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The history of computing in Mexico cannot be thought without the name of Prof. Harold V. McIntosh (1929–2015). For almost 50 years, in Mexico, he contributed to the development of computer science with wide international recognition. Approximately in 1964, McIntosh began working in the Physics Department of the Advanced Studies Center (CIEA) of the National Polytechnic Institute (IPN), now called CINVESTAV. In 1965, at the National Center of Calculus (CeNaC), he was a founding member of the Master in Computing, first in Latin America. With the support of Mario Baez Camargo and Enrique Melrose, McIntosh continues his research of Martin-Baltimore Computer Center and University of Florida at IBM 709.

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We describe the design and implementation of a modular and distributed robot that physically simulates functioning of a 2-symbols Turing machine. The robot is constructed with Cubelets (small autonomous robot-cubes used for teaching basic robotics and programming for kids) and Lego® bricks (thus the robot is called CULET). The Cubelets robotic blocks allow for a high level programming: instead of a traditional code, the robots are programmed by assembling various elementary blocks of robots together. We illustrate how read and write operations are physically implemented by the CULET.

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 (resources) 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.

Harold V. McIntosh mars 11, 1929 — november 30, 2015
Harold V. McIntosh died November 30, 2015 in Puebla, Mexico. He was an American mathematical physicist who became interested in what is now known as computer algebra to solve problems in physics, leading to his early adoption of the programming language LISP and to programming language design. In addition, his deep understanding of Weyl’s theory for second order differential equations, Schrödinger quantization as an eigenvalue problem and his proposed computational scheme for Weyl’s mfunction
provided a novel way to investigate metastable states in atomic and molecular physics and reformulate standard scattering theory from a new angle.
McIntosh was born in Colorado in 1929. In 1949 he received a B.Sc. in physics from the Colorado Agricultural and Mechanical College, and in 1952 he received a M.Sc. in mathematics from Cornell University.
Mac (as he preferred to be called) was widely regarded for his research, writing and teaching. Even as a graduate student his gift for inducing people to learn was evident. In a profile of Sheldon Glashow published in The Atlantic Monthly in 1984, (1) Glashow asserted that what he learned as an undergraduate at Cornell from Mac about group theory “was as relevant as any course [he] took there.”
Mac did further graduate studies at Brandeis, but stopped before receiving a Ph.D. to take a job at the Aberdeen Proving Ground. Two years later, he moved to RIAS (Research Institute for Advanced Studies), a division of the Glenn L. Martin Company. Around 1962 he accepted a position in the Physics and Astronomy department and the Quantum Theory Project at the University of Florida. After two years at the University of Florida, Mac was invited to work in Mexico, where he was offered “access to all the computer time he could use,” an offer that, he
said, was fully honored.
Mac worked from 1964 to 1965 at the Department of Physics of the CIEA del IPN, now Cinvestav (Center for Research and Advanced Studies of the National Polytechnic Institute); the design and implementation of the programming language CONVERT took place during this period. From 1965 to 1966, Mac was director of the programming department at the Electronic Computing Center of the National Autonomous University of Mexico, where he designed and developed the programming language REC.
Over the following nine years, Mac was a professor at the School of Physics and Mathematics (ESFM) of the IPN, where he became coordinator of the Applied Mathematics group. Under his guidance, compilers for REC were built for newer computers arriving at the IPN’s CeNaC (National Computing Center), and he personally developed software packages for use in the various courses he taught. Of fourteen bachelor’s theses he directed at the ESFM, one stands out for having been published as three separate articles in the Journal of Mathematical Physics, one of which (2) discusses a problem in a class that is now called “MICZ Kepler systems”, the initials standing for McIntosh, Cisneros and Zwanziger. Also from this period, Mac’s paper Symmetry and Degeneracy (3) was cited enthusiastically three times in the second edition of Herbert Goldstein’s renowned classical mechanics book.4 He took a one-year leave from ESFM in 1972 to obtain his Ph.D. in Quantum Chemistry, which was awarded with the highest distinction, at Uppsala University. Mac’s contributions to the Uppsala Resonance Group led to several doctoral dissertations in Sweden.
Between 1970 and 1975 Mac was also a consultant at the National Nuclear Energy Institute (INEN, now ININ), and in 1975 he and his group moved to the Autonomous University of Puebla (UAP), where he founded the Department of Microcomputer Applications in the UAP’s Institute of Sciences, and where he remained until his passing. He taught courses to computer science students from UAP’s School of Physical and Mathematical Sciences and over the last two and a half decades his interests turned to the study of cellular automata, in which he also became a recognized expert.
Mac will be missed by his friends, colleagues and former students, especially for his lifelong dedication to teaching, high standards and uncompromising principles.
1. R.P. Crease and C.C. Mann, “How the Universe works,” The Atlantic Monthly, Aug. 1984, pp. 66–93.
2. H.V. McIntosh and A. Cisneros, “Degeneracy in the Presence of a Magnetic Monopole,” J. Math. Phys. 11, 896–916 (1970).
3. H.V. McIntosh, “Symmetry and Degeneracy,” in Group Theory and its Applications, Vol. 2, Ernest M. Loebl, ed. (New York: Academic Press, 1971, pp. 75–144)
4. Herbert Goldstein, Classical Mechanics, 2nd. ed. (Reading, MA: AddisonWesley, 1980).
Submitted by: Gerardo Cisneros1 and Erkki Brändas2
Affiliations:
1 Mexico City
2 Uppsala University
Uppsala, Sweden

