Common Techniques For Generating Fractals
Images of fractals can be created by fractal generating programs.

 Strange attractors – use iterations of a map or solutions of a system of initialvalue differential equations that exhibit chaos (e.g., see multifractal image)

 Lsystems  use string rewriting; may resemble branching patterns, such as in plants, biological cells (e.g., neurons and immune system cells), blood vessels, pulmonary structure, etc. (e.g., see Figure 5) or turtle graphics patterns such as spacefilling curves and tilings

 Escapetime fractals – use a formula or recurrence relation at each point in a space (such as the complex plane); usually quasiselfsimilar; also known as "orbit" fractals; e.g., the Mandelbrot set, Julia set, Burning Ship fractal, Nova fractal and Lyapunov fractal. The 2d vector fields that are generated by one or two iterations of escapetime formulae also give rise to a fractal form when points (or pixel data) are passed through this field repeatedly.

 Random fractals – use stochastic rules; e.g., Lévy flight, percolation clusters, self avoiding walks, fractal landscapes, trajectories of Brownian motion and the Brownian tree (i.e., dendritic fractals generated by modeling diffusionlimited aggregation or reactionlimited aggregation clusters).

 Finite subdivision rules use a recursive topological algorithm for refining tilings and they are similar to the process of cell division. The iterative processes used in creating the Cantor set and the Sierpinski carpet are examples of finite subdivision rules, as is barycentric subdivision.
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