Types of Patterns

Arithmetic patterns add the same amount each step: 3, 7, 11, 15. Geometric patterns multiply by the same factor: 2, 6, 18, 54. Chaotic patterns look random but follow fixed rules — weather is famously chaotic yet not truly random.

Nature builds with patterns at every scale. The branching of rivers mirrors the branching of lungs, trees, and lightning. This repetition across scales is the hallmark of fractals. Mathematician Benoit Mandelbrot showed these shapes have fractional dimensions — a coastline is rougher than a line but smoother than a plane.