arXiv subjects

Genaro J. Martinez

Publications and source records attributed to Genaro J. Martinez.

At least 19 recordsLinked to original sources

arXiv2025

Post-apocalyptic computing from cellular automata

Cellular automata are arrays of finite state machines that can exist in a finite number of states. These machines update their states simultaneously based on specific local rules that govern their interactions. This framework provides a simple yet powerful model for studying complex systems and emergent behaviors. We revisit and reconsider the traditional notion of an algorithm, proposing a novel perspective in which algorithms are represented through the dynamic state-space configurations of cellular automata. By doing so, we establish a conceptual framework that connects computation to physical processes in a unique and innovative way. This approach not only enhances our understanding of computation but also paves the way for the future development of unconventional computing devices. Such devices could be engineered to leverage the inherent computational capabilities of physical, chemical, and biological substrates. This opens up new possibilities for designing systems that are more efficient, adaptive, and capable of solving problems in ways that traditional silicon-based computers cannot. The integration of cellular automata into these domains highlights their potential as a transformative tool in the ongoing evolution of computational theory and practice.

nlin.CG↗

arXiv2024

On complexity of colloid cellular automata

The colloid cellular automata do not imitate the physical structure of colloids but are governed by logical functions derived from the colloids. We analyse the space-time complexity of Boolean circuits derived from the electrical responses of colloids: ZnO (zinc oxide, an inorganic compound also known as calamine or zinc white, which naturally occurs as the mineral zincite), proteinoids (microspheres and crystals of thermal abiotic proteins), and combinations thereof to electrical stimulation. To extract Boolean circuits from colloids, we send all possible configurations of two-, four-, and eight-bit binary strings, encoded as electrical potential values, to the colloids, record their responses, and thereby infer the Boolean functions they implement. We map the discovered functions onto the cell-state transition rules of cellular automata (arrays of binary state machines that update their states synchronously according to the same rule) -- the colloid cellular automata. We then analyse the phenomenology of the space-time configurations of the automata and evaluate their complexity using measures such as compressibility, Shannon entropy, Simpson diversity, and expressivity. A hierarchy of phenomenological and measurable space-time complexity is constructed.

nlin.CG↗

arXiv2022

Computing with Modular Robots

Propagating patterns are used to transfer and process information in chemical and physical prototypes of unconventional computing devices. Logical values are represented by fronts of traveling diffusive, trigger or phase waves. We apply this concept of pattern based computation to develop experimental prototypes of computing circuits implemented in small modular robots. In the experimental prototypes the modular robots Cubelets are concatenated into channels and junction. The structures developed by Cubelets propagate signals in parallel and asynchronously. The approach is illustrated with a working circuit of a one-bit full adder. Complementarily a formalization of these constructions are developed across Sleptsov nets. Finally, a perspective to swarm dynamics is discussed.

cs.RO↗

arXiv2021

On Wave-Based Majority Gates with Cellular Automata

We demonstrate a discrete implementation of a wave-based majority gate in a chaotic Life-like cellular automaton. The gate functions via controlling of patterns' propagation into stationary channels. The gate presented is realisable in many living and non-living substrates that show wave-like activity of its space-time dynamics or pattern propagation. In the gate a symmetric pattern represents a binary value 0 while a non-symmetric pattern represents a binary value 1. Origination of the patterns and their symmetry type are encoded by the particle reactions at the beginning of computation. The patterns propagate in channels of the gate and compete for the space at the intersection of the channels. We implement 3-inputs majority gates using a W topology showing additional implementations of 5-inputs majority gates and one tree (cascade) majority gate.

cs.ET↗

arXiv2021

Visualization of the Computation Process of a Universal Register Machine

Universal register machine, a formal model of computation, can be emulated on the array of the Game of Life, a two-dimensional cellular automaton. We perform spectral analysis on the computation dynamical process of the universal register machine on the Game of Life. The array is divided into small sectors and the power spectrum is calculated from the evolution in each sector. The power spectrum can be classified into four categories by its shape; null, white noise, sharp peaks, and power law. By representing the shape of power spectrum by a mark, we can visualize the activity of the sector during the computation process. For example, the track of pulse moving between components of the universal register machine and the position of frequently modified registers can be identified. This method can expose the functional difference in each region of computing machine.

cs.FL↗

arXiv2020

Random Expansion Method for the Generation of Complex Cellular Automata

The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic background. Frequently, this type of automata has been found through either an exhaustive search or a meticulous construction of the evolution rule. In this study, the specification of cellular automata with complex behaviors was obtained by utilizing randomly generated specimens. In particular, it proposed that a cellular automaton of $n$ states should be specified at random and then extended to another automaton with a higher number of states so that the original automaton operates as a periodic background where the additional states serve to define the gliders. Moreover, this study presented an explanation of this method. Furthermore, the random way of defining complex cellular automata was studied by using mean-field approximations for various states and local entropy measures. This specification was refined with a genetic algorithm to obtain specimens with a higher degree of complexity. With this methodology, it was possible to generate complex automata with hundreds of states, demonstrating that randomly defined local interactions with multiple states can construct complexity.

