Examples of Fractal Geometry
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 Dimension Adsorbate Molecule Irregular Surface Adsorbent Particle Char Particle
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