Fractal geometry is a branch of mathematics that studies shapes and patterns that repeat at different scales. Unlike traditional geometry, which deals with simple shapes like squares and circles, fractals can be incredibly complex and detailed. A common example of a fractal is the Mandelbrot set, where zooming in reveals more intricate patterns that look similar to the whole shape. Fractals are not just theoretical; they appear in nature as well. For instance, the branching of trees, the structure of snowflakes, and the formation of coastlines all exhibit fractal-like properties. This fascinating geometry helps scientists and artists understand and create complex designs that mimic the beauty of the natural world.