A
fractal is a natural phenomenon or a mathematical
set that exhibits a repeating pattern that displays at every scale. It is also known as
expanding symmetry or
evolving symmetry. If the replication is exactly the same at every scale, it is called a
self-similar pattern. An example of this is the
Menger Sponge. Fractals can also be nearly the same at different levels. This latter pattern is illustrated in the magnifications of the Mandelbrot set. Fractals also include the idea of a detailed pattern that repeats itself.