Fractals are generally self-similar and independent of scale.
Fractals also describe many real-world objects, such as clouds, mountains, turbulence, and coastlines, that do not correspond to simple geometric shapes. Benoit Mandelbrot gives a mathematical definition of a fractal as a set for which the Hausdorff Besicovich dimension strictly exceeds the topological dimension. However, he is not satisfied with this definition as it excludes sets one would consider fractals. Mandelbrot set Classic Mandelbrot set fractal. Lorenz attractor Lorenz two lobe attractor - orbit in three dimensions.