Abstract: In this talk, I will describe some of the cellular automaton models that have been discussed in physics literature. The aim is to emphasize the diversity of the models, and the real world problems for which these serve as simple models. I will try to show, by examples, the questions of interest to physicists, and the techniques used to determine these. I will start by discussing the box-ball system as a simple model showing “solitons”. Then I discuss the abelian distributed processors model, and its special case the abelian sandpile model on a square lattice. The abelian group structure, characterization of the steady state, and the fat tail in the distribution of avalanches will be discussed. Lastly, I will discuss briefly some probabilistic cellular automata models for modelling relaxation of spins of a magnet, and epidemic spread. I will mention some recent work on stochastic predator-prey system called chase-escape percolation.
Abstract: Brownian Circuits use the fluctuations of signals, implemented by tokens, to drive computation. They have been shown to significantly reduce the required complexity of circuits or platforms implementing these circuits, such as Cellular Automata. The original model of Brownian Circuits eyes computation models, in which operations on individual tokens are at the core. This presentation discusses models in which masses of tokens are used as signals in Brownian Circuits, in particular Neural Networks. We show how previously proposed Brownian Circuit primitives can be employed to implement neural functionality, like thresholding, synchronization, and learning.
Abstract: Cellular automata have a long and rich history of being computational worlds where researchers can study the dynamics of living systems. While these worlds evolve according to relatively simple rules, the resulting state-space dynamics can be complex enough to be irreducible. This is ideal for studying aspects of living systems. Living systems are bound by the laws of physics (and chemistry), yet they cannot be described or predicted using these same laws. Instead, biology evolves according to emergent laws on different scales of spatial organization that continuously change over time. In this talk, I briefly overview the history of cellular automata being used to study living systems and then introduce modern approaches. I also summarize my current and recent work on using cellular automata to understand various aspects of life, including open-endedness and emergent functionality.
Abstract: With his seminal book Stephen Wolfram postulated "A New Kind of Science" for the mathematical model of cellular automata. Focusing a ‘new kind of art’ this paper changes perspective asking for a new aesthetics in a more philosophical sense. Here it reflects the power of the self-organization principle creating complexity based on a minimal set of conditions. Looking back to history, the complete discretization of space, time and state inherent to automata was considered in two complementary conceptual ways: On the one hand it was interpreted as a discrete “caricature” (Bossel 1994) of dynamical systems, especially of models based on continuous differential equations. On the other hand it was comprehended as a digital “calculating space” (Zuse 1969) representing more fundamental physics underlying existing physical models as for instance in quantum physics ('t Hooft 2015). In a more methodological sense, there are two complementary aesthetics reflecting cellular automata either visually or more inspired by music:
- The “morphological” approach practises a visual-formal analysis and classification of activity patterns revealing similarities to the use of visual analogies in art history.
- A musical approach works on a higher abstraction level. Here the behaviour of automata could be analyzed statistically and translated into more temporal patterns. In a special case, a meta behaviour can be highlighted as the composer Iannis Xenakis used it in a sequence of his piece "Horos" to switch instrumentation in case of certain cell configurations (Solomos 2005).
This aesthetic conceptualization finally ends up in the question, if there are visual patterns and sound sequences inherent to automata. Last but not least the automata aesthetics can be understood also as a plea for the arts switching from the simplicity of beauty towards the sublimity of complexity.