Search results
Results from the WOW.Com Content Network
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 ...
Chaotic maps and iterated functions often generate fractals. Some fractals are studied as objects themselves, as sets rather than in terms of the maps that generate them. This is often because there are several different iterative procedures that generate the same fractal. See also Universality (dynamical systems).
No fractal appears. If the chaos game is run with a square, no fractal appears and the interior of the square fills evenly with points. However, if restrictions are placed on the choice of vertices, fractals will appear in the square. For example, if the current vertex cannot be chosen in the next iteration, this fractal appears:
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 ...
Fractals are of particular relevance in the field of chaos theory because they show up in the geometric depictions of most chaotic processes (typically either as attractors or as boundaries between basins of attraction). [29]
The unfinished Alan Moore 1990 comic book series Big Numbers used Mandelbrot's work on fractal geometry and chaos theory to underpin the structure of that work. Moore at one point was going to the name the comic book series The Mandelbrot Set .
The Fractal flame is an example of an IFS with nonlinear functions. The most common algorithm to compute IFS fractals is called the " chaos game ". It consists of picking a random point in the plane, then iteratively applying one of the functions chosen at random from the function system to transform the point to get a next point.
An example of chaotic mixing In chaos theory and fluid dynamics , chaotic mixing is a process by which flow tracers develop into complex fractals under the action of a fluid flow. The flow is characterized by an exponential growth of fluid filaments.