Chaos Lab

Discrete map · 1D · dim 1

Tent map

Piecewise-linear cousin of the logistic map with the same topological structure but no quadratic curvature. The full tent (μ = 2) is conjugate to the logistic at r = 4 and to the Bernoulli shift on binary strings.

Bifurcation diagram of the tent map across μ ∈ [1, 2]. Above μ = 1 the orbit is chaotic everywhere.

Equations

x_{n+1} = μ · min(x_n, 1 − x_n)

At a glance

Parametersμ ∈ (1, 2]
Chaotic forμ > 1
Lyapunov exponentλ = ln μ
HistoryStudied extensively from the 1970s onward.

Try it

Open the interactive playground at /tools/cobweb.

See also

Test your knowledge

8-question flashcard quiz on tent map

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