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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 Ljapunow exponents (Lyapunow diagrams or Ljapunow fractals or Markus- Ljapunov diagrams). [3] 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. [14] 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. [15] [16]
As editor:
The Sierpiński triangle, also called the Sierpiński gasket or Sierpiński sieve, is a fractal attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self-similar sets—that is, it is a mathematically generated pattern that is reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński, but appeared as a decorative pattern many centuries before the work of Sierpiński.
The Game of Life, also known simply as 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.
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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.
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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:
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
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