In wolframs "A new Kind of Science" there is a long discussion of not only the fact that leaf arrangement tends to use the golden ratio and that it is optimal for the plant. But also he describes a model (using cellular automata) that explains why such a pattern might emerge naturally. Unfortunately i don't remember all the details but it was a compelling use case for why automata might be a good model for natural phenomenon.
The Secret of the Fibonacci Sequence in Trees
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Re: The Secret of the Fibonacci Sequence in Trees
#22Just say fractals. We already knew they appear everywhere in nature.
Why stop there. Just say stuff. We already knew stuff appears everywhere in nature.
Cause exact words have exact meanings. Fib sequence != fractals
Re: The Secret of the Fibonacci Sequence in Trees
#23Trees also optimize for shading their competitors and avoiding being shaded, not just for efficiently gathering raw light. Understanding the shading factor would require extensive field work and Monte Carlo analysis.
Re: The Secret of the Fibonacci Sequence in Trees
#24> Scientists and naturalists have discovered the Fibonacci sequence appearing in many forms in nature, such as the shape of nautilus shells, the seeds of sunflowers, falcon flight patterns and galaxies flying through space. What's more mysterious is that the "divine" number equals your height divided by the height of your torso, and even weirder, the ratio of female bees to male bees in a typical hive! (Livio) Except…
(repeating from other thread): http://www.wolframscience.com/nksonline/page-410#previous has something to say about how the golden ratio can pop out without being encoded directly in plant phylotaxis.
Re: The Secret of the Fibonacci Sequence in Trees
#25> Scientists and naturalists have discovered the Fibonacci sequence appearing in many forms in nature, such as the shape of nautilus shells, the seeds of sunflowers, falcon flight patterns and galaxies flying through space. What's more mysterious is that the "divine" number equals your height divided by the height of your torso, and even weirder, the ratio of female bees to male bees in a typical hive! (Livio) Except…
(repeating from other thread): http://www.wolframscience.com/nksonline/page-410#previous has something to say about how the golden ratio can pop out without being encoded directly in plant phylotaxis.
Looks interesting--will read later, thanks!
Re: The Secret of the Fibonacci Sequence in Trees
#26Here's a little something that most people don't know, that I picked up from my architecturally interested father long ago: The French architect Le Corbusier ( http://en.wikipedia.org/wiki/Le_Corbusier ) made use of Fibonacci sequences to create his famous "Modulor" ( http://www.apprendre-en-ligne.net/blog/images/architecture/m... - "A harmonic measure to the human scale, universally applicable to architecture and me…
If the height of your desk, chairs, tables, kitchen sink and cupboards are determined by anything other than the size of resp. your (or at least, 'an average') torso, calves, torso, legs and total body length, you live in a weird house. If you look long enough, you can find 'patterns' everywhere.
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Re: The Secret of the Fibonacci Sequence in Trees
#27This is a question that fascinated Alan Turing, who wrote a classic paper called "The Chemical Basis of Morphogenesis" and other unfinished papers about the subject (some published in a book called "Morphogenesis"). He used lots of heavy math that came so naturally to him, to model plant growth as a reaction-diffusion system running in a ring of cells (the stem of the plant). By computing the reactions by hand on paper, he studied how cells could grow into "parastichy" with spiral patterns related by Fibbonachi numbers. http://botanydictionary.org/parastichy.html
http://www.dna.caltech.edu/courses/cs191/paperscs191/turing....
Re: The Secret of the Fibonacci Sequence in Trees
#28In wolframs "A new Kind of Science" there is a long discussion of not only the fact that leaf arrangement tends to use the golden ratio and that it is optimal for the plant. But also he describes a model (using cellular automata) that explains why such a pattern might emerge naturally. Unfortunately i don't remember all the details but it was a compelling use case for why automata might be a good model for natural ph…
That was just Stephen Wolfram channeling Alan Turing but not giving him credit.
Re: The Secret of the Fibonacci Sequence in Trees
#29I wish Aidan had been allowed to write this in his own words, rather than his parent's / someone else's words. On the other hand, whoever's taking care of him behind the scenes has done an incredible job. I'd even say Aidan's "set for life"; that might seem over the top, but consider... this link will forever be associated with his name. It demonstrates that even at age 13, he was a very capable real-world problem so…
Hopefully his parents will say, "Wow, you worked so hard on this." Anything except, "Look how smart you are!"
Those comments breed laziness and allow people to say, "I guess I'm just not as smart in this area."