Search results
Results from the WOW.Com Content Network
Pietronero argues that the universe shows a definite fractal aspect over a fairly wide range of scale, with a fractal dimension of about 2. [3] The fractal dimension of a homogeneous 3D object would be 3, and 2 for a homogeneous surface, whilst the fractal dimension for a fractal surface is between 2 and 3.
Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. [2]
The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics. Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of Olbers' paradox (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a sufficient, but not ...
More precisely, this example works to explain a kind of math called chaos theory, which looks at how small changes made to a system’s initial conditions—like the extra gust of wind from a ...
The Beauty of Fractals is a 1986 book by Heinz-Otto Peitgen and Peter Richter which publicises the fields of complex dynamics, chaos theory and the concept of fractals. It is lavishly illustrated and as a mathematics book became an unusual success. The book includes a total of 184 illustrations, including 88 full-colour pictures of Julia sets.
The back of the book, and a summary of its content, reads, "The science of chaos is forcing scientists to rethink Einstein's fundamental assumptions regarding the way the universe behaves. Chaos theory has already shown that simple systems, obeying precise laws, can nevertheless act in a random manner.
Mitchell Jay Feigenbaum / ˈ f aɪ ɡ ə n ˌ b aʊ m / (December 19, 1944 – June 30, 2019) was an American mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constants.
If the Universe is a complex system affected by chaos then its invariant set (a fixed state of rest) is likely to be a fractal. According to Palmer this could resolve problems posed by the Kochen–Specker theorem , which appears to indicate that physics may have to abandon the idea of any kind of objective reality, and the apparent paradox of ...