👉 The math behind the concept of fractals, which are geometric shapes that exhibit self-similarity at various scales, involves mathematical functions like iterated function systems (IFS) and affine transformations. These systems use repeated application of simple rules to generate complex patterns, where each transformation is a scaled and shifted version of the previous one. The key equation here is often expressed as \(x_{n+1} = f(x_n)\), where \(f\) is the transformation function, and \(x_n\) represents the position at the nth iteration. Fractals emerge from these iterative processes, creating intricate structures that display detail at every level of magnification. This self-similarity is a hallmark of fractals, making them fascinating in fields like mathematics, computer graphics, and nature studies.
