Fractals as geometric patterns

To define fractals, three concepts have to be understood: recursion, infinity, and scale. A fractal is a geometrical feature resulting from a pattern that recurs at infinitely smaller scales. Fractals form an important mathematical concept as they describe how numerous elements of nature are created: Trees, dandelions, the respiratory system, snowflakes, etc.. What makes fractals extremely interesting is that they are more than just a geometric procedure that we use to model the natural elements; they capture nature's philosophy/essence. Similar nature-essence-capturing concepts include non-gradient topology optimization procedures such as evolutionary structural optimization.