Fractal Geometry

Fractional geometry and fractal geometry

Fractional Geometry is a branch of geometry that deals with so-called fractional geometric objects, mainly in practice in n-dimensional Euclidean spaces, but the relevant general framework is that of separable complete metric spaces. The adjective fractional first appeared in geometry in the work of A. Besicovitch (1930s), although it was introduced into analysis as early as the 17th century by G. Leibniz to qualify certain exponents of functions.

The concept of dimension plays a key role in fractional geometry, with the Hausdorff and Besicovitch dimension introduced by F. Hausdorff (1919), then studied in detail by A. Besicovitch (1929, 1934, 1935, 1937). Dimension Theory is a branch of General Topology [AF97][AF98] , first rigorously investigated by K. Menger. Menger (1928). The geometric study of fractional dimensions was initiated by J. Marstrand (1954).

Fractal geometry is concerned with fractal geometric objects, i.e. fractional objects with a spatial structure that follows a deterministic or probabilistic rule involving internal self-similarity. The adjective fractal was introduced by B. Mandelbrot in 1967 , who was responsible for the widespread popularization