Alan Turing theoretical biology |

## Turing pattern

During morphogenesis,
mathematical rules describe
the generation of stripes, spots,
spirals, hexagons,
scales, and hairs.
*instability can be triggered by random disturbances*
Morphogens diffuse
through cells, assuming
biological functions,
and forming waves
of reactions.
*and may result in patterns in nature*

## Reaction-diffusion systems

How morphogenesis arises from homogeneity How combustion spreads across available fuels How blood and lymphatic vessels form in embryos How coats and colorations develop in animals How action potentials travel through nerves How biological populations spread How ecosystems are invaded by non-native species How tumors spread and wounds heal

## Tractable patterns

When initial conditions are not homogeneous, or when multiple morphogenes operate in the same space and time simplifying assumptions make theoretical analysis tractable but our analysis is strengthened by the consideration that during the growth of an organism spatial patterns arise spontaneously.

## Living patterns

The mind sees patterns in random noise. It’s what we do. An orderly routine takes less energy. Why live in chaos? Water, when freezing, releases heat, giving snowflakes.

Alan Turing presented differential equations to describe the ideal behaviors of systems with simplified geometries. How does pattern arise from homogeneity? Key factors are time and randomness.

See also in

The book of science:Population pressure—Thomas Robert MalthusReadings in wikipedia: