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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).
Mohamed El Naschie (Arabic: محمد النشائي, born 1943) [1] is an Egyptian engineer and the former editor of a controversial journal, Chaos, Solitons & Fractals.The controversy concerned El Naschie's publication, over many years, of over 300 papers of questioned scientific merit authored by himself in his own journal with little or no apparent peer review.
Solitary wave in a laboratory wave channel. In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable, in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets.
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]
These subregions are called bands. When there are multiple bands, the orbit moves through each band in a regular order, but the values within each band are irregular. Such chaotic orbits are called band chaos or periodic chaos, and chaos with k bands is called k -band chaos. Two-band chaos lies in the range 3.590 < r < 3.675, approximately.
spatial solitons: the nonlinear effect can balance the dispersion. The electromagnetic field can change the refractive index of the medium while propagating, thus creating a structure similar to a graded-index fiber . [ 2 ]
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The Hénon attractor is a fractal, smooth in one direction and a Cantor set in another. Numerical estimates yield a correlation dimension of 1.21 ± 0.01 or 1.25 ± 0.02 [ 2 ] (depending on the dimension of the embedding space) and a Box Counting dimension of 1.261 ± 0.003 [ 3 ] for the attractor of the classical map.