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mathematics, in pictures
Concept

Universality

The property of a system able to simulate any computation whatever, and therefore as powerful as any computer.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

perioddoubles at r =gap ratio22.998304—43.4488464.743183.5438344.6385163.5643124.6464323.568719—each doubling is found by bisection, and each ratio is measured from the two gaps beside itthe last one is 4.646; Feigenbaum's constant is 4.6692, and it is the same for any map with a smooth hump

A constant that does not care which map

The gaps between successive period doublings shrink by a factor. Measure that factor for the logistic map and you get 4.669. Measure it for a completely different map and you get 4.669, and nobody expected that.

dynamics · period doubling rule 110: the eight neighbourhoods, read as the bits of 11060 rows from a random row

The rule that computes

One of the 256 elementary rules can run any program. Not simulate one, not approximate one — a machine that can compute anything computable, built from a lookup table with eight rows and nothing else.

dynamics · cellular automata

Named alongside it

The objects these essays reach for when they reach for this one.

BifurcationCellular automatonComputationConvergenceFeigenbaum constantGliderHalting problemIterationLocalityLogistic mapPeriod doublingRenormalisation

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