Real landscapes however, have varying behavior at different scales. Technically speaking, any surface in three-dimensional space has a topological dimension of 2, and therefore any fractal surface in three-dimensional space has a Hausdorff dimension between 2 and 3. Whether or not natural landscapes behave in a generally fractal manner has been the subject of some research. Computer-generated fractal wooded hills using Visual Nature Studio. Computer generated fractal terrain using Perlin noise with Adobe Photoshop and Terragen. Behavior of natural landscapes A fractal landscape rendered in Terragen. Loren Carpenter refined the techniques of Mandelbrot to create an alien landscape. The first use of a fractal-generated landscape in a film was in 1982 for the movie Star Trek II: The Wrath of Khan. Shearer, the generation of natural looking surfaces and landscapes was a major turning point in art history, where the distinction between geometric, computer generated images and natural, man made art became blurred. īecause the intended result of the process is to produce a landscape, rather than a mathematical function, processes are frequently applied to such landscapes that may affect the stationarity and even the overall fractal behavior of such a surface, in the interests of producing a more convincing landscape.Īccording to R. The modeling of the Earth's rough surfaces via fractional Brownian motion was first proposed by Benoit Mandelbrot. 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. Many natural phenomena exhibit some form of statistical self-similarity that can be modeled by fractal surfaces. In other words, the surface resulting from the procedure is not a deterministic, but rather a random surface that exhibits fractal behavior. Stochastically generated naturalistic terrain Use of triangular fractals to create a mountainous terrain.Ī fractal landscape or fractal surface is generated using a stochastic algorithm designed to produce fractal behavior that mimics the appearance of natural terrain.
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