👉 At its core, the extraordinary math of fractals lies in their ability to generate intricate, self-similar patterns infinitely across scales, revealing the same structure no matter how much you zoom in. Using simple iterative formulas—like the Mandelbrot set’s equation \( z_{n+1} = z_n^2 + c \)—mathematicians can produce complex, boundary-rich shapes with stunning detail. This process, where a rule is repeatedly applied, uncovers hidden symmetries and connections between geometry, chaos theory, and even quantum mechanics, demonstrating how order can emerge from simplicity through recursive, infinitely nested logic.
