In mathematics, the **tent map** with parameter μ is the real-valued function f_{μ} defined by

the name being due to the tent-like shape of the graph of f_{μ}. For the values of the parameter μ within 0 and 2, f_{μ} maps the unit interval into itself, thus defining a discrete-time dynamical system on it (equivalently, a recurrence relation). In particular, iterating a point x_{0} in gives rise to a sequence :

where μ is a positive real constant. Choosing for instance the parameter μ=2, the effect of the function f_{μ} may be viewed as the result of the operation of folding the unit interval in two, then stretching the resulting interval to get again the interval . Iterating the procedure, any point x_{0} of the interval assumes new subsequent positions as described above, generating a sequence x_{n} in .

The case of the tent map is a non-linear transformation of both the bit shift map and the *r*=4 case of the logistic map.

Read more about Tent Map: Behaviour, Magnifying The Orbit Diagram, Asymmetric Tent Map

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### Famous quotes containing the words map and/or tent:

“A *map* of the world that does not include Utopia is not worth even glancing at, for it leaves out the one country at which Humanity is always landing.”

—Oscar Wilde (1854–1900)

“His genius can cover all the land with gorgeous palaces, but the reader does not abide in them, but pitches his *tent* rather in the desert and on the mountain-peak.”

—Henry David Thoreau (1817–1862)