The maths behind living forms and shapes

Posted on 5. март 2010

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[This was prepared for a flyer of SIAM, to be distributed in American schools. Hence, the peculiar format.]

Terms important in the study of organism form:
genetics, randomness, pattern formation, nonlinear dynamics, emergent phenomena

Uses and applications:
How  to make the spots on a leopard and the stripes on a zebra?
How does the egg of the frog decide which end will become the head and which – the bum? Who divides the worm in regular segments and positions the teeth of the crocodile around its jaw?

How it works:
Ever noticed the perfect form of the shells of tiny sea molluscs scattered on the beach, or the arrangement of petals in a beautiful flower? Their order and symmetry immediately remind one of geometry classes in school. Their mathematical origins have been recognized since ancient times, and have even inspired new concepts, such as the logarithmic spiral. But most forms in Nature are far from the neat lines of Maths. In fact, irregularity, uniqueness and individuality are the properties most associated with living organisms! One man’s fingerprints don’t match those of any other.

Our bodies are shaped, on one hand, by a program stored in our genes, and on the other, by a zillion random events interfering while this program is executed in the womb. Today we have made a list of all the human genes but we still know little about how they result in us having arms and legs, fingers and feathers. Or indeed – intricate fingerprints. Yet, Maths is entering an age where rules (physical and genetic), chance and chaos can be tackled together, and the results could be shapes and patterns in space: some regular, others – not visibly. The power of Nonlinear Dynamics, Emergent Phenomena, Pattern Formation, Theory of Chaos, is just beginning to be employed in close conjunction with Biology. The sorts of questions we can answer already? See „Uses and Applications“ above!

Interesting Fact:
Think for a minute, is the zebra a black animal with white stripes, or vice versa – white with black stripes? Ready with your answer? Prof. James Murrey, one of the most prominent specialists on math biology and animal patterns, conducted an informal survey among his lecture audiences. He found out that white people mostly perceive zebras as having white fur with black stripes, while black people consider them black with white stripes. Maths tells us that the latter is the correct answer!

Further:
You can read more in J D Murrey’s extensive book „Mathematical Biology“, Springer-Verlag, 3rd ed., 2002

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Posted in: Science tales