Fractal Solid Textures: Some Examples

TL;DR: In this article, the authors describe various fractal procedural textures serving as models of natural phenomena, such as thin, wispy clouds in a blue sky, which can be constructed from any basis function; the basis function that is most often chosen is the Perlin noise function.

Abstract: This chapter describes various fractal procedural textures serving as models of natural phenomena. They are divided into four elements of the ancients: air, fire, water, and earth. The chapter describes the most common, quick, and easy cloud texture and discusses a few two-dimensional models that are significant aesthetically. One of the simplest and most often used fractal textures is a simple representation of thin, wispy clouds in a blue sky. The fractals can be constructed from any basis function; the basis function that is most often chosen is the Perlin noise function. The composition of noise functions to provide distortion is useful in another aspect of modeling clouds: emulating the streaming of clouds that are stretched by winds. Modeling of the clouds is presented in the chapter on different scales. One of these scales is a distorted large-scale distribution comprising a weighting function, which is applied to smaller-scale cloud features. The undistorted small features correspond to the phenomenon of viscosity, which damps turbulence at small scales. This may serve as the first step in the direction of multifractal models, as the fractal behavior is different at different scales, and therefore may require more than one value or measure to characterize the fractal behavior.