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In mathematics, a fractal is a subset of a Euclidean space for which the fractal dimension strictly exceeds the topological dimension. Fractals appear the same at different levels, as illustrated in successive magnifications of the Mandelbrot set; because of this, fractals are encountered ubiquitously in nature. Fractals exhibit similar patterns at increasingly small scales called self similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, it is called affine self-similar. Fractal geometry lies within the mathematical branch of topology.
Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still images, animations, and media. Fractal art developed from the mid-1980s onwards. It is a genre of computer art and digital art which are part of new media art. The mathematical beauty of fractals lies at the intersection of generative art and computer art. They combine to produce a type of abstract art.
A Belousov–Zhabotinsky reaction, or BZ reaction, is one of a class of reactions that serve as a classical example of non-equilibrium thermodynamics, resulting in the establishment of a nonlinear chemical oscillator. The only common element in these oscillators is the inclusion of bromine and an acid. The reactions are important to theoretical chemistry in that they show that chemical reactions do not have to be dominated by equilibrium thermodynamic behavior. These reactions are far from equilibrium and remain so for a significant length of time and evolve chaotically. In this sense, they provide an interesting chemical model of nonequilibrium biological phenomena; as such, mathematical models and simulations of the BZ reactions themselves are of theoretical interest, showing phenomenon as noise-induced order.
Boris Pavlovich Belousov was a Soviet chemist / biophysicist who discovered the Belousov–Zhabotinsky reaction in the early 1950s. His work initiated the field of modern nonlinear chemical dynamics.
In mathematics, the Lyapunov time is the characteristic timescale on which a dynamical system is chaotic. It is named after the Russian mathematician Aleksandr Lyapunov. It is defined as the inverse of a system's largest Lyapunov exponent.
Bromic acid, also known as hydrogen bromate, is an oxoacid with the molecular formula HBrO3. It only exists in aqueous solution. It is a colorless solution that turns yellow at room temperature as it decomposes to bromine. Bromic acid and bromates are powerful oxidizing agents and are common ingredients in Belousov–Zhabotinsky reactions. Belousov-Zhabotinsky reactions are a classic example of non-equilibrium thermodynamics.
The science of pattern formation deals with the visible, (statistically) orderly outcomes of self-organization and the common principles behind similar patterns in nature.
Algorithmic art, also known as algorithm art, is art, mostly visual art, of which the design is generated by an algorithm. Algorithmic artists are sometimes called algorists.
A chemical computer, also called reaction-diffusion computer, BZ computer or gooware computer is an unconventional computer based on a semi-solid chemical "soup" where data are represented by varying concentrations of chemicals. The computations are performed by naturally occurring chemical reactions.
A billiard-ball computer, a type of conservative logic circuit, is an idealized model of a reversible mechanical computer based on Newtonian dynamics, proposed in 1982 by Edward Fredkin and Tommaso Toffoli. Instead of using electronic signals like a conventional computer, it relies on the motion of spherical billiard balls in a friction-free environment made of buffers against which the balls bounce perfectly. It was devised to investigate the relation between computation and reversible processes in physics.
Chaos computing is the idea of using chaotic systems for computation. In particular, chaotic systems can be made to produce all types of logic gates and further allow them to be morphed into each other.
A chemical oscillator is a complex mixture of reacting chemical compounds in which the concentration of one or more components exhibits periodic changes, They are a class of reactions that serve as an example of non-equilibrium thermodynamics with far-from-equilibrium behavior. The reactions are theoretically important in that they show that chemical reactions do not have to be dominated by equilibrium thermodynamic behavior.
Simon El'evich Shnol is a biophysicist, and a historian of Soviet science. He is a professor at Physics Department of Moscow State University and a member of Russian Academy of Natural Sciences. His fields of interest are the oscillatory processes in biology, the theory of evolution, Chronobiology, and the history of science. He has mentored many successful scientists, including Anatoly Zhabotinsky.
Andrew Adamatzky is a British computer scientist, who is a Director of the Unconventional Computing Laboratory and Professor in Unconventional Computing at the Department of Computer Science and Creative Technology, University of the West of England in Bristol, United Kingdom.
Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.
Autowaves are self-supporting non-linear waves in active media. The term is generally used in processes where the waves carry relatively low energy, which is necessary for synchronization or switching the active medium.
Chaotic cryptology includes two integral opposite parts: Chaotic cryptography and Chaotic cryptanalysis. Chaotic cryptography is the application of the mathematical chaos theory to the practice of the cryptography, the study or techniques used to privately and securely transmit information with the presence of a third-party or adversary. Since first being investigated by Robert Matthews in 1989, the use of chaos in cryptography has attracted much interest; however, long-standing concerns about its security and implementation speed continue to limit its implementation.
Endre Kőrös is, in the field of nonlinear chemical dynamics, mostly known for developing the FKN mechanism, a description of the Belousov–Zhabotinsky reaction involving 11 reactions and 12 species in 1972 with his colleagues Richard J. Field and Richard M. Noyes.
Muthusamy Lakshmanan is an Indian theoretical physicist and a Ramanna fellow of the Department of Science and Technology at the Centre for Nonlinear Dynamics of Bharathidasan University. He has held several research fellowships which included Raja Rammanna fellowship of Department of Atomic Energy, Alexander von Humboldt fellowship, Japan Society for the Promotion of Science fellowship, Royal Society Nuffield Foundation fellowship, and NASI-Senior Scientist Platinum Jubilee Fellowship.
References
- Motoike I., Adamatzky A. "Three-valued logic gates in reaction-diffusion excitable media." Chaos, Solitons & Fractals 24 (2005) 107-114
- Adamatzky, A. "Collision-based computing in Belousov–Zhabotinsky medium." Chaos, Solitons & Fractals 21:(5), (2004), p1259-1264 doi : 10.1016/j.chaos.2003.12.068
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