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Gingerbreadman Map
In dynamical systems theory, the Gingerbreadman map is a chaotic two-dimensional map. It is given by the piecewise linear transformation:. See in particular Fig. 3.3. : \begin x_ = 1 - y_n + , x_n, \\ y_ = x_n \end See also * List of chaotic maps In mathematics, a chaotic map is a map (namely, 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 functi ... References External links * Chaotic maps Exactly solvable models {{fractal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical Systems Theory
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called ''continuous dynamical systems''. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called ''discrete dynamical systems''. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations. This theory deals with the long-term qualitative behav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaos Theory
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas. Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Chaotic Maps
In mathematics, a chaotic map is a map (namely, 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. Chaotic maps often generate fractals. Although a fractal may be constructed by an iterative procedure, some fractals are studied in and of themselves, as sets rather than in terms of the map that generates them. This is often because there are several different iterative procedures to generate the same fractal. List of chaotic maps List of fractals * Cantor set * de Rham curve * Gravity set, or Mitchell-Green gravity set * Julia set - derived from complex quadratic map * Koch snowflake - special case of de Rham curve * Lyapunov fractal * Mandelbrot set - derived from complex quadratic map * Menger sponge * Newton fractal * Nova fractal - derived from Newton fractal * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaotic Maps
Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program was able to be seen on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kids, Cartoon Network and Disney XD. It was brought over to the United States from Denmark by Bryan C. Gannon and Chaotic USA Entertainment Group, and produced by Chaotic USA Entertainment Group, 4Kids Productions and Bardel Entertainment. The trading card game came out 6 September 2006 in the U.S. and Canada. Each card comes with a unique code which the owner can upload onto the Chaotic website. This allows the owner to trade and play online using their own card collection. The game was well known to be the only game with a TV show, an online game, and a TCG that were all integrated. However, the online game is currently closed. History Chaotic started out as a trading card game known as "Grolls and Gorks" and an idea for a cartoon se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
