Examples of Fractal Geometry

Abstract

Examples of fractal geometry abound. As mentioned earlier, the fractal dimension, d_F, is constrained by the topological dimension, d_T, from below and the Euclidean dimension, d_E, from above. The fractal dimension of a rugged line on the plane with an Euclidean dimension of 2 is between 1 and 2, as demonstrated in Figure 2–5. Similarly, the fractal dimension of a rugged line is between 1 and 3 in the space with an Euclidean dimension of 3. Relatively simple examples include, among others, the Cantor set whose topological and Euclidean dimensions are 0 and 1, respectively, and 0 < d_F < 1, and the irregular surface of a particulate object, e. g., a catalyst, whose topological and Euclidean dimensions are 2 and 3, respectively, and 2 < d_F ≤ 3.