fractal dimension

In mathematics, a fractal is a complex geometric shape that differs from the simple figures of Euclidean geometry. Fractals are useful for describing irregularly shaped objects and phenomena found in nature, such as coastlines and mountain ranges. The term "fractal" comes from the Latin word for "fragmented".1

A key characteristic of fractals is their fractal dimension, a mathematical parameter that is typically a non-integer, or fraction, rather than a whole number. This concept was introduced by mathematician Felix Hausdorff and further developed by Benoit Mandelbrot, who also coined the term "fractal". Fractal dimension indicates the complexity of a shape and can be illustrated by the snowflake curve, which has a fractal dimension of approximately 1.26. Fractals have found applications in various fields, including computer graphics and the study of physical systems with random features.12