Fractals Are Typically Not Self-Similar

This course explains the concept of fractal dimension, focusing on shapes whose "Hausdorff dimension" exceeds their "topological dimension". It covers the definition of fractals according to Mandelbrot, the distinction between Hausdorff and topological dimensions, and examples like the Mandelbrot set and the Sierpinski pyramid. The course explores how roughness levels determine dimensions, with integer dimensions possible in certain cases. The teaching method involves a technical explanation with visual aids and examples. The intended audience includes individuals interested in mathematics, geometry, and fractal geometry.