Fractals: Dimensions and Applications

This lecture covers the concept of fractals, defined as forms repeated over scales and exhibiting self-similarity. It explains fractal dimensions, including integer and Hausdorff dimensions, illustrated with examples like Koch Curve and Cantor Dust. The lecture also delves into fractional Brownian motion, roughness control, and multifractals, highlighting the heterogeneity of fractal systems. It explores the simulation of mountain formation through erosion processes and the interplay between erosion and vegetation in landscape authoring. Real-world applications and examples of multifractal terrains are discussed, emphasizing the complexity and versatility of fractal geometry in various fields.