Axiomatic Cellular Automata Modelling as a Promising Way to A General Theory of Ecological Physics

Advantages of the cellular automata modelling. The discrete nature of the real world is naturally to model using discrete mathematics. Cellular automata are the most effective mathematical tool for creating discrete models of complex systems. Logical cellular automata are most effective for individual-based modelling in terms of local dependencies. A particular advantage of the individual-based cellular automata models is that they are able to reflect holistic spatial-temporal mechanisms of dynamic interrelations among all levels of population ecosystem between individuals and their mini habitats and between their mini habitats and the whole ecosystem (macro habitat). The advantages of deterministic cellular automata models are in clarity of their cause-effect relationships, the absence of rounding errors (accuracy), in the simplicity of setting boundary conditions, solvability and holistic relationship of local and global characteristics of models, a detailed mapping of spatial-temporal events. An important feature of this modelling approach is the need for formulation of adequate axioms, based on properties of modelling objects. Correct formulation of the basic interpretations requires a deep and holistic objective knowledge of simulated phenomena. The lattice size, initial cell-states pattern of the whole cellular-automaton field (initial pattern), the type of a neighbourhood and the rules of transitions between states of elementary cell are the key parameters in the cellular-automata modelling. The presented here method can be used in different areas of modelling of competition of agents of any nature. The deterministic cellular automata modelling may be considered as a simple universal inference automaton of mechanistic insight into studied phenomena as it is based on a detailed visualisation of dynamics of all interrelated processes of a complex system under study. A white-box cellular automata modelling is the most direct way to gain a mechanistic insight into a complex system under study. The main problem of such modelling is a creation of adequate axioms. . Let us formulate our understanding of white-box model. White box (‘clear box’, ‘glass box’, ‘open box’) model has a ‘transparent walls’-all events at all levels of the simulated dynamic system and at all stages of its dynamics are directly visible. White box model directly shows mechanistic mechanisms of the studied phenomena. It allows to obtain a new physical understanding of the studied system and to predict its future development. We consider the cellular automata method developed in this study as the white box modelling. A deterministic, individual-based logical cellular-automata method developed in this study is the most suitable tool for search of the mechanistic mechanisms of complex systems. It is the white-box modelling method based on physically interpreted ecological axioms. These cellular automaton works as a visualising inference automaton of mechanistic insight into studied phenomena. It provides reducing of complex holistic dynamics of inter specific competition to the level of simple logical axioms. Deterministic, individualand logic-based cellular automata allow creating white-box mechanistic models of complex systems. This approach allows us to naturally decompose the complex system to the homologous constituent elements, to define the possible states of these elements and transitional logic between these states, taking into account the local conditions of each individual element. The key stage of the cellular automata modelling of a complex system is a formulation of physically adequate axioms. These axioms must represent the highest possible degree of physical generalization of a studied complex system. The necessity of adequate basic understanding of a research area is the main difficulty here. A system of axioms created on the basis of this fundamental understanding is used for formulating rules of automatic logical Volume 2 Issue 1 2017