Fractals and chaos theory

Fractals are complex patterns that look similar at different scales, created through simple repeating processes, like snowflakes or coastlines. Chaos theory studies how small changes in initial conditions can lead to vastly different outcomes, making systems like weather or markets unpredictable over time. Together, they reveal how intricate, seemingly random structures and behaviors can emerge from simple rules and sensitive dependence on initial factors, highlighting the interconnectedness and complexity inherent in natural and mathematical systems.