Examples of Fractal Geometry

Abstract

Examples of fractal geometry abound. As mentioned earlier, the fractal dimension, dF, is constrained by the topological dimension, dT, from below and the Euclidean dimension, dE, 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 < dF < 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 < dF ≤ 3.KeywordsFractal DimensionAdsorbate MoleculeIrregular SurfaceAdsorbent ParticleChar ParticleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.