The tent map is a piecewise linear, one-dimensional map on the interval ![[0,1]](/images/equations/TentMap/Inline1.svg)
exhibiting chaotic dynamics and given by
 |
(1)
|
The first few iterations of (1) give
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
where 
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
.
The natural invariant of the tent map is 
.
An asymmetric generalization with slopes 
and 
connects the tent map with Pisot
numbers. When 
and 
are both Pisot
numbers and algebraic units, their contracting algebraic
conjugates define a tent tile (Scheicher et al.
2026).
