mandelbrot set x px x px mathematics '''fractal''' subset euclidean space fractal dimension strictly exceeds topological dimension fractals appear different scales illustrated successive magnifications mandelbrot set ref name mandelbrot ref name falconer ref name patterns ref name vicsek fractals often exhibit similar patterns increasingly smaller scales property called self similarity also known expanding symmetry unfolding symmetry replication exactly every scale menger sponge ref name gouyet called affine self similar fractal geometry lies within mathematical branch
Formal science Mathematics Applied mathematics Dynamical systems Fractal geometry