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Mario Markus (born 29 July 1944) is a German-Chilean physicist who worked for a long time in the Max Planck Institute for Molecular Physiology in Dortmund. In addition to his scientific work, Markus has exhibited his own computer graphics, as well as written novels and poetry and translated Spanish poems.
In 1970 he obtained his physics diploma under Konrad Tamm at the Institute for Applied Physics at the University of Heidelberg with a thesis on the Pinch-Effekt in plasmas made up of electrons and holes in semiconductors. From March 1970 to 1973 he conducted research for his doctorate on instabilities in plasmas at this institute. At the beginning of 1973 he received his doctorate (Dr. rer. nat.). After working as an assistant at the Institute for Theoretical Physics at the University of Heidelberg, he moved to the Max Planck Institute for Biophysics in Frankfurt am Main in April 1974. From January 1975 he was a research associate at the former Max Planck Institute (MPI) for Nutritional Physiology (today's MPI for Molecular Physiology) in Dortmund in the department of the biochemist and biophysicist Benno Hess. [1] In 1988 he habilitated at the University of Dortmund, where he was first appointed a lecturer and then, in August 1997, an associate professor.
In addition to his scientific work, he has published several volumes of poetry, a novel, a comic and works on computer graphics. [2]
Since the 1980s, Markus has created numerous works and presented exhibitions with computer graphics based on his novel representation of Lyapunov fractals, also called Ljapunow exponents, Lyapunow diagrams, Ljapunow fractals or Markus- Ljapunov diagrams. It should be noted, however, that many of these representations do not meet the mathematical definition of fractals, in which sections are similar or equal to the overall picture. In 2009 he published a comprehensive book on that subject with a CD-ROM for the reader to create such graphics: the German book “Die Kunst der Mathematik” (The Art of Mathematics), which was also published in Spanish. Below are some examples of Markus Ljapunov diagrams that appear in that book.
Markus discovered and described in detail a special type of crystals. These are 2D crystals, which are formed when microscope slides are wetted with a hydrophilic substance and allowed to dry. [13] A drop of a chemical solution spontaneously spreads over the entire slide and crystallizes in a form that is completely different from known 3D crystals or monomolecular 2D crystals. Examples of Markus’ 2D crystals are shown here below.
Mario Markus coined the term "ludic science" (Latin: ludus, the game). In cooperation with the German Society of Chemists (Gesellschaft Deutscher Chemiker, GdCh) Mario Markus has offered an annual prize of 10,000 euros since 2022 for outstanding "ludic" scientific achievements. In order to finance the award, he leaves his house worth almost one million euros to the Gesellschaft deutscher Chemiker in his testament. [14] [15]
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The Game of Life, also known as Conway's Game of Life or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. It is Turing complete and can simulate a universal constructor or any other Turing machine.
A cellular automaton is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling.
In mathematics, Lyapunov fractals are bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population, r, periodically switches between two values A and B.
Calculating Space is Konrad Zuse's 1969 book on automata theory. He proposed that all processes in the universe are computational. This view is known today as the simulation hypothesis, digital philosophy, digital physics or pancomputationalism. Zuse proposed that the universe is being computed by some sort of cellular automaton or other discrete computing machinery, challenging the long-held view that some physical laws are continuous by nature. He focused on cellular automata as a possible substrate of the computation, and pointed out that the classical notions of entropy and its growth do not make sense in deterministically computed universes.
In a cellular automaton, a Garden of Eden is a configuration that has no predecessor. It can be the initial configuration of the automaton but cannot arise in any other way. John Tukey named these configurations after the Garden of Eden in Abrahamic religions, which was created out of nowhere.
A block cellular automaton or partitioning cellular automaton is a special kind of cellular automaton in which the lattice of cells is divided into non-overlapping blocks and the transition rule is applied to a whole block at a time rather than a single cell. Block cellular automata are useful for simulations of physical quantities, because it is straightforward to choose transition rules that obey physical constraints such as reversibility and conservation laws.
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.
Rule 184 is a one-dimensional binary cellular automaton rule, notable for solving the majority problem as well as for its ability to simultaneously describe several, seemingly quite different, particle systems:
The Curtis–Hedlund–Lyndon theorem is a mathematical characterization of cellular automata in terms of their symbolic dynamics. It is named after Morton L. Curtis, Gustav A. Hedlund, and Roger Lyndon; in his 1969 paper stating the theorem, Hedlund credited Curtis and Lyndon as co-discoverers. It has been called "one of the fundamental results in symbolic dynamics".
A ludic interface is an inherently "playful" type of computer interface. This field of human–computer interaction research and design draws on concepts introduced by Dutch historian and cultural theorist Johan Huizinga in the book Homo Ludens . Huizinga's work is considered an important contribution to the development of game studies.
The movable cellular automaton (MCA) method is a method in computational solid mechanics based on the discrete concept. It provides advantages both of classical cellular automaton and discrete element methods. One important advantage of the MCA method is that it permits direct simulation of material fracture, including damage generation, crack propagation, fragmentation, and mass mixing. It is difficult to simulate these processes by means of continuum mechanics methods, so some new concepts like peridynamics are required. Discrete element method is very effective to simulate granular materials, but mutual forces among movable cellular automata provides simulating solids behavior. As the cell size of the automaton approaches zero, MCA behavior approaches classical continuum mechanics methods. The MCA method was developed in the group of S.G. Psakhie
Classic epidemic models of disease transmission are described in Compartmental models in epidemiology. Here we discuss the behavior when such models are simulated on a lattice. Lattice models, which were first explored in the context of cellular automata, act as good first approximations of more complex spatial configurations, although they do not reflect the heterogeneity of space. Lattice-based epidemic models can also be implemented as fixed agent-based models.
A reversible cellular automaton is a cellular automaton in which every configuration has a unique predecessor. That is, it is a regular grid of cells, each containing a state drawn from a finite set of states, with a rule for updating all cells simultaneously based on the states of their neighbors, such that the previous state of any cell before an update can be determined uniquely from the updated states of all the cells. The time-reversed dynamics of a reversible cellular automaton can always be described by another cellular automaton rule, possibly on a much larger neighborhood.
In mathematics, a surjunctive group is a group such that every injective cellular automaton with the group elements as its cells is also surjective. Surjunctive groups were introduced by Gottschalk (1973). It is unknown whether every group is surjunctive.
Stochastic cellular automata or probabilistic cellular automata (PCA) or random cellular automata or locally interacting Markov chains are an important extension of cellular automaton. Cellular automata are a discrete-time dynamical system of interacting entities, whose state is discrete.
Rubidium hydrogen sulfate, sometimes referred to as rubidium bisulfate, is the half neutralized rubidium salt of sulfuric acid. It has the formula RbHSO4.
Federación Obrera de Magallanes was a trade union movement based in Punta Arenas, Chile, active between 1911 and the mid-1920s. FOM was targeted in a deadly arson attack in 1920.
Diario Financiero is a Chilean economic newspaper founded by a group of journalists from the Economy and Business Corps of El Mercurio on October 25, 1988. It is currently controlled by the Claro Group. The tabloid has been using the orange paper that distinguishes economic media in the world since its June 19, 1989 edition, such as the Financial Times and Il Sole 24 ORE. Its main competence is the "Economy and Business" body of El Mercurio, Pulso of the Copesa and Estrategia.
Rubidium sulfide is an inorganic compound and a salt with the chemical formula Rb2S. It is a white solid with similar properties to other alkali metal sulfides.
Ruthenium(III) fluoride is a fluoride of ruthenium, with the chemical formula of RuF3.