In mathematics, the tent map with parameter μ is the real-valued function fμ defined by
the name being due to the tent-like shape of the graph of fμ. For the values of the parameter μ within 0 and 2, fμ maps the unit interval into itself, thus defining a discrete-time dynamical system on it (equivalently, a recurrence relation). In particular, iterating a point x0 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 fμ 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 x0 of the interval assumes new subsequent positions as described above, generating a sequence xn 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
Famous quotes containing the words tent and/or map:
“At last I feel the equal of my parents. Knowing you are going to have a child is like extending yourself in the world, setting up a tent and saying “Here I am, I am important.” Now that I’m going to have a child it’s like the balance is even. My hand is as rich as theirs, maybe for the first time. I am no longer just a child.”
—Anonymous Father. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 5 (1978)
“In my writing I am acting as a map maker, an explorer of psychic areas ... a cosmonaut of inner space, and I see no point in exploring areas that have already been thoroughly surveyed.”
—William Burroughs (b. 1914)