I have been looking at sunflower, pinecone and branching patterns and the difference to hexagonal close-packing patterns such as in honeycombs and wasp nests.
In my google research I came across a fun blog from product designer Markus Kittner talking about "generative design and learning from nature" - and "structural tessellations and morphologies".
In the case of the Fibonacci sequence that we see in some growth patterns in nature we have a very simple input operation, that starts with the number one and simply is adding the previous number to it: i.e. the Fibonacci sequence is 1, 1+0 = 1, 1+1 = 2, 1+2 = 3, 2+3 = 5, 3+5 = 8, etc.
See more about generative design here:
http://74fdc.wordpress.com/2012/07/02/generative-design-learning-from-nature/
Find out more about the structure and economy of hexagonal honeycomb packing:
http://74fdc.wordpress.com/2012/02/10/structural-tessellations-and-morphologies/
Generative design and structural tessellations - such as seen in sunflowers, pinecones, branching patterns, and wasp nests and honeycombs, are fun applied math and design topics to explore with students K-12 both in the indoor and outdoor classroom.
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