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Tent Map


TentMapIterations

A piecewise linear, one-dimensional map on the interval [0,1] exhibiting chaotic dynamics and given by

 x_(n+1)=mu(1-2|x_n-1/2|).
(1)

The first few iterations of (1) give

x_1=-mu(2|x_0-1/2|-1)
(2)
x_2=-mu(2|mu(1-2|x_0-1/2|)-1/2|-1)
(3)
x_3=-mu(2|mu(2-|mu(1-2|x_0-1/2|)-1/2|)-1/2|-1),
(4)

where x_0 is the initial value, plotted above through five iterations (with increasing iteration number indicated by colors; 1 is red, 2 is yellow, 3 is green, 4 is blue, and 5 is violet) for various values of mu.

The natural invariant of the tent map is rho=1.


See also

2x mod 1 Map, Logistic Map

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Cite this as:

Weisstein, Eric W. "Tent Map." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TentMap.html

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