Fractal landscapes are computer-generated surfaces that use stochastic algorithms to mimic the natural appearance and fractal behavior of real terrain, often exhibiting statistical self-similarity. Benoit Mandelbrot first proposed modeling Earth's rough surfaces using fractional Brownian motion, and their development became a major turning point in art history, blurring the distinction between geometric, computer-generated images and natural, man-made art. A significant early application was in the 1982 film Star Trek II: The Wrath of Khan, where Loren Carpenter refined these techniques to create an alien world.
Despite their realistic appearance, natural landscapes rarely behave in a perfectly fractal manner across all scales or locations, exhibiting varying statistical properties that simple fractal functions cannot fully replicate. Real terrains also lack the uniform statistical properties or the balance of minima and maxima seen in simple fractals. Consequently, more sophisticated "multi-fractal" techniques are often employed, using different fractal dimensions for various scales to more accurately model the complex features of real-world terrain.