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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 ...
A Poincaré plot, named after Henri Poincaré, is a graphical representation used to visualize the relationship between consecutive data points in time series to detect patterns and irregularities in the time series, revealing information about the stability of dynamical systems, providing insights into periodic orbits, chaotic motions, and bifurcations.
Over a period of 24 years (January 1957 – December 1980), Martin Gardner wrote 288 consecutive monthly "Mathematical Games" columns for Scientific American magazine. During the next 5 + 1 ⁄ 2 years, until June 1986, Gardner wrote 9 more columns, bringing his total to 297. During this period other authors wrote most of the columns.
Download as PDF; Printable version ... Analysis on fractals or calculus on fractals is a generalization of ... This page was last edited on 13 July 2024, ...
Display a year or month calendar Template parameters [Edit template data] Parameter Description Type Status Year year the ordinal year number of the calendar Default current Number suggested Month month whether to display a single month instead of a whole year, and which one Default empty Example current, next, last, 1, January String suggested Show year show_year whether to display the year ...
The seven states of randomness in probability theory, fractals and risk analysis are extensions of the concept of randomness as modeled by the normal distribution. These seven states were first introduced by Benoît Mandelbrot in his 1997 book Fractals and Scaling in Finance, which applied fractal analysis to the study of risk and randomness. [1]
The image shows D (Q) spectra from a multifractal analysis of binary images of non-, mono-, and multi-fractal sets. As is the case in the sample images, non- and mono-fractals tend to have flatter D (Q) spectra than multifractals. The generalized dimension also gives important specific information.
Lyapunov fractals can be calculated in more than two dimensions. The sequence string for a n-dimensional fractal has to be built from an alphabet with n characters, e.g. "ABBBCA" for a 3D fractal, which can be visualized either as 3D object or as an animation showing a "slice" in the C direction for each animation frame, like the example given ...
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