Fractal surface in the context of "Self-similarity"

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⭐ Core Definition: Fractal surface

A fractal landscape or fractal surface is generated using a stochastic algorithm designed to produce fractal behavior that mimics the appearance of natural terrain. In other words, the surface resulting from the procedure is not a deterministic, but rather a random surface that exhibits fractal behavior.

Many natural phenomena exhibit some form of statistical self-similarity that can be modeled by fractal surfaces. Moreover, variations in surface texture provide important visual cues to the orientation and slopes of surfaces, and the use of almost self-similar fractal patterns can help create natural looking visual effects.The modeling of the Earth's rough surfaces via fractional Brownian motion was first proposed by Benoit Mandelbrot.

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Fractal surface in the context of Surface

A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object. It is the portion or region of the object that can first be observed and with which other objects first interact.

The concept of surface has been abstracted and formalized in mathematics, specifically in geometry. Depending on the properties on which the emphasis is given, there are several inequivalent such formalizations that are all called surface, sometimes with a qualifier such as algebraic surface, smooth surface or fractal surface.

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LINKED FROM (PARENTS)
← Surface
LINKS TO (CHILDREN)
Triangle → Fractal → Stochastic → Terrain → Surface → Self-similarity → Fractal dimension → Surface texture → Fractional Brownian motion → Benoit Mandelbrot →