Based on the provided sources, here is a brief explanation of fractals, their properties, and their real-world applications:

What are Fractals? Coined by mathematician Benoit Mandelbrot, fractals are infinitely complex geometric shapes characterized by "self-similarity"—meaning their smaller parts are reduced-size copies of the overall whole. Unlike classical Euclidean geometry (which relies on smooth, idealized shapes like lines and spheres), fractals possess non-integer "fractional dimensions." This allows them to accurately measure and describe the roughness, fragmentation, and irregularity of the real world.

Presence in Nature and Biology Fractals are ubiquitous in the natural world. They perfectly model complex structures that traditional math cannot, such as coastlines, clouds, mountains, snowflakes, and river networks. In biolo ...