Fractals

In mathematics, a fractal is a subset of a Euclidean space for which the fractal dimension strictly exceeds the topological dimension. Fractals appear the same at different levels, as illustrated in successive magnifications of the Mandelbrot set; because of this, fractals are encountered ubiquitously in nature. Fractals exhibit similar patterns at increasingly small scales called self similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, it is called affine self-similar. Fractal geometry lies within the mathematical branch of topology.