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A fractal landscape is essentially a two-dimensional form of the fractal coastline, which can be considered a stochastic generalization of the Koch curve. The Hausdorff-Besicovitch dimension, D, is a fraction between 2 and 3. The Mandelbrot set, named after its discoverer, is a famous example of a fractal. ...
Stochastic, from the Greek stochos or goal, means of, relating to, or characterized by conjecture; conjectural; random. ...
The first four iterations of the Koch snowflake The Koch curve is a mathematical curve, and one of the earliest fractal curves to have been described. ...
In mathematics, the Hausdorff dimension is an extended non-negative real number, that is in the closed infinite interval [0, ∞], associated to any metric space . ...
A way to make such a landscape is to employ the random midpoint displacement algorithm, in which a square is subdivided into four smaller equal squares and the center point is vertically offset by some random amount. The process is repeated on the four new squares, and so on, until the desired level of detail is reached. Since there are many fractal procedures (such as Perlin noise) capable of creating terrain data, however, the term "fractal landscape" has become more generic. The Harvesters, by Pieter Brueghel the Elder, 1565: Peace and agriculture in a pre-Romantic ideal landscape, without sublime terrors The term Landscape as most westerners use it, is completely entrenched in western notions of land, nature and art. ...
In plane geometry, a square is a polygon with four equal sides and equal angles. ...
Perlin noise is a function which uses an interpolation function to combine noise-generating functions, and has been used to produce natural textures on computer-generated objects for motion pictures special effects. ...
Kenton "Doc Mojo" Musgrave is considered a leading authority on fractal landscapes and his most recent computer program, MojoWorld, is one of the more convenient ways to investigate them. The core of Dr. Musgrave's work in this area centered on rendering planetary bodies from orbital heights smoothly down to the surface with adaptive level of detail. Mojoworld basically makes this process interactive for anyone with a sufficiently powerful PC. Another highly popular program in this vein is Matt Fairclough's Terragen. Categories: Computer stubs | 3D graphics software ...
Although fractal landscapes look natural at first glance, repeated exposure brings disappointment to those who expect eroded mountains. The main complaint is that simple fractal processes do not (and perhaps cannot) mimic actual geological and weathering functions.
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