Minimum complexity of a chaotic system

Bifurcation diagram of a logistic map, displaying chaotic behaviour past a threshold
Simple systems can also produce chaos without relying on
differential equations. An example is the
logistic map, which is a difference equation (
recurrence relation) that describes population growth over time. Another example is the
Ricker model of population dynamics.
Even the evolution of simple discrete systems, such as
cellular automata, can heavily depend on initial conditions.
Stephen Wolfram has investigated a cellular automaton with this property, termed by him
rule 30.
A minimal model for conservative
(reversible) chaotic behavior is provided by
Arnold's cat map.
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