nlin.CG↗

arXiv2020

On complex dynamics from reversible cellular automata

Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing instances of complex cellular automata; however, most of the proposed methods are based on a careful search or a meticulous construction of evolution rules. This paper presents the emergence of complex behaviors based on reversible cellular automata. In particular, this paper shows that reversible cellular automata represent an adequate framework to obtain complex behaviors adding only new random states. Experimental results show that complexity can be obtained from reversible cellular automata appending a proportion of about two times more states at random than the original number of states in the reversible automaton. Thus, it is possible to obtain complex cellular automata with dozens of states. Complexity appears to be commonly obtained from reversible cellular automata, and using other operations such as permutations of states or row and column permutations in the evolution rule. The relevance of this paper is to present that reversibility can be a useful structure to implement complex behaviors in cellular automata.

nlin.CG↗

arXiv2020

On patterns and dynamics of Rule 22 cellular automaton

Rule 22 elementary cellular automaton (ECA) has a 3--cell neighborhood, binary cell states, where a cell takes state `1' if there is exactly one neighbor, including the cell itself, in state `1'. In Boolean terms the cell-state transition is a XOR function of three cell states. In physico--chemical terms the rule might be seen as describing propagation of self-inhibiting quantities/species. Space-time dynamics of Rule 22 demonstrates non-trivial patterns and quasi-chaotic behavior. We characterize the phenomena observed in this rule using mean field theory, attractors, de Bruijn diagrams, subset diagrams, filters, fractals and memory.

nlin.CG↗

arXiv2020

Computational universality of fungal sandpile automata

Hyphae within the mycelia of the ascomycetous fungi are compartmentalised by septa. Each septum has a pore that allows for inter-compartmental and inter-hyphal streaming of cytosol and even organelles. The compartments, however, have special organelles, Woronin bodies, that can plug the pores. When the pores are blocked, no flow of cytoplasm takes place. Inspired by the controllable compartmentalisation within the mycelium of the ascomycetous fungi we designed two-dimensional fungal automata. A fungal automaton is a cellular automaton where communication between neighbouring cells can be blocked on demand. We demonstrate computational universality of the fungal automata by implementing sandpile cellular automata circuits there. We reduce the Monotone Circuit Value Problem to the Fungal Automaton Prediction Problem. We construct families of wires, cross-overs and gates to prove that the fungal automata are P-complete.

cs.ET↗

arXiv2020

Fungal Automata

We study a cellular automaton (CA) model of information dynamics on a single hypha of a fungal mycelium. Such a filament is divided in compartments (here also called cells) by septa. These septa are invaginations of the cell wall and their pores allow for flow of cytoplasm between compartments and hyphae. The septal pores of the fungal phylum of the Ascomycota can be closed by organelles called Woronin bodies. Septal closure is increased when the septa become older and when exposed to stress conditions. Thus, Woronin bodies act as informational flow valves. The one dimensional fungal automata is a binary state ternary neighbourhood CA, where every compartment follows one of the elementary cellular automata (ECA) rules if its pores are open and either remains in state `0' (first species of fungal automata) or its previous state (second species of fungal automata) if its pores are closed. The Woronin bodies closing the pores are also governed by ECA rules. We analyse a structure of the composition space of cell-state transition and pore-state transitions rules, complexity of fungal automata with just few Woronin bodies, and exemplify several important local events in the automaton dynamics.

nlin.CG↗

arXiv2019

Universal One-Dimensional Cellular Automata Derived for Turing Machines and its Dynamical Behaviour

Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular automaton with a 2-linear time and display its spatial dynamics. Three particular Turing machines are converted in three universal one-dimensional cellular automata, they are: binary sum, rule 110 and a universal reversible Turing machine.

nlin.CG↗

arXiv2019

Brief Notes and History Computing in Mexico during 50 years

The history of computing in Mexico can not 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.

cs.GL↗

arXiv2018

Logical Gates via Gliders Collisions

An elementary cellular automaton with memory is a chain of finite state machines (cells) updating their state simultaneously and by the same rule. Each cell updates its current state depending on current states of its immediate neighbours and a certain number of its own past states. Some cell-state transition rules support gliders, compact patterns of non-quiescent states translating along the chain. We present designs of logical gates, including reversible Fredkin gate and controlled NOT gate, implemented via collisions between gliders.

nlin.CG↗

arXiv2016

On plant roots logical gates

Theoretical constructs of logical gates implemented with plant roots are morphological computing asynchronous devices. Values of Boolean variables are represented by plant roots. A