Complexity of Langton's Ant

The virtual ant introduced by C. Langton has an interesting behavior, which has been studied in several contexts. Here we give a construction to calculate any boolean circuit with the trajectory of a single ant. This proves the P-hardness of the system and implies, through the simulation of one dimensional cellular automata and Turing machines, the universality of the ant and the undecidability of some problems associated to it.Comment: 8 pages, 9 figures. Complements at http://www.dim.uchile.cl/~agajardo/langto

Multi-Agent Fitness Functions For Evolutionary Architecture

The dynamics of crowd movements are self-organising and often involve complex pattern formations. Although computational models have recently been developed, it is unclear how well their underlying methods capture local dynamics and longer-range aspects, such as evacuation. A major part of this thesis is devoted to an investigation of current methods, and where required, the development of alternatives. The main purpose is to utilise realistic models of pedestrian crowds in the design of fitness functions for an evolutionary approach to architectural design. We critically review the state-of-the-art in pedestrian and evacuation dynamics. The concept of 'Multi-Agent System' embraces a number of approaches, which together encompass important local and longer-range aspects. Early investigations focus on methods-cellular automata and attractor fields-designed to capture these respective levels. The assumption that pattern formations in crowds result from local processes is reflected in two dimensional cellular automata models, where mathematical rules operate in local neighbourhoods. We investigate an established cellular automata and show that lane-formation patterns are stable only in a low-valued density range. Above this range, such patterns suddenly randomise. By identifying and then constraining the source of this randomness, we are only able to achieve a small degree of improvement. Moreover, when we try to integrate the model with attractor fields, no useful behaviour is achieved, and much of the randomness persists. Investigations indicate that the unwanted randomness is associated with 2-lattice phase transitions, where local dynamics get invaded by giant-component clusters during the onset of lattice percolation. Through this in-depth investigation, the general limits to cellular automata are ascertained-these methods are not designed with lattice percolation properties in mind and resulting models depend, often critically, on arbitrarily chosen neighbourhoods. We embark on the development of new and more flexible methodologies. Rather than treating local and global dynamics as separate entities, we combine them. Our methods are responsive to percolation, and are designed around the following principles: 1) Inclusive search provides an optimal path between a pedestrian origin and destination. 2) Dynamic boundaries protect search and are based on percolation probabilities, calculated from local density regimes. In this way, more robust dynamics are achieved. Simultaneously, longer-range behaviours are also specified. 3) Network-level dynamics further relax the constraints of lattice percolation and allow a wider range of pedestrian interactions. Having defined our methods, we demonstrate their usefulness by applying them to lane-formation and evacuation scenarios. Results reproduce the general patterns found in real crowds. We then turn to evolution. This preliminary work is intended to motivate future research in the field of Evolutionary Architecture. We develop a genotype-phenotype mapping, which produces complex architectures, and demonstrate the use of a crowd-flow model in a phenotype-fitness mapping. We discuss results from evolutionary simulations, which suggest that obstacles may have some beneficial effect on crowd evacuation. We conclude with a summary, discussion of methodological limitations, and suggestions for future research

Analogies Between Complex Systems and Phases of Matter

The behavior of a complex system in a changing environment is strongly affected by the system's architecture. We present an analogy between the major phases of matter (solid, liquid, gas) and three major generic architectures of complex systems: tree structures, layered structures and grid networks. This analogy is realized using a graph-based formalism, with nodes and edges in a given configuration. Solid materials are akin to tree structures, especially when we consider that most solids actually have cracks. Solids with cracks between their components can be modeled by nodes (representing each component) and their interconnection, leading to a tree structured hierarchy. Gases made up of molecules can be modeled by nodes (the molecules) with local interconnections representing nearby molecules in space, thus forming a grid network. Liquids can form layers as in a mixture of oil and water. We represent this by connections that are densely horizontal within layers as well as sparsely vertical between layers. A key issue for complex systems is the ease by which they may be changed, which we call the system’s flexibility. Our definition of flexibility indicates that tree structures, like solids, are relatively inflexible and that grid networks, like gases, are extremely flexible, possibly leading to loss of control and chaotic behavior. Like liquids, layered systems are intermediate in flexibility and controllability. Solids, even with cracks, are relatively difficult to modify, whereas gases change internal form so quickly that they can only be constrained; not controlled. Liquids are intermediate in their ability to change form internally. Just as heating solids can lead to liquids, and heating liquids can result in gases, we shall present transformations in the interconnection structure of systems, analogous to heating, that change tree structures into layered ones and layered structures into networks

Explaining Emergence

Emergence is a pregnant property in various fields. It is the fact for a phenomenon to appear surprisingly and to be such that it seems at first sight that it is not possible to predict its apparition. That is the reason why it has often been said that emergence is a subjective property relative to the observer. Some mathematical systems having very simple and deterministic rules nevertheless show emergent behavior. Studying these systems shed a new light on the subject and allows to define a new concept, computational irreducibility, which deals with behaviors that even though they are totally deterministic cannot be predicted without simulating them. Computational irreducibility is then a key for understanding emergent phenomena from an objective point of view that does not need the mention of any observer.Comment: 13 pages, 15 figures, to appear in the forthcoming proceedings of the UM6P Science Week 2023 Complexity Summi

Aesthetic Programming

Aesthetic Programming explores the technical as well as cultural imaginaries of programming from its insides. It follows the principle that the growing importance of software requires a new kind of cultural thinking — and curriculum — that can account for, and with which to better understand the politics and aesthetics of algorithmic procedures, data processing and abstraction. It takes a particular interest in power relations that are relatively under-acknowledged in technical subjects, concerning class and capitalism, gender and sexuality, as well as race and the legacies of colonialism. This is not only related to the politics of representation but also nonrepresentation: how power differentials are implicit in code in terms of binary logic, hierarchies, naming of the attributes, and how particular worldviews are reinforced and perpetuated through computation. Using p5.js, it introduces and demonstrates the reflexive practice of aesthetic programming, engaging with learning to program as a way to understand and question existing technological objects and paradigms, and to explore the potential for reprogramming wider eco-socio-technical systems. The book itself follows this approach, and is offered as a computational object open to modification and reversioning