Search results
Results from the WOW.Com Content Network
Template documentation Parameters This template's initial visibility currently defaults to autocollapse , meaning that if there is another collapsible item on the page (a navbox, sidebar , or table with the collapsible attribute ), it is hidden apart from its title bar; if not, it is fully visible.
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.
The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical, while figures and images made it possible to ...
More precisely, this example works to explain a kind of math called chaos theory, which looks at how small changes made to a system’s initial conditions—like the extra gust of wind from a ...
In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Stephen Smale while studying the behavior of the orbits of the van der Pol oscillator. The action of the map is defined geometrically by ...
Orbit diagram for the Hénon map with b=0.3.Higher density (darker) indicates increased probability of the variable x acquiring that value for the given value of a.Notice the satellite regions of chaos and periodicity around a=1.075-- these can arise depending upon initial conditions for x and y.
To see how this number arises, consider the real one-parameter map =.Here a is the bifurcation parameter, x is the variable. The values of a for which the period doubles (e.g. the largest value for a with no period-2 orbit, or the largest a with no period-4 orbit), are a 1, a 2 etc.
If the left, center, and right cells are denoted (p,q,r) then the corresponding formula for the next state of the center cell can be expressed as p xor (q or r). It is called Rule 30 because in binary, 00011110 2 = 30. The following diagram shows the pattern created, with cells colored based on the previous state of their neighborhood.