O autômato celular Game of LIFE (GL) exibe comportamento coletivo não-trivial (Classe IV de Wolfram) a partir de regras locais simples. Na década de 1990, conjecturou-se que o autômato seria um exemplo de sistema não-conservativo com criticalidade auto-organizada. Nesse trabalho refutamos essa conjectura verificando que o regime transiente para estados absorventes não escala de forma correta para redes grandes. Usando uma aproximação de campo médio com considerações sobre interfaces para a rede quadrada, definimos um parâmetro de controle sigma0 relacionado com a razão de ramificação da interface da fase absorvente. A partir da análise de um grande número de autômatos celulares (6144), encontramos uma transição de fase descontínua no espaço de regras dos autômatos celulares totalistas. Também encontramos que o GL é um autômato celular quasi-crítico, com sigma0=1.006, ou seja, o GL equivale a um processo de nucleação quasi-crítico. Mostramos que essa quasi-criticalidade é resultado da coexistência e competição entre a fase viva e a fase morta: embora o LIFE esteja destinado à extinção (ao estado absorvente morto), o decaimento é adiado devido a um forte ralentamento crítico. / The cellular automaton Game of LIFE exhibits non-trivial collective behavior (Wolfram Class IV) from local simple rules. In the 1990s, it was conjectured that the automaton would be an example of self-organized criticality in non-conservative systems. In this work we refute this conjecture by verifying that the transient regime to absorbing states does not scale for large lattice sizes. By using a mean-field approximation with considerations about interfaces in square lattices, we define a control parameter sigma0 related to the interfacial absorbing phase branching rate. From the analysis of a large number of cellular automata (6144), we find a discontinuous phase transition in the cellular automata rule space. We also find that LIFE is a quasi-critical cellular automaton, with sigma0=1.006, that is, LIFE is a quasi-critical nucleation process. It is shown that this quasi-criticality is a result of coexistence and competition between the living and dead phases: although LIFE is destined to extinction (to the dead absorbing state), this decay is delayed due to a strong critical slowing down.

O autômato celular Game of LIFE (GL) exibe comportamento coletivo não-trivial (Classe IV de Wolfram) a partir de regras locais simples. Na década de 1990, conjecturou-se que o autômato seria um exemplo de sistema não-conservativo com criticalidade auto-organizada. Nesse trabalho refutamos essa conjectura verificando que o regime transiente para estados absorventes não escala de forma correta para redes grandes. Usando uma aproximação de campo médio com considerações sobre interfaces para a rede quadrada, definimos um parâmetro de controle sigma0 relacionado com a razão de ramificação da interface da fase absorvente. A partir da análise de um grande número de autômatos celulares (6144), encontramos uma transição de fase descontínua no espaço de regras dos autômatos celulares totalistas. Também encontramos que o GL é um autômato celular quasi-crítico, com sigma0=1.006, ou seja, o GL equivale a um processo de nucleação quasi-crítico. Mostramos que essa quasi-criticalidade é resultado da coexistência e competição entre a fase viva e a fase morta: embora o LIFE esteja destinado à extinção (ao estado absorvente morto), o decaimento é adiado devido a um forte ralentamento crítico. / The cellular automaton Game of LIFE exhibits non-trivial collective behavior (Wolfram Class IV) from local simple rules. In the 1990s, it was conjectured that the automaton would be an example of self-organized criticality in non-conservative systems. In this work we refute this conjecture by verifying that the transient regime to absorbing states does not scale for large lattice sizes. By using a mean-field approximation with considerations about interfaces in square lattices, we define a control parameter sigma0 related to the interfacial absorbing phase branching rate. From the analysis of a large number of cellular automata (6144), we find a discontinuous phase transition in the cellular automata rule space. We also find that LIFE is a quasi-critical cellular automaton, with sigma0=1.006, that is, LIFE is a quasi-critical nucleation process. It is shown that this quasi-criticality is a result of coexistence and competition between the living and dead phases: although LIFE is destined to extinction (to the dead absorbing state), this decay is delayed due to a strong critical slowing down.

John Horton Conway was a British mathematician in the twentieth century. He made notable achievements in fields such as algebra, number theory, and knot theory. He was a renowned professor at Cambridge University and later Princeton. His contributions to algebra include his discovery of the Conway group, a group in twenty-four dimensions, and the Conway Constellation. He contributed to number theory with his development of the surreal numbers. His Game of Life earned him long-lasting fame. He contributed to knot theory with his developments of the Conway polynomial, Conway sphere, and Conway notation.

The goal of this master thesis is to examine possibilities of realizing comptutational structures in cellular automata. The work describes the fundamental principles of cellular automata and summarizes some ways of how to achive the specified goal. An overview of Turing-complete and other specialized computational tasks is proposed considering both 1D and 2D cellular automata. It is shown that different computational scenarios in cellular automata can be considered with various setups of the input and output arrangements. With regard to showed inputs and outputs arrangement, sets of tests is designed to find solutions of choosen computational structures on cellular automata with use of choosen evolutionary algorithm. Found solutions are compared by computational resources consumption and difficulty of discovery later.

Development of a game in the form of software for game-based learning poses significant technical challenges for educators, researchers, game designers, and software engineers. The game development consists of a set of complex processes requiring multi-faceted knowledge in multiple disciplines such as digital graphic design, education, gaming, instructional design, modeling and simulation, psychology, software engineering, visual arts, and the learning subject area. Planning and managing such a complex multidisciplinary development project require unifying methodologies for development and software quality evaluation and should not be performed in an ad hoc manner. This dissertation presents such methodologies named: GAMED (diGital educAtional gaMe dEvelopment methoDology) and IDEALLY (dIgital eDucational gamE softwAre quaLity evaLuation methodologY). GAMED consists of a body of methods, rules, and postulates and is embedded within a digital educational game life cycle. The life cycle describes a framework for organization of the phases, processes, work products, quality assurance activities, and project management activities required to develop, use, maintain, and evolve a digital educational game from birth to retirement. GAMED provides a modular structured approach for overcoming the development complexity and guides the developers throughout the entire life cycle. IDEALLY provides a hierarchy of 111 indicators consisting of 21 branch and 90 leaf indicators in the form of an acyclic graph for the measurement and evaluation of digital educational game software quality. We developed the GAMED and IDEALLY methodologies based on the experiences and knowledge we have gained in creating and publishing four digital educational games that run on the iOS (iPad, iPhone, and iPod touch) mobile devices: CandyFactory, CandySpan, CandyDepot, and CandyBot. The two methodologies provide a quality-centered structured approach for development of digital educational games and are essential for accomplishing demanding goals of game-based learning. Moreover, classifications provided in the literature are inadequate for the game designers, engineers and practitioners. To that end, we present a taxonomy of games that focuses on the characterization of games. / Ph. D.