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Tommaso Bolognesi Planar Trinet Dynamics with Two Rewrite Rules A deterministic network mobile automaton is proposed for the creation of planar trivalent networks (trinets) based on the application of only two simple rewrite rules. The possible Brownian dynamics of the control point are enumerated and explored. A useful behavioral complexity indicator is introduced, called the revisit indicator, exposing a variety of emergent features, involving periodic, nested, and random-like dynamics. Regular structures obtained include one-dimensional graphs, oscillating rings, and the two-dimensional hexagonal grid. In two cases only, out of over a thousand that were inspected, a remarkably fair, random-like revisit indicator is found, with trinets that exhibit a slow, square-root growth rate. Some properties of these surprising computations are investigated. Finally, one two-dimensional case is found that seems to be unique in the way regularity and randomness are mixed.
Two-dimensional reversible cellular automata constructions may have utility for modeling problems that entail inherently reversible processes, such as optical propagation. This paper speculates on the potential of methods articulated in A New Kind of Science [1] for addressing inverse problems in optical scatterometry, and then describes preliminary work for two-dimensional reversible cellular automaton schemes.
This paper describes an exploration into what can be done with cellular automata to reinvent and re-engineer electronics in a new kind of physics implemented as a system of cellular automaton rules. An engineering approach is used, working forward to achieve a practical goal while introducing tools. The practical goal is to start from an electron level and obtain a working resistor–capacitor (RC) phase shift oscillator. This goal is achieved, and the oscillator is demonstrated. The paper tells the story of this adventure, including the experiences of failures, retries, work-arounds, and success.
Continuing arguments presented [1] or announced [2, 3] here, zero-divisor (ZD) foundations for scale-free networks (evinced, in particular, in the “fractality” of the Internet) are decentralized. Spandrels, quartets of ZD-free or “hidden” box-kite-like structures (HBKs) in the 2^(N+1)-ions, are “exploded” from (and uniquely linked to) each standard box-kite in the 2^N-ions, N≥4. Any HBK houses, in a cowbird’s nest, exactly one copy of the (ZD-free) octonions, the recursive basis for all ZD ensembles. Each is a potential way-station for alien-ensemble infiltration in the large, or metaphor-like jumps, in the small. Cowbirding models what evolutionary biologists [4], and structural mythologist Claude Lévi-Strauss before them [5], term bricolage: the opportunistic co-opting of objects designed for one purpose to serve others unrelated to it. Such arguments entail a switch of focus, from the octahedral box-kite’s four triangular sails, to its trio of square catamarans and their box-kite-switching twist products.
The main goal of this paper is to develop tools for constructing different kinds of abstract automata based on cellular automata. We call this engineering problem cellular engineering. Different levels of computing systems and models are considered. The emphasis is made on the top-level model called a grid automaton. Our goal is to construct grid automata using cellular automata. To achieve this, we develop a specific technology based on multilevel finite automata. It is proved that two-dimensional cellular automata allow the construction of some types of grid automata, as well as Turing machines and pushdown automata.
We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models.
The iterated finite automaton (IFA) was invented by Stephen Wolfram for studying the conventional finite state automaton (FSA) by means of A New Kind of Science methodology. An IFA is a composition of an FSA and a tape with limited cells. The complexity of behaviors generated by various FSAs operating on different tapes can be visualized by two-dimensional patterns. Through enumerating all possible two-state and three-color IFAs, this paper shows that there are a variety of complex behaviors in these simple computational systems. These patterns can be divided into eight classes such as regular patterns, noisy structures, complex behaviors, and so forth. Also they show the similarity between IFAs and elementary cellular automata. Furthermore, any cellular automaton can be emulated by an IFA and vice versa. That means IFAs support universal computation.
Positive feedbacks between vegetation and fire disturbance may lead to nonlinear ecosystem responses to variation in fire regime. We used a cellular automaton model of fire–vegetation dynamics based on pine savanna communities to explore the potential for fire–vegetation feedbacks to lead to ecological thresholds and abrupt transitions between alternate ecosystem states. We show that (i) ecosystems can rapidly move between grassland and forest states in response to gradual changes in fire regimes or initial landscape composition and that (ii) hurricane disturbances can mediate the frequency of fire that leads to ecological thresholds. Nonlinear ecosystem dynamics lead to sensitivity to initial conditions and bistable ecological communities that can exist in either a grassland or forest state under the same disturbance frequency. Our results indicate that gradual changes in global climate that influence disturbance frequency may result in the rapid transformation of landscapes through feedbacks between fire and vegetation.
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