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.
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.
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