Fractal Dimensions: Seeing the World in a New Way

Mountains to Music: How Fractal Geometry Shapes Our World

I was fascinated when I first read about fractal dimensions when I was in college. The fractal dimension of a coastline changes with the scale that was used!

Fractal dimensions is a novel concept that has intrigued mathematicians, scientists, and artists alike for several decades. It provides a unique way of understanding and characterizing complex, irregular shapes and patterns that are often found in nature and human-made objects.

Fractals are a class of geometric objects that exhibit self-similarity at different scales. This means that as you zoom in or out of a fractal, the pattern or shape remains the same or similar. For example, the coastline of a country looks very similar when viewed from space or when viewed up close. Similarly, the branches of a tree look similar to the entire tree, and the leaves of a fern look similar to the entire fern. Fractals are often used to model natural phenomena such as clouds, mountains, lightning, and the human circulatory system, among others.

The concept of fractal dimensions was introduced by the mathematician Benoit Mandelbrot in the 1960s. The fractal dimension is a measure of the degree of self-similarity of a fractal object. Unlike Euclidean…