This paper examines the claim that cellular automata (CA) belonging to
Class III (in Wolfram's classification) are capable of (Turing
universal) computation. We explore some chaotic CA (believed to belong
to Class III) reported over the course of the CA history, that may be
candidates for universal computation, hence spurring the discussion on
Turing universality on both Wolfram's classes III and IV.
Available online at: http://arxiv.org/abs/1304.1242

One-dimensional cellular automata are dynamical systems characterized by discreteness (in space and time), determinism and local interaction. We present a procedure in order to calculate ancestors for a given sequence of states, this procedure is based on a special kind of graph called subset diagram. We use this diagram to specify subset tables for calculating ancestors which are not Garden-of-Eden sequences, hence the process is able to yield ancestors in several generations. Some examples are illustrated using the cellular automaton Rule 110 which is the most interesting automaton of two states and three neighbors.

This paper explains the properties of amalgamations and permutations of states in the matrix representation of reversible one-dimensional cellular automata where both evolution rules have neighborhood size 2 and a Welch index equal to 1. These properties are later used for constructing reversible automata and defining a compact nomenclature to identify them. Some examples are provided.

Gliders in one-dimensional cellular automata are compact groups of
non-quiescent and non-ether patterns (ether represents a periodic background)
translating along automaton lattice. They are cellular-automaton analogous of
localizations or quasi-local collective excitations travelling in a spatially
extended non-linear medium. They can be considered as binary strings or symbols
travelling along a one-dimensional ring, interacting with each other and
changing their states, or symbolic values, as a result of interactions. We
analyse what types of interaction occur between gliders travelling on a
cellular automaton `cyclotron' and build a catalog of the most common
reactions. We demonstrate that collisions between gliders emulate the basic
types of interaction that occur between localizations in non-linear media:
fusion, elastic collision, and soliton-like collision. Computational outcomes
of a swarm of gliders circling on a one-dimensional torus are analysed via
implementation of cyclic tag systems.

Reversible cellular automata (RCA) are models of massively parallel computation that preserve information. They consist of
an array of identical finite state machines that change their states synchronously according to a local update rule. By selecting
the update rule properly the system has been made information preserving, which means that any computation process can be
traced back step-by-step using an inverse automaton. We investigate the maximum range in the array that a cell may need to
see in order to determine its previous state. We provide a tight upper bound on this inverse neighborhood size in the one-dimensional
case: we prove that in a RCA with n states the inverse neighborhood is not wider than n–1, when the neighborhood in the forward direction consists of two consecutive cells. Examples are known where range n–1 is needed, so the bound is tight. If the forward neighborhood consists of m consecutive cells then the same technique provides the upper bound n
m − 1–1 for the inverse direction.

We report recent developments in the modeling of fluid dynamics, and give experimental results (including dynamical exponents) obtained using cellular automata machines. Because of their locality and uniformity, cellular automata lend themselves to an extremely efficient physical realization; with a suitable architecture, an amount of hardware resources comparable to that of a home computer can achieve (in the simulation of cellular automata) the performance of a conventional supercomputer.

Collision-Based Computing presents a unique overview of computation with mobile self-localized patterns in non-linear media, including computation in optical media, mathematical models of massively parallel computers, and molecular systems.
It covers such diverse subjects as conservative computation in billiard ball models and its cellular-automaton analogues, implementation of computing devices in lattice gases, Conway's Game of Life and discrete excitable media, theory of particle machines, computation with solitons, logic of ballistic computing, phenomenology of computation, and self-replicating universal computers.
Collision-Based Computing will be of interest to researchers working on relevant topics in Computing Science, Mathematical Physics and Engineering. It will also be useful background reading for postgraduate courses such as Optical Computing, Nature-Inspired Computing, Artificial Intelligence, Smart Engineering Systems, Complex and Adaptive Systems, Parallel Computation, Applied Mathematics and Computational Physics.

Reversible one-dimensional cellular automata are studied from the perspective of Welch Sets. This paper presents an algorithm to generate random Welch sets that define a reversible cellular automaton. Then, properties of Welch sets are used in order to establish two bipartite graphs describing the evolution rule of reversible cellular automata. The first graph gives an alternative representation for the dynamics of these systems as block mappings and shifts. The second graph offers a compact representation for the evolution rule of reversible cellular automata. Both graphs and their matrix representations are illustrated by the generation of random reversible cellular automata with 6 and 18 states.

We present computer models of nano-scale computing circuits based on propagation of localised excitations or defects in complexes of polymer chain rings. A cyclotron automata are sets of rings of one-dimensional array of finite states (cellular automata) which exhibits a wide range of travelling localisations (gliders). When information (e.g. values of logical variables) is encoded in the initial positions and velocity vectors of the gliders the cyclotron automata are becoming power abstract machines which execute high-performance computing. The computing is based on collisions between the mobile localisations. We present collisions that emulate basic types of interactions between localisations typical for spatially-extended non-linear media: fusion, particles, elastic collision, and soliton-like collision, all they implement basic computing primitives. Mobile localisations in complex one-dimensional cellular automata are compact sets of non-quiescent patterns translating along evolution space. These non-trivial patterns can be coded as binary strings (regular expressions) or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions and computation.

A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations). The constructions proposed are based on universality of elementary cellular automaton rule 110, cyclic tag systems, supercolliders, and computing on rings.

This volume, with a foreword by Sir Roger Penrose, discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? How does nature compute? The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and philosophical implications. The volume provides a state-of-the-art collection of technical papers and non-technical essays, representing a field that assumes information and computation to be key in understanding and explaining the basic structure underpinning physical reality. It also includes a new edition of Konrad Zuse's “Calculating Space” (the MIT translation), and a panel discussion transcription on the topic, featuring worldwide experts in quantum mechanics, physics, cognition, computation and algorithmic complexity. The volume is dedicated to the memory of Alan M Turing — the inventor of universal computation, on the 100th anniversary of his birth, and is part of the Turing Centenary celebrations. © 2013 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.

The purpose of this paper is to prove a conjecture made by Stephen Wolfram in 1985, that an elementary one dimensional cellular automaton known as "Rule 110" is capable of universal computation. I developed this proof of his conjecture while assisting Stephen Wolfram on research for A New Kind of Science [1].

A classic problem in elementary cellular automata (ECAs) is the
specification of numerical tools to represent and study their dynamical
behaviour. Mean field theory and basins of attraction have been commonly
used; however, although the first case gives the long term estimation of
density, frequently it does not show an adequate approximation for the
step-by-step temporal behaviour; mainly for non-trivial behaviour. In
the second case, basins of attraction display a complete representation
of the evolution of an ECA, but they are limited up to configurations of
32 cells; and for the same ECA, one can obtain tens of basins to
analyse. This paper is devoted to represent the dynamics of density in
ECAs for hundreds of cells using only two surfaces calculated by the
nearest-neighbour interpolation. A diversity of surfaces emerges in this
analysis. Consequently, we propose a surface and histogram based
classification for periodic, chaotic and complex ECA.

Two algorithms for calculating reversible one-dimensional cellular automata of neighborhood size 2 are presented. It is explained how this kind of automata represents all the rest. Using two basic properties of these systems such as the uniform multiplicity of ancestors and Welch indices, these algorithms only require matrix products and the transitive closure of binary relations to yield the calculation of reversible automata. The features, advantages and dierences of these algorithms are described and results for re- versible automata of 3, 4, 5 and 6 states are comprised.

From the Preface (See Front Matter for full Preface) Man has within a single generation found himself sharing the world with a strange new species: the computers and computer-like machines. Neither history, nor philosophy, nor common sense will tell us how these machines will affect us, for they do not do "work" as did machines of the Industrial Revolution. Instead of dealing with materials or energy, we are told that they handle "control" and "information" and even "intellectual processes." There are very few individuals today who doubt that the computer and its relatives are developing rapidly in capability and complexity, and that these machines are destined to play important (though not as yet fully understood) roles in society's future. Though only some of us deal directly with computers, all of us are falling under the shadow of their ever-growing sphere of influence, and thus we all need to understand their capabilities and their limitations. It would indeed be reassuring to have a book that categorically and systematically described what all these machines can do and what they cannot do, giving sound theoretical or practical grounds for each judgment. However, although some books have purported to do this, it cannot be done for the following reasons: a) Computer-like devices are utterly unlike anything which science has ever considered---we still lack the tools necessary to fully analyze, synthesize, or even think about them; and b) The methods discovered so far are effective in certain areas, but are developing much too rapidly to allow a useful interpretation and interpolation of results. The abstract theory---as described in this book---tells us in no uncertain terms that the machines' potential range is enormous, and that its theoretical limitations are of the subtlest and most elusive sort. There is no reason to suppose machines have any limitations not shared by man.

We demonstrate the structural invertibility of all reversible one- and two-dimensional cellular automata. More precisely,
we prove that every reversible two-dimensional cellular automaton can be expressed as a combination of four block permutations,
and some shift-like mappings. Block permutations are very simple functions that uniformly divide configurations into rectangular
regions of equal size and apply a fixed permutation on all regions.

Conservative logic is a comprehensive model of computation which explicitly reflects a number of fundamental principles of physics, such as the reversibility of the dynamical laws and the conservation of certainadditive quantities (among which energy plays a distinguished role). Because it more closely mirrors physics than traditional models of computation, conservative logic is in a better position to provide indications concerning the realization of high-performance computing systems, i.e., of systems that make very efficient use of the computing resources actually offered by nature. In particular, conservative logic shows that it is ideally possible to build sequential circuits with zero internal power dissipation. After establishing a general framework, we discuss two specific models of computation. The first uses binary variables and is the conservative-logic counterpart of switching theory; this model proves that universal computing capabilities are compatible with the reversibility and conservation constraints. The second model, which is a refinement of the first, constitutes a substantial breakthrough in establishing a correspondence between computation and physics. In fact, this model is based on elastic collisions of identical balls, and thus is formally identical with the atomic model that underlies the (classical) kinetic theory of perfect gases. Quite literally, the functional behavior of a general-purpose digital computer can be reproduced by a perfect gas placed in a suitably shaped container and given appropriate initial conditions.

In this paper, we investigate some combinatorial aspects ofC-surjective local maps, i.e., local maps inducing surjective global maps,C
F
-surjective local maps, i.e., local maps inducing surjective restrictions of global maps on the setC
F
of finite configurations, andC-injective local maps, i.e., local maps inducing injective local maps, of one-dimensional tessellation automata.We introduce a pair of right and left bundle-graphs and a pair of right and left-bundle-graphs for everyC-surjective local map. We give characterizations forC
F
-surjectivity,C-injectivity and some other properties ofC-surjective local maps in relation to these bundle-graphs. We also establish some properties of the inverse of aC-injective local map.

In this paper we investigate the possible neighborhood size of the inverse automaton of some types of one-dimensional reversible cellular automata. Considering only the case when the local function is a size two map, we give a quadratic upper bound for the neighborhood size of the inverse automaton. We show that this bound can be lowered in some particular cases, and give an algorithm for computing these better bounds.

An algorithm is presented for determining reversibility characteristics of 1-dimensional cellular automaton laws. The concept of local reversibility is defined. Each locally reversible automaton is shown to be isomorphic to a member of the class of “center-reversible” automata. Algorithms are described for generating the set of center-reversible laws and the set of center-reversible additive laws.

A programming language is described which is applicable to problems conveniently described by transformation rules. By this we mean that patterns may be prescribed, each being associated with a skeleton, so that a series of such pairs may be searched until a pattern is found which matches an expression to be transformed. The conditions for a match are governed by a code which allows sub-expressions to be identified and eventually substituted into the corresponding skeleton. The primitive patterns and primitive skeletons are described, as well as the principles which allow their elaboration into more complicated patterns and skeletons. The advantages of the language are that it allows one to apply transformation rules to lists and arrays as easily as strings, that both patterns and skeletons may be defined recursively, and that as a consequence programs may be stated quite concisely.

neurons The human brain consists of about 10 11 neurons of various types; each neuron typically connects, via an axon that eventually branches out into strands and substrands, to many thousand neurons. The firing of a neuron is mostly an all-or-nothing business; this discrete character is retained as the pulse travels down an axon. However, upon arrival to a destination neuron the pulse is handled by a synaptic interface characterized by an analog parameter (typically, an excitation or inhibition weight) whose value may be to some extent history-dependent. The complete physiological picture is rather complex. A drastically simplified model of a neuron, proposed by McCulloch and Pitts[38], is shown in Fig. 5. The neuron can be in one of two states, +1 and Gamma1, which may be thought of as `on' and `off', or `true' and `false'; this state appears at the neuron's output. The inputs may come from other neurons or from external stimuli. State updating may be synchronous (all neurons ...

MBLISP was never properly documented, although some of its features were the subject of a series of Program Notes from the Quantum Chemistry Group of the University of Florida. One

- H V Mcintosh

McIntosh HV. The fundamental logic translator I. A scheme for the automatic programming of large electronic computers. Baltimore: RIAS. (Technical report 62-2); The fundamental logic translator II. List processor. Baltimore: RIAS.
(Technical report 62-9). MBLISP was never properly documented, although some of its features were the subject
of a series of Program Notes from the Quantum Chemistry Group of the University of Florida. One, "Operators for
MBLISP", Program Note no. 9, has some importance as a precursor of the REC, 1962.

The mathematical theory of machines, Boolean algebra, combinatorial and sequential circuits, semigroups. Escuela Superior de Física y Matemáticas

- H V Mcintosh

McIntosh HV. The mathematical theory of machines, Boolean algebra, combinatorial and sequential circuits, semigroups. Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, México, 1967.

Ecuaciones diferenciales y teoría de weyl sistemas lineales de ecuaciones diferenciales con un enfoque geométrico-matricial. México: Porra Print

- S V Chapa-Vergara
- A Menéses
- H V Mcintosh

Chapa-Vergara SV, Menéses A, McIntosh HV. Ecuaciones diferenciales y teoría de weyl sistemas lineales de ecuaciones diferenciales con un enfoque geométrico-matricial. México: Porra Print; 2015.

- M M Soriano
- C Lemaitre
- Primera Década De La Computación En Mxico

Soriano MM, Lemaitre C. Primera década de la computación en Mxico: 1958-1968. Ciencia y Desarrollo. Vol. 60-61.
CONACyT; 1985.

Calculating ancestors in one-dimensional cellular automata

- J C Seck-Tuoh-Mora
- G J Martínez
- H V Mcintosh

Seck-Tuoh-Mora JC, Martínez GJ, McIntosh HV. Calculating ancestors in one-dimensional cellular automata. Inter J
Mod Phys C. 2004;15(8):1151-1169.

Procedures for calculating reversible one-dimensional cellular automata

- J C Seck-Tuoh-Mora
- S V Chapa-Vergara
- G J Martínez

Seck-Tuoh-Mora JC, Chapa-Vergara SV, Martínez GJ, et al. Procedures for calculating reversible one-dimensional
cellular automata. Phys D Nonlinear Phen. 2005;202(1-2):134-141.

Rule 110 as it relates to the presence of gliders

- H V Mcintosh

McIntosh HV. Rule 110 as it relates to the presence of gliders. 1999. Available from: http://delta.cs.cinvestav.mx/ mcintosh/comun/RULE110W/rule110.pdf

Computing with virtual cellular automata collider

- G J Martínez
- A Adamatzky
- H V Mcintosh

Martínez GJ, Adamatzky A, McIntosh HV. Computing with virtual cellular automata collider. Proceedings of the 2015
Science and Information Conference (SAI);

- U K London

London, UK, 2017. p. 62-68. DOI:10.1109/SAI.2015.7237127

Difusión y divulgación de la computación cuántica en méxico y allende sus fronteras

- S E Venegas Andraca

Venegas Andraca SE. Difusión y divulgación de la computación cuántica en méxico y allende sus fronteras. XXII
Congreso Nacional de Divulgación de la Ciencia y la Técnica. Guanajuato, Mxico: Universidad de Guanajuato; 2018.

- G J Martínez
- Obituary
- V Harold
- Mcintosh

Martínez GJ. Obituary: prof. Harold V. McIntosh. J Cell Auto. 2016;11(23):265-269.

13 volumes of the collection of SIG/M programs (Special Interest Group for Computer of New Jersey), dedicated to the distribution of CP/M programs. Each volume was distributed on an 8-inch disc

- H V Mcintosh

McIntosh HV. 13 volumes of the collection of SIG/M programs (Special Interest Group for Computer of New Jersey),
dedicated to the distribution of CP/M programs. Each volume was distributed on an 8-inch disc. Especially a program
from this collection, 80T86, originally written in Convert, was widely used in the US. UU To translate programs in 8080
processor code to programs for the 8086 processor. 1986.