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Bill M. Williams (1932–2019) [1] was an American trader and author of books on trading psychology, technical analysis, and chaos theory [2] in trading the stock, commodity, and foreign exchange (Forex) markets. His study of stock market data led him to develop a number of technical analyses that identify trends in the financial markets.
His current venture is "Fractal Market Cycles and Regimes" at www.edgarepeters.com. [2] His books include Chaos and Order in the Capital Markets (According to WorldCat, the book is held in 813 libraries, [3]) Fractal Market Analysis (held in 580 libraries [4]) and Patterns in the Dark: Understanding Risk and Financial Crisis with Complexity ...
While an optimally packed fractal appears only for a defined value of r, i.e., r opt, it is possible to play the chaos game using other values as well.If r>1 (the point x k+1 jumps at a greater distance than the distance between the point x k and the vertex v), the generated figure extends outside the initial polygon. [5]
XaoS is an interactive fractal zoomer program.It allows the user to continuously zoom in or out of a fractal in real-time. XaoS is licensed under GPL.The program is cross-platform, and is available for a variety of operating systems, including Linux, Windows, Mac OS X, BeOS and others.
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).
Chaos theory has been used for many years in cryptography. In the past few decades, chaos and nonlinear dynamics have been used in the design of hundreds of cryptographic primitives. These algorithms include image encryption algorithms, hash functions, secure pseudo-random number generators, stream ciphers, watermarking, and steganography. [123]
Fractal branching of trees. Fractal analysis is assessing fractal characteristics of data.It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset, or a pattern or signal extracted from phenomena including topography, [1] natural geometric objects, ecology and aquatic sciences, [2] sound, market fluctuations ...
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