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The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical, while figures and images made it possible to ...
Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they scale . Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension ...
The unfinished Alan Moore 1990 comic book series Big Numbers used Mandelbrot's work on fractal geometry and chaos theory to underpin the structure of that work. Moore at one point was going to the name the comic book series The Mandelbrot Set .
Alongside fractals, chaos theory ranks as an essentially universal influence on patterns in nature. There is a relationship between chaos and fractals—the strange attractors in chaotic systems have a fractal dimension. [64]
His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and ...
More than a decade after Richardson completed his work, Benoit Mandelbrot developed a new branch of mathematics, fractal geometry, to describe just such non-rectifiable complexes in nature as the infinite coastline. [10] His own definition of the new figure serving as the basis for his study is: [11] I coined fractal from the Latin adjective ...
While Linde's theory shows fractality at scales likely larger than the observable universe, theories like causal dynamical triangulation [9] and the asymptotic safety approach to quantum gravity [10] are fractal at the opposite extreme, in the realm of the ultra-small near the Planck scale.
Chaotic maps and iterated functions often generate fractals. Some fractals are studied as objects themselves, as sets rather than in terms of the maps that generate them. This is often because there are several different iterative procedures that generate the same fractal. See also Universality (dynamical systems).