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Graphs of maps, especially those of one variable such as the logistic map, are key to understanding the behavior of the map. One of the uses of graphs is to illustrate fixed points, called points. Draw a line y = x (a 45° line) on the graph of the map. If there is a point where this 45° line intersects with the graph, that point is a fixed point.
add a new (,) pair to the collection, mapping the key to its new value. Any existing mapping is overwritten. The arguments to this operation are the key and the value. Remove or delete remove a (,) pair from the collection, unmapping a given key from its value. The argument to this operation is the key.
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.
An associative array stores a set of (key, value) pairs and allows insertion, deletion, and lookup (search), with the constraint of unique keys. In the hash table implementation of associative arrays, an array A {\displaystyle A} of length m {\displaystyle m} is partially filled with n {\displaystyle n} elements, where m ≥ n {\displaystyle m ...
Map functions can be and often are defined in terms of a fold such as foldr, which means one can do a map-fold fusion: foldr f z . map g is equivalent to foldr (f . g) z. The implementation of map above on singly linked lists is not tail-recursive, so it may build up a lot of frames on the stack when called with a large list. Many languages ...
This set of intervals is the Julia set of the map – that is, it is the smallest invariant subset of the real line under this map. If μ is greater than the square root of 2, these intervals merge, and the Julia set is the whole interval from μ − μ 2 /2 to μ/2 (see bifurcation diagram).
A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes. [4] The contour interval of a contour map is the difference in elevation between successive contour lines. [5] The gradient of the function is always perpendicular to the contour ...
An associative container uses an associative array, map, or dictionary, composed of key-value pairs, such that each key appears at most once in the container. The key is used to find the value, the object, if it is stored in the container. Associative containers are used in programming languages as class templates.