Pattern formation in biology

The greatest computer scientist of

all time, Alan Turing made a crucial

contribution to pattern formation as well

Finally: what Turing found was very counterintuitive: the addition of diffusion makes a system unstable! Since diffusion blurs a pattern, you'd think it'd dampen out, not accentuate fluctuations!

Here's a simulation

you'll be able to run

and play with to see how patterns form in Turing's model:

https://deutsch.physics.ucsc.edu/phys180/patterns.html

Diffusion and reactions

of different chemical species

can lead to patterns, but is this

related to biological patterns?

Turing came up with a model and made predictions that were testable.

http://www.sjsu.edu/faculty/watkins/murray.htm

The most important prediction is that you get stripes on tails and spots on bodies but never the converse.

He wondered, how it was that cows

got their spots?

Here is an example of what

happens when you mix up

the right bunch of chemicals:

He thought of a model

involving two or more

"morphigens". They'd diffuse

react with each other, diffuse some more, react some more, etc.

But can just a mix of chemicals show patterns?

A tree, a leaf, fur, feathers, wings, fins, feet.

How much of pattern formation is billions of years of biological software deciding how the the organism should look, and how much is due to simple physical principles?

Patterns on the wings of a butterfly, the spots on a fish, or the coat on zebra.

Pattern Formation in Biology

What creates the structures that we see? There are many different kinds of structures seen across nature.

An important feature of fractal is "scale invariance". You can see that illustrated here:

http://en.wikipedia.org/wiki/Scale_invariance

The process

illustrated there is actually just 1d diffusion!

There are other

mechanisms that are also

important and physics/math based. One is self similar structures that are common in nature.

Development

Fractals occur in a large number

of mathematical and physical

contexts:

http://en.wikipedia.org/wiki/Fractal

In the fruit fly, the

genetic mechanisms

have been elucidated in

detail

And of course, occur in plants, and

also in physiology: https://fractalfoundation.org/OFC/OFC-1-2.html

There is the development of structure in an embryo. This has been studied extensively in the fruit fly.

Related to fractals, are the

growth of dendrites exhibited

by snowflakes

A simple physical model considering

diffusion, surface tension, and the

production of latent heat explains

a lot of what is seen. You'll explore this

also in the homework.

This is an example of a "fractal".

It starts out with multiple nuclei that divide in a highly orchestrated way

This process ends up with

a beautiful maggot being

formed: