In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition … See more The term "fractal" was coined by the mathematician Benoît Mandelbrot in 1975. Mandelbrot based it on the Latin frāctus, meaning "broken" or "fractured", and used it to extend the concept of theoretical fractional See more The history of fractals traces a path from chiefly theoretical studies to modern applications in computer graphics, with several notable people contributing canonical fractal … See more Images of fractals can be created by fractal generating programs. Because of the butterfly effect, a small change in a single variable can have an unpredictable outcome. • Iterated function systems (IFS) – use fixed geometric … See more • Mathematics portal • Banach fixed point theorem • Bifurcation theory • Box counting • Cymatics • Determinism See more The word "fractal" often has different connotations for the lay public as opposed to mathematicians, where the public is more likely to be familiar with fractal art than the mathematical concept. The mathematical concept is difficult to define formally, even for … See more One often cited description that Mandelbrot published to describe geometric fractals is "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"; this is … See more Simulated fractals Fractal patterns have been modeled extensively, albeit within a range of scales rather than infinitely, owing to the practical limits of physical … See more WebSep 29, 2014 · The term ‘fractal’ (from the Latin fractus, meaning ‘broken’), introduced by Benoit Mandelbrot about 25 years ago, is used to characterize spatial and/or temporal phenomena that are continuous but not differentiable.Geometrically, a fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least …

Minkowski–Bouligand dimension - Wikipedia

WebJul 8, 2024 · In his 1202 treatise, Book of Calculation, Fibonacci described the numerical sequence that now bears his name: 1, 2, 3, 5, 8, 13, 21... and on into infinity. Divide … WebJan 1, 2012 · Abstract and Figures. For understanding the growth mechanisms of DNA fractal links, we constructed a series of Sierpinski links with different fractal number n based on k-tangle models and deduced ... unfinished gasoline

Iterated function system - Wikipedia

WebOlder Fractals of the Day are saved in an archive. If your browser supports Java, you might enjoy the applet that creates a new fractal image every five seconds or so. If you would … WebMar 23, 2024 · fractal: [noun] any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when … http://docs.fractal-link.com/ unfinished furniture woodstock ga