Automaton game4/11/2023 The scaling is universal in the sense that the exponents that characterize correlation functions do not depend on details of the local rules. This refutes speculations that self-organized criticality is a consequence of local conservation11, and supports its relevance to the natural phenomena above, as these do not involve any locally conserved quantities. By contrast to these previous studies, where a local quantity was conserved, 'Life' has no local conservation laws and therefore represents a new type of universality class for self-organized criticality. Such self-organized criticality provides a general mechanism for the emergence of scale-free structures3-5, with possible applications to earth-quakes6,7, cosmology8, turbulence9, biology and economics10. We show that local configurations in the "Game of Life" self-organize into a critical state. Here we adopt a different approach, by using concepts of statistical mechanics to study the system's long-time and large-scale behaviour. Previous interest in 'Life' has focused on the generation of complexity in local configurations indeed, the system has been suggested to mimic aspects of the emergence of complexity in nature1,2. Despite its simplicity, the complex dynamics of the game are poorly understood. It simulates, by means of a simple algorithm, the dynamical evolution of a society of living organisms. THE 'Game of Life'1,2 is a cellular automaton, that is, a lattice system in which the state of each lattice point is determined by local rules. More complicated cellular automata are briefly considered, and connections with dynamical systems theory and the formal theory of computation are discussed. Statistical properties of the structures generated are found to lie in two universality classes, independent of the details of the initial state or the cellular automaton rules. With "random" initial configurations, the irreversible character of the cellular automaton evolution leads to several self-organization phenomena. LIFE's absorbing states in a square lattice, which have a stationary density ($\rho=0$) and an active phase density, with $\rho=0.37$, which contrasts with LIFE's mean-field return map predicts an absorbing vacuum phase Seen as a continuous order-disorder transition in cellular automata (CA) rule Further work and variations of the model were also examined.Ĭonway's cellular automaton Game of LIFE has been conjectured to be aĬritical (or quasicritical) dynamical system. The way that signals (or life) propagate across the grid was described, along with a discussion on how this model could be compared with brain dynamics. As first steps in our study, we used the GoL to simulate the evolution of several neurons (i.e., a statistically significant set, typically a million neurons) and their interactions with the surrounding ones, as well as signal transfer in some simple scenarios. For instance, the timestep is arbitrary, as are the spatial dimensions. We have also considered that the model maintains sufficient flexibility. The model has some important features (i.e., pseudo-criticality, 1/f noise, universal computing), which represent good reasons for its use in brain dynamics modelling. In this work, we explored the possibility of studying brain dynamics using cellular automata, more precisely the famous Game of Life (GoL). Nowadays, computer simulation is playing a key role in the study of such an immense variety of problems. Population decays slower than a hypothetical slope equal to a (fast decaying) negative golden number.īrain dynamics, neuron activity, information transfer in brains, etc., are a vast field where a large number of questions remain unsolved. This result suggests that individual cell For GoL simulations, the Good distribution presented the best performance in log-log linear regression models for individual cell population, whose exponents were far from the golden number. In addition, the Zeta distribution is linked to the famous golden number. The Lerch distribution is then generated, where the Zipf, Zipf-Mandelbrot, Good and Zeta distributions are analyzed as particular cases. In particular, the nonsymmetric entropy is maximized to lead to a general Zipf's law under the special auxiliary information parameters based on Hurwitz-Lerch Zeta function. In this work, GoL is connected to the entropy concept through the maximum nonsymmetric entropy (MaxNSEnt) principle. The GoL frequency distribution of events on log-log scale has been proved to satisfy the power-law scaling. Conway's Game of Life (GoL) is a biologically inspired computational model which can approach the behavior of complex natural phenomena such as the evolution of ecological communities and populations.
0 Comments
Leave a Reply.AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |