes to infinity.

Grow cell, turn, grow cell turn, etc. But how much of a rotation should you perform for each step? The pattern is made most efficient with a certain amount of turning. One of the greatest beauties of nature is that evolution solves mathematical problems on its own over time. The sunflower contains the best solution to the problem. The link has a little app that lets you try different rotation values and it builds a sunflower based on them. It turns out that Phi (1.61803...) is the best solution.

The golden ratio exists all over nature because the optimal growth solution has evolved over time. That's pretty amazing.


This all makes me think that the Fibonacci sequence might lead to some interesting Minecraft designs...