What is the mathematical basis of fractals?
A fractal is a geometric shape that when zoomed in on, will look approximately the same as it did before. Fractal geometry is a more complex version of regular Euclidean geometry. Euclidean geometry included just circles, squares, triangles, hexagons, octagons and all other regular shapes. Fractal geometry is the study of fractals and all of its components. Fractal geometry, out of all of its other uses, is mainly used to describe every other shape possible that isn’t classified into regular Euclidean geometry. Although not many people know what a fractal is, they encounter them on a regular basis and fractals have many uses all of which are extremely overlooked by many people.
Benoit B. Mandelbrot has written: 'Gaussian self-affinity and fractals' -- subject- s -: Electronic noise, Fractals, Multifractals 'The - Mis - Behavior of Markets' 'The fractal geometry of nature' -- subject- s -: Geometry, Mathematical models, Fractals, Stochastic processes 'Fractals' -- subject- s -: Geometry, Mathematical models, Fractals, Stochastic processes
Benoit Mandelbrot made mathematical accomplishments in physics, information theory, and finance. However, he is by far best known for his organization and rigorous development of the geometric objects known as fractals, a word which he invented. Specifically, his studies of fractals lead to his development of what are now called Mandelbrot sets, which provided the spark that started the fire with regards to the research of chaos theory.
Fractals are situations where the geometry seems best approximated by an infinitely "branching" sequence - used, for example, in modeling trees. For work on fractals that I have done as a theoretician, I recommend the included links. I just happen to have an original answer, and I want to make it known.
Benoit Mandelbrot is the man who is usually credited to have discovered fractals in the year 1975. He was the first person to use this word and was also the first man to represent them in visual form. But history also shows that some facts about fractals were known to mathematicians as early as the 17th century.
Management Science Theory gives a quantitative basis for decision making. It specially deals with the development of mathematical models to aid in decision making and problem solving. This theory holds that managing is a logical and rationale process, so it can be expressed in terms of mathematical models.