Thesis (MScEng)--University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references and index.

This thesis aims to better represent a framework for asynchrony. Traditional asynchronous models, particularly those used to simulate cellular automata, have used stochasticity or randomness to generate update times. We claimthat, while they may make good representations of their application, such asynchronousmethods rid themodel of the essence of interesting asynchronous processes. Thus, we attempt to better harness the aspects internal to the decision process of such discretely dynamic cells as those in cellular automata.We propose the maxmin-m model as a suitable model for the asynchronous computation of cellular automata. The model uses maxmin-plus algebra, a special case of which is max-plus algebra. This algebra arises naturally from the cellular automaton requirement that a cell receives the state of its neighbours before updating. The maxmin-m model allows each cell to update after it receives m out of a possible n neighbours' states.The max-plus model shows that, while update times may be asynchronous in real time, there is no loss of information, since the corresponding asynchronous process is bijectively related to the synchronous model. In turn, the cellular automaton output, measured by the Shannon and word entropies, is shown to vary little from the synchronous model. Moreover, this type of asynchrony is simple, i.e. it is deterministically obtained due to the linearity of max-plus algebra.Indeed, the maxmin-m model is also shown to be deterministic and always reaches periodic behaviour. In the long time limit, this model is shown to be represented by a max-plus model, supporting its determinism further. Consequently, the complexity of such a model may be thought to be limited. However, we show through large scale experiments that the case where m is approximately n/2 generates most complex behaviour in terms of large periods and transients to the aforementioned periodic orbits. In particular, the complexity is empirically shown to obey a bell form as a function of m (where m ranges from 1 to n). The resulting cellular automaton simulations indicate a correspondence from the complexity of the update times. Therefore, cellular automaton behaviour may be predictable with the type of asynchrony employed in this thesis.

We extend earlier cellular automata models of spatially extended hypercycles by including an explicit genetic component into the model. This allows us to study the sequence evolution of hypercyclically coupled molecular replicators in addition to considering their population dynamics and spatial organization. In line with previous models, that considered either spatial organization or sequence evolution alone, we find both temporal oscillations of the relative concentration of the species forming the hypercycles as well as the formation of spatial organisations including spiral waves. We also confirm the greatly increased robustness of the spatially extended hypercycle against various classes of parasites. We find the sequence evolution of each of the hypercyclically coupled populations proceeds (after an inital selection-dominated phase) in a drift-like manner that can be described by a diffusion process in sequence space. Kimura's theory of neutral evolution is therefore applicable on long time-scales despite the fact that the hypercycle exhibits extreme periodic changes in population sizes and that are governed solely by frequency-dependent selection.

In order to identify complex systems capable of modeling artificial life, we study the notion of complexity within a class of dynamical systems called cellu- lar automata. We present a novel classification of cellular automata dynamics, which helps us identify interesting behavior in large automaton spaces. We give a detailed comparison of our results to previous methods of dynamics classification. In the second part of the thesis, we study the backward dynamics of cellular au- tomata. We present a novel representation of one-dimensional cellular automata, which can be used to charcterize all their garden of eden configurations. We demonstrate the usefulness of this method on examples. 1

This thesis seeks to experiment with the culmination of social, natural and built paradigms of sustainability using digital generation as an architectural process. Specifically, this thesis will explore cellular automaton and modular design approaches in the context of multifamily housing, asking if we can quantify the qualities of equitable housing and guide digital algorithms to generate efficient, flexible, human centered designs. Cellular automaton is a term used to describe a phenomenon in which the growth of one cell in a plant or animal is entirely dependent upon the already existing adjacent cell. Digital cellular automaton is a mathematical, rule based tool used to generate patterns or to map complex systems; similarly, the generation of new cells is entirely dependent on the environment it is being born into. The aim of this work is to translate human centered parameters and local architectural guidelines into an algorithm with rules which can be easily manipulated to produce comparable digitally generated forms. The parameters will be based on an architectural program consisting of a multi-unit mixed income residential building located in, and designed for the residents of, Northampton, Massachusetts. Northampton is an exemplary small-scale city; a historic New England town with housing problems reminiscent of a larger urban area. The selected site allows for investigations of density, growth, adaptation and modular design in a way that could be applied to not only similarly sized cities, but regions of varying density based on their own local parameters. For a relevant output, the parameters and data put into the algorithm must be humanized, individualized, or in the case of this work, curated to reflect and serve a specific community. Cellular automaton allows for varied pattern generation and for the exploration of repeating modules as well as allow for future adaptations to evolving housing needs and sustainability targets. The goal is to create a supportive system of habitat that allows for growth potential and flexibility without sacrificing quality of life for the inhabitants.

Die Arbeit bildet einen Einstieg in das Themengebiet der prozeduralen Karten Generierung mit Cellular Automata und verweist auf fortführende Möglichkeiten. Es wird gezeigt, wie eine zwei-dimensionale und hexagonale Terrain-Karte für Strategiespiele mit Cellular Automata erzeugt werden kann. Dazu wird eine allgemeine Einführung zu zellulären Automaten gegeben. Zusätzlich werden Fashion-based Cellular Automata und Cellular Automata mit mehreren aktiven Zellen erklärt. Es werden die Anforderungen an eine Karte des Strategie-Genres bestimmt, wobei der Fokus, auf dem durch Civilisation definierten Sub-Genre liegt. Anschließend wird gezeigt, wie die verschiedenen Bestandteile der Karte jeweils mit einem Cellular Automaton generiert werden können. Zu diesen werden Vorteile und Nachteile dargestellt und dabei auf die Performance eingegangen. Es zeigt sich das zelluläre Automaten in der Lage sind eine geeignete Karte zu erzeugen.:1 Einleitung 1.1 Videospiele im Trend 1.2 Produktionsaufwand 1.3 Prozedurale Content Generierung 1.4 Cellular Automata 1.5 Kartengenerierung 1.6 Aufbau der Arbeit 1.7 Verwendete Werkzeuge 2 Hintergrund 2.1 Cellular Automata 2.1.1 Grundsätze 2.1.2 Initiale globale Konfiguration eines CA 2.1.3 CA-Ansätze 2.1.3.1 Lattice Gases 2.1.3.2 CA mit mehreren aktiven Zellen 2.1.3.3 Fashion-based 3 Anforderungsanalyse 3.1 Eingrenzung der Karte 3.2 Betrachtete Spiele 3.3 Analyse der Karten 3.4 Anforderungen 4 Implementierung 4.1 Schichtenmodell 4.1.1 Regionen 4.1.1.1 Ansatz 4.1.1.2 Resultat 4.1.2 Höhenstufen 4.1.2.1 Ansatz 4.1.2.2 Resultat 4.1.3 Flüsse 4.1.3.1 Initiale Konfiguration 4.1.3.2 Flussrichtung 4.1.3.3 Resultat 4.1.4 Ressourcen 4.1.4.1 Wälder 4.1.4.2 Allgemeine Ressourcen 4.1.4.3 Siedlungen 4.1.5 Dynamische Veränderungen 4.1.6 Performance 5 Fazit 5.1 Ausblick 6 Verzeichnisse 6.1 Literaturverzeichnis 6.2 Abbildungsverzeichnis 6.3 Tabellenverzeichnis

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