Embossed Fractal Flowers #1
by Bruce Nutting
Title
Embossed Fractal Flowers #1
Artist
Bruce Nutting
Medium
Painting - Digital
Description
Common techniques for generating fractals
Images of fractals can be created by fractal generating programs.
Iterated function systems – use fixed geometric replacement rules; may be stochastic or deterministic;[34] e.g., Koch snowflake, Cantor set, Haferman carpet,[35] Sierpinski carpet, Sierpinski gasket, Peano curve, Harter-Heighway dragon curve, T-Square, Menger sponge
Strange attractors – use iterations of a map or solutions of a system of initial-value differential equations that exhibit chaos (e.g., see multifractal image)
L-systems - use string rewriting; may resemble branching patterns, such as in plants, biological cells (e.g., neurons and immune system cells[18]), blood vessels, pulmonary structure,[36] etc. (e.g., see Figure 5) or turtle graphics patterns such as space-filling curves and tilings
Escape-time fractals – use a formula or recurrence relation at each point in a space (such as the complex plane); usually quasi-self-similar; 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 escape-time 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 diffusion-limited aggregation or reaction-limited aggregation clusters).[5]
A fractal generated by a finite subdivision rule for an alternating link
Finite subdivision rules use a recursive topological algorithm for refining tilings[37] and they are similar to the process of cell division.[38] The iterative processes used in creating the Cantor set and the Sierpinski carpet are examples of finite subdivision rules, as is barycentric subdivision.
Impart created with rfractals.
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February 5th, 2015
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