1952

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.