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 MapExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Tent Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TentMap.html