Zone Patcher
Fractal Geometry Zone
www.flickr.com/photos/psychoactivartz/3534301065/sizes/l/
Although Mandelbrot invented the word fractal, some objects featured in The Fractal Geometry of Nature had been previously described by other mathematicians (the Mandelbrot set being a notable exception). However, they had been regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them around into essential tools for the long-stalled effort of extending the scope of science to non-smooth parts of the real world. He highlighted their common properties, such as self-similarity (linear, non-linear, or statistical), scale invariance and (usually) non-integer Hausdorff dimension.
He also emphasized the use of fractals as realistic and useful models of many phenomena in the real world that can be viewed as rough. Natural fractals include the shapes of mountains, coastlines and river basins; the structure of plants, blood vessels and lungs; the clustering of galaxies; Brownian motion. Man-made fractals include stock market prices but also music, painting and architecture. Far from being unnatural, Mandelbrot held the view that fractals were, in many ways, more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry.
The word "fractal" has two related meanings. In colloquial usage, it denotes a shape that is recursively constructed or self-similar, that is, a shape that appears similar at all scales of magnification and is therefore often referred to as "infinitely complex." In mathematics a fractal is a geometric object that satisfies a specific technical condition, namely having a Hausdorff dimension greater than its topological dimension. The term fractal was coined in 1975 by Benoît Mandelbrot, from the Latin fractus, meaning "broken" or "fractured."
...it's mysterious how beautifully da universe is designed. Music and art are in and out of every part of it and us. No wonder (yes! wonder!) we are creative beings.
Fractal Geometry Zone
www.flickr.com/photos/psychoactivartz/3534301065/sizes/l/
Although Mandelbrot invented the word fractal, some objects featured in The Fractal Geometry of Nature had been previously described by other mathematicians (the Mandelbrot set being a notable exception). However, they had been regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them around into essential tools for the long-stalled effort of extending the scope of science to non-smooth parts of the real world. He highlighted their common properties, such as self-similarity (linear, non-linear, or statistical), scale invariance and (usually) non-integer Hausdorff dimension.
He also emphasized the use of fractals as realistic and useful models of many phenomena in the real world that can be viewed as rough. Natural fractals include the shapes of mountains, coastlines and river basins; the structure of plants, blood vessels and lungs; the clustering of galaxies; Brownian motion. Man-made fractals include stock market prices but also music, painting and architecture. Far from being unnatural, Mandelbrot held the view that fractals were, in many ways, more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry.
The word "fractal" has two related meanings. In colloquial usage, it denotes a shape that is recursively constructed or self-similar, that is, a shape that appears similar at all scales of magnification and is therefore often referred to as "infinitely complex." In mathematics a fractal is a geometric object that satisfies a specific technical condition, namely having a Hausdorff dimension greater than its topological dimension. The term fractal was coined in 1975 by Benoît Mandelbrot, from the Latin fractus, meaning "broken" or "fractured."
...it's mysterious how beautifully da universe is designed. Music and art are in and out of every part of it and us. No wonder (yes! wonder!) we are creative beings.