April 6

Fractals and Self-Similarity

Fractals are patterns that repeat at every scale, showing self-similarity whether you zoom in or out. Benoit Mandelbrot discovered that coastlines have no definitive length - measuring with smaller rulers gives longer measurements indefinitely. Fractals model natural patterns like trees, rivers, clouds, and mountains better than traditional geometry. The Mandelbrot set, visualized in stunning images, emerges from a simple equation yet contains infinite complexity.