In mathematics , the Hausdorff dimension (also known as the Hausdorff–Besicovitch dimension ) is an extended non-negative real number associated with any metric space .
Snowflakes forming complex symmetrical patterns is an example of emergence in a physical system. In philosophy , systems theory , science , and art , emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions.
In mathematics , in the field of differential equations , a boundary value problem is a differential equation together with a set of additional restraints, called the boundary conditions . A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them.
In mathematics , the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties. It was discovered in 1874 by Henry John Stephen Smith [ 1 ] [ 2 ] [ 3 ] [ 4 ] and introduced by German mathematician Georg Cantor in 1883. [ 5 ] [ 6 ]
Visual representation of a strange attractor An attractor is a set towards which a variable , moving according to the dictates of a dynamical system , evolves over time.
The Sierpinski carpet is a plane fractal first described by Wacław Sierpiński in 1916.