The Influence of Benoît B . Mandelbrot on Mathematics

Fractal - Wikipedia, the free encyclopedia

A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iterati...

Bric - a - brac of Creative Computing : Studying Fractal Shapes

54 Generally, a fractal most often referred to as “a rough shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole.” The father of fractal geometry Benoît Mandelbrot formulated this term in 1975. A fractal has a complicated shape. Certain features characterize a graphical representation of the fractal by mathematical equation: it is self...

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

Influence of Magnetic Wire Positions on free convection of Fe3O4-Water nanofluid in a Square Enclosure Utilizing with MAC Algorithm

The augment of heat transfer and fluid of buoyancy-driven flow of Fe3O4-Water nanofluid in a square cavity under the influence of an external magnetic field is studied numerically. Cold temperature is applied on the side (vertical) walls and high temperature is imposed on the bottom wall while the top wall is kept at thermally insulated. The governing non-dimensional differential equations are ...

Mathematical methods used in monofractal and multifractal analysis for the processing of biological and medical data and images

An object is self-similar if it can be decomposed into smaller copies of itself (the structure of the whole is contained in its parts) (Mandelbrot 1982; Falconer 2003). Not all irregular shapes found in nature are necessarily fractals (Losa 2009). Monofractal objects are mainly characterized by four properties: a) irregularity of the shape; b) self-similarity of the structure; c) non-integer or...