In mathematics , a class of complex geometric shapes that commonly exhibit the property of self-similarity.
Fractals are distinct from the simple figures of classical, or Euclidean , geometry.
They are capable of describing the many irregularly shaped objects or spatially nonuniform phenomena in nature that cannot be accommodated by Euclidean geometry. Theoretically, the result would be a figure of finite area but with a perimeter of infinite length, with an infinite number of vertices. In mathematical terms, such a curve cannot be differentiated . Many such self-repeating figures can be constructed, and when they first appeared in the 19th century they were considered bizarre. The Polish-born French mathematician Benoit B. Mandelbrot discovered fractal geometry in the 1970s.