Design Implications of Model-Generated Urban Data

Published by the Architectural Research Centers Consortium under the terms of the Attribution-NonCommercial-ShareAlike 4.0 International license.The staggering complexity of urban environment and long timescales in the causal mechanisms prevent designers to fully understand the implications of their design interventions. In order to investigate these causal mechanisms and provide measurable trends, a model that partially replicates urban complexity has been developed. Using a cellular automata approach to model land use types and markets for products, services, labour and property, the model has enabled numerical experiments to be carried out. The results revealed causal mechanisms and performance metrics obtained in a much shorter timescale than the real-life processes, pointing to a number of design implications for urban environments.Peer reviewedFinal Published versio

Cellular Automata are Generic

Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular automaton with unconstrained topology and with the power to create new cells. The advantage is that the latter is closer to physical reality. The overhead of our simulation is quadratic.Comment: In Proceedings DCM 2014, arXiv:1504.0192

Growth and Decay in Life-Like Cellular Automata

We propose a four-way classification of two-dimensional semi-totalistic cellular automata that is different than Wolfram's, based on two questions with yes-or-no answers: do there exist patterns that eventually escape any finite bounding box placed around them? And do there exist patterns that die out completely? If both of these conditions are true, then a cellular automaton rule is likely to support spaceships, small patterns that move and that form the building blocks of many of the more complex patterns that are known for Life. If one or both of these conditions is not true, then there may still be phenomena of interest supported by the given cellular automaton rule, but we will have to look harder for them. Although our classification is very crude, we argue that it is more objective than Wolfram's (due to the greater ease of determining a rigorous answer to these questions), more predictive (as we can classify large groups of rules without observing them individually), and more accurate in focusing attention on rules likely to support patterns with complex behavior. We support these assertions by surveying a number of known cellular automaton rules.Comment: 30 pages, 23 figure

A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton

We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of the intrinsically universal QCA. Several steps of the intrinsically universal QCA then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA.Comment: 13 pages, 7 figures. In Proceedings of the 4th International Conference on Language and Automata Theory and Applications (LATA 2010), Lecture Notes in Computer Science (LNCS). Journal version: arXiv:0907.382

A Quantum Game of Life

This research describes a three dimensional quantum cellular automaton (QCA) which can simulate all other 3D QCA. This intrinsically universal QCA belongs to the simplest subclass of QCA: Partitioned QCA (PQCA). PQCA are QCA of a particular form, where incoming information is scattered by a fixed unitary U before being redistributed and rescattered. Our construction is minimal amongst PQCA, having block size 2 x 2 x 2 and cell dimension 2. Signals, wires and gates emerge in an elegant fashion.Comment: 13 pages, 10 figures. Final version, accepted by Journ\'ees Automates Cellulaires (JAC 2010)

Scale-invariant cellular automata and self-similar Petri nets

Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, "solve" the halting problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations. On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one shows indeterministic behavior whereas the second one halts. Both models are capable of challenging our understanding of computability, causality, and space-time.Comment: 35 pages, 5 figure