How Life Makes Patterns — From Rules, Matter, and Environment to Form
Begin where a rabbit recurrence is often mistaken for a universal golden spiral, then meet four distinct kinds of model: angular placement, interacting and diffusing substances, local neighbor rules, and recursive branching grammars. Travel from sequences and phyllotaxis in Pisa and Paris through growth and matter in Leipzig and Dundee; reaction–diffusion in Manchester; local rules in Utrecht and Cambridge; fractals and growth grammars in Yorktown Heights and Calgary; and physical, numerical, organismal, and molecular tests in Paris, Los Alamos, Kyoto, Bern, Freiburg, and Barcelona. This is not a story in which nature obeys one formula. Rules, materials, boundaries, growth, and environment jointly select form.
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1202
Pisa
Counting Rabbit Reproduction with a Recurrence — Fibonacci’s Liber Abaci
Leonardo of Pisa included an idealized rabbit-breeding problem in the 1202 Liber Abaci. A sequence in which the two preceding terms produce the next compressed growth into a rule where earlier states generate a later state. He did not study plant phyllotaxis or the golden angle, however, and real rabbit populations do not ignore seasons, death, and resources as the problem does.
Replay on the map from scene 1Scene index