In some recent papers (G. ‘t Hooft and others), it has been argued that quantum mechanics can arise from classical cellular automata. Nonetheless, G. Shpenkov has proved that the classical wave equation makes it possible to derive a periodic table of elements, which is very close to Mendeleyev’s one, and describe also other phenomena related to the structure of molecules. Hence the classical wave equation complements Schrödinger’s equation, which implies the appearance of a cellular automaton molecular model (...) starting from classical wave equation. The other studies show that the microworld is constituted as a tessellation of primary topological balls. The tessellattice becomes the origin of a submicrospic mechanics in which a quantum system is subdivided to two subsystems: the particle and its inerton cloud, which appears due to the interaction of the moving particle with oncoming cells of the tessellattice. The particle and its inerton cloud periodically change the momentum and hence move like a wave. The new approach allows us to correlate the Klein-Gordon equation with the deformation coat that is formed in the tessellatice around the particle. The submicroscopic approach shows that the source of any type of wave movements including the Klein-Gordon, Schrödinger, and classical wave equations is hidden in the tessellattice and its basic exciations – inertons, carriers of mass and inert properies of matter. We also discuss possible correspondence with Konrad Zuse’s calculating space. (shrink)

Cellular automata (henceforth: CA) are discrete, abstract computational systems that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields. Firstly, CA are (typically) spatially and temporally discrete: they are composed of a finite or denumerable set of homogeneous, simple units, the atoms or cells. At each time unit, the cells instantiate one of a finite set of states. They evolve in parallel at discrete time (...) steps, following state update functions or dynamical transition rules: the update of a cell state obtains by taking into account the states of cells in its local neighborhood (there are, therefore, no actions at a distance). Secondly, CA are abstract, as they can be specified in purely mathematical terms and implemented in physical structures. Thirdly, CA are computational systems: they can compute functions and solve algorithmic problems. Despite functioning in a different way from traditional, Turing machine-like devices, CA with suitable rules can emulate a universal Turing machine, and therefore compute, given Turing's Thesis, anything computable.... (shrink)

In this paper I explore the question of how artificial life might be used to get a handle on philosophical issues concerning the mind-body problem. I focus on questions concerning what the physical precursors were to the earliest evolved versions of intelligent life. I discuss how cellular automata might constitute an experimental platform for the exploration of such issues, since cellular automata offer a unified framework for the modeling of physical, biological, and psychological processes. I discuss (...) what it would take to implement in a cellular automaton the evolutionary emergence of cognition from non-cognitive artificial organisms. I review work on the artificial evolution of minimally cognitive organisms and discuss how such projects might be translated into cellular automata simulations. (shrink)

Cellular Automata (CA) based simulations are widely used in a great variety of domains, fromstatistical physics to social science. They allow for spectacular displays and numerical predictions. Are they forall that a revolutionary modeling tool, allowing for “direct simulation”, or for the simulation of “the phenomenon itself”? Or are they merely models "of a phenomenological nature rather than of a fundamental one”? How do they compareto other modeling techniques? In order to answer these questions, we present a systematic (...) exploration of CA’s various uses. (shrink)

A cellular automaton that is related to the "mosaic cycle concept" is considered. We explain why such automata sustain very often, but not always, n-periodic trajectories (n being the number of states of the automaton). Our work is a first step in the direction of a theory of these type of automata which might be useful in modeling mosaic successions.

The objective of this paper is analyzing to which extent the multiverse hypothesis provides a real explanation of the peculiarities of the laws and constants in our universe. First we argue in favor of the thesis that all multiverses except Tegmark’s “mathematical multiverse” are too small to explain the fine tuning, so that they merely shift the problem up one level. But the “mathematical multiverse" is surely too large. To prove this assessment, we have performed a number of experiments with (...) cellular automata of complex behavior, which can be considered as universes in the mathematical multiverse. The analogy between what happens in some automata (in particular Conway’s “Game of Life") and the real world is very strong. But if the results of our experiments can be extrapolated to our universe, we should expect to inhabit—in the context of the multiverse—a world in which at least some of the laws and constants of nature should show a certain time dependence. Actually, the probability of our existence in a world such as ours would be mathematically equal to zero. In consequence, the results presented in this paper can be considered as an inkling that the hypothesis of the multiverse, whatever its type, does not offer an adequate explanation for the peculiarities of the physical laws in our world. (shrink)

Causal Bayes nets (CBNs) can be used to model causal relationships up to whole mechanisms. Though modelling mechanisms with CBNs comes with many advantages, CBNs might fail to adequately represent some biological mechanisms because—as Kaiser (2016) pointed out—they have problems with capturing relevant spatial and structural information. In this paper we propose a hybrid approach for modelling mechanisms that combines CBNs and cellular automata. Our approach can incorporate spatial and structural information while, at the same time, it comes (...) with all the merits of a CBN representation of mechanisms. (shrink)

Some years ago, Hidding et al. suggest that the emergence of intricate and pervasive weblike structure of the Universe on Megaparsec scales can be approximated by a well-known equation from fluid mechanics, the Burgers’ equation. The solution to this equation can be obtained from a geometrical formalism. The resulting Adhesion formalism provides deep insight into the dynamics and topology of the Cosmic Web. It uncovers a direct connection between the conditions in the very early Universe and the complex spatial patterns (...) that emerged out of these under the influence of gravity. In the present paper, we describe a cellular automaton model of the Burgers’ equation, which can be investigated via a fast computer simulation. In the end, this suggests a Cellular Automata Adhesion Model of the Universe. (shrink)

Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular automata theory follows, whose relativistic limit of small wave-vector provides the free dynamics of quantum field theory. The QCA theory can be regarded as an extended quantum field theory that describes in a unified way all scales ranging from an hypothetical discrete Planck scale up to the usual (...) Fermi scale. The present paper reviews the automaton theory for the Weyl field, and the composite automata for Dirac and Maxwell fields. We then give a simple analysis of the dynamics in the momentum space in terms of a dispersive differential equation for narrowband wave-packets. We then review the phenomenology of the free-field automaton and consider possible visible effects arising from the discreteness of the framework. We conclude introducing the consequences of the automaton dispersion relation, leading to a deformed Lorentz covariance and to possible effects on the thermodynamics of ideal gases. (shrink)

In this paper we give a new proof of Richardson's theorem [31]: a global function G[MATHEMATICAL DOUBLE-STRUCK CAPITAL A] of a cellular automaton [MATHEMATICAL DOUBLE-STRUCK CAPITAL A] is injective if and only if the inverse of G[MATHEMATICAL DOUBLE-STRUCK CAPITAL A] is a global function of a cellular automaton. Moreover, we show a way how to construct the inverse cellular automaton using the method of feasible interpolation from [20]. We also solve two problems regarding complexity of cellular (...) automata formulated by Durand [12]. (shrink)

Instead of considering »being with« in terms of non-problematic, machine-like places, where reliable entities assemble in stable relationships, STS conjures up a world where the achievement of chancy stabilisations and synchronisations is local. We have to analyse how and where a certain regularity and predictability in the intersection of scientists and their instruments, say, or of human individuals and groups, is produced. The paper reviews models of emergence drawn from the history of cybernetics—the canonical »black box,« homeostats, and cellular (...) automata—to enrich our imagination of the stabilisation process, and discusses the concept of »variety« as a way of clarifying its difficulty, with the antiuniversities of the 1960s and the Occupy movement as examples. Failures of »being with« are expectable. In conclusion, the paper reviews approaches to collective decision-making that reduce variety without imposing a neoliberal hierarchy. (shrink)

The paradox of biological diversity is the key problem of theoretical ecology. The paradox consists in the contradiction between the competitive exclusion principle and the observed biodiversity. The principle is important as the basis for ecological theory. On a relatively simple model we show a mechanism of indefinite coexistence of complete competitors which violates the known formulations of the competitive exclusion principle. This mechanism is based on timely recovery of limiting resources and their spatio-temporal allocation between competitors. Because of limitations (...) of the black-box modeling there was a problem to formulate the exclusion principle correctly. Our white-box multiscale model of two-species competition is based on logical deterministic individual-based cellular automata. This approach provides an automatic deductive inference on the basis of a system of axioms, and gives a direct insight into mechanisms of the studied system. It is one of the most promising methods of artificial intelligence. We reformulate and generalize the competitive exclusion principle and explain why this formulation provides a solution of the biodiversity paradox. In addition, we propose a principle of competitive coexistence. (shrink)

Instead of considering »being with« in terms of non-problematic, machine-like places, where reliable entities assemble in stable relationships, STS conjures up a world where the achievement of chancy stabilisations and synchronisations is local.We have to analyse how and where a certain regularity and predictability in the intersection of scientists and their instruments, say, or of human individuals and groups, is produced.The paper reviews models of emergence drawn from the history of cybernetics—the canonical »black box,« homeostats, and cellular automata—to (...) enrich our imagination of the stabilisation process, and discusses the concept of »variety« as a way of clarifying its difficulty, with the antiuniversities of the 1960s and the Occupy movement as examples. Failures of »being with« are expectable. In conclusion, the paper reviews approaches to collective decision-making that reduce variety without imposing a neoliberal hierarchy. (shrink)

We present a distributed control modeling approach for an automated manufacturing system based on the dynamics of one-dimensional cellular automata. This is inspired by the fact that both cellular automata and manufacturing systems are discrete dynamical systems where local interactions given among their elements can lead to complex dynamics, despite the simple rules governing such interactions. The cellular automaton model developed in this study focuses on two states of the resources of a manufacturing system, namely, (...) busy or idle. However, the interaction among the resources such as whether they are shared at different stages of the manufacturing process determines the global dynamics of the system. A procedure is shown to obtain the local evolution rule of the automaton based on the relationships among the resources and the material flow through the manufacturing process. The resulting distributed control of the manufacturing system appears to be heterarchical, and the evolution of the cellular automaton exhibits a Class II behavior for some given disordered initial conditions. (shrink)

Complexity is pleased to announce the installment of Prof Hiroki Sayama as its new Chief Editor. In this Editorial, Prof Sayama describes his feelings about his recent appointment, discusses some of the journal’s journey and relevance to current issues, and shares his vision and aspirations for its future.

After leading to a new axiomatic derivation of quantum theory, the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles, the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. (...) Being discrete it can describe localized states and measurements, solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (shrink)