👉 The math behind the concept of fractals is rooted in self-similarity and scaling, particularly through the use of iterative functions and geometric transformations. Fractals are geometric shapes that display intricate patterns repeating at different scales, meaning they look similar whether you zoom in or out. This self-similarity is often achieved using iterative processes where a function is repeatedly applied to a point or shape, scaling and transforming it in a specific way. For example, the Mandelbrot set is generated by iterating a complex function and checking if the output remains bounded; points that escape to infinity form the boundary of the set. The math involves understanding limits, complex numbers, and dynamical systems, illustrating how simple rules can generate incredibly complex and beautiful patterns.
