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A fractal landscape is a surface generated using a stochastic algorithm designed to produce fractal behaviour that mimics the appearance of natural terrain. In other words, the result of the procedure is not a deterministic fractal surface, but rather a random surface that exhibits fractal behaviour. Many natural phenomena exhibit some form of statistical self-similarity that can be modeled by fractal surfaces.〔''Advances in multimedia modeling: 13th International Multimedia Modeling'' by Tat-Jen Cham 2007 ISBN 3-540-69428-5 page ()〕 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.〔''Human symmetry perception and its computational analysis'' by Christopher W. Tyler 2002 ISBN 0-8058-4395-7 pages 173–177 ()〕 The modeling of the Earth's rough surfaces via fractional Brownian motion was first proposed by Benoît Mandelbrot.〔''Dynamics of Fractal Surfaces'' by Fereydoon Family and Tamas Vicsek 1991 ISBN 981-02-0720-4 page 45 ()〕 Because 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. According to R. R. 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.〔Rhonda Roland Shearer "Rethinking Images and Metaphors" in ''The languages of the brain'' by Albert M. Galaburda 2002 ISBN 0-674-00772-7 pages 351–359 ()〕 The first use of a fractal-generated landscape in a film was in 1982 for the movie ''Star Trek II: The Wrath of Khan''. Loren Carpenter refined the techniques of Mandelbrot to create an alien landscape. ==Behaviour of natural landscapes== Whether or not natural landscapes behave in a generally fractal manner has been the subject of some research. 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.〔Lewis〕 Real landscapes however, have varying behaviour at different scales. This means that an attempt to calculate the 'overall' fractal dimension of a real landscape can result in measures of negative fractal dimension, or of fractal dimension above 3. In particular, many studies of natural phenomena, even those commonly thought to exhibit fractal behaviour, do not in fact do so over more than a few orders of magnitude. For instance, Richardson's examination of the western coastline of Britain showed fractal behaviour of the coastline over only two orders of magnitude.〔Richardson〕 In general, there is no reason to suppose that the geological processes that shape terrain on large scales (for example plate tectonics) exhibit the same mathematical behaviour as those that shape terrain on smaller scales (for instance soil creep). Real landscapes also have varying statistical behaviour from place to place, so for example sandy beaches don't exhibit the same fractal properties as mountain ranges. A fractal function, however, is statistically stationary, meaning that its bulk statistical properties are the same everywhere. Thus, any real approach to modeling landscapes requires the ability to modulate fractal behaviour spatially. Additionally real landscapes have very few natural minima (most of these are lakes), whereas a fractal function has as many minima as maxima, on average. Real landscapes also have features originating with the flow of water and ice over their surface, which simple fractals cannot model.〔Ken Musgrave, 1993〕 It is because of these considerations that the simple fractal functions are often inappropriate for modeling landscapes. More sophisticated techniques (known as 'multifractal' techniques) use different fractal dimensions for different scales, and thus can better model the frequency spectrum behaviour of real landscapes〔Joost van Lawick van Pabst et al.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fractal landscape」の詳細全文を読む スポンサード リンク
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