Fractal Dimensions in Nature and Mathematics - 2019

Explore the fascinating world of fractal dimensions in nature and mathematics through this illuminating lecture by Stefano Luzzatto. Delve into an alternative definition of geometric object dimensions that extends to fractal dimensions, and examine simple examples of shapes with non-integer dimensions. Discover how fractal geometry can more accurately model natural objects compared to classical Euclidean shapes. Investigate the occurrence of fractal dimensions in mathematical fields like Dynamical Systems, and learn about intriguing concepts such as the Snowflake example, Julia Sets, and the Mandelbrot Set. Gain insights into the measure formula and its applications in understanding complex geometric structures.

Introduction
Definition of dimensions
Snowflake example
First step
Examples
Measure
Formula
Mandelbrot
Dynamical System
Julia Sets
Mandelbrot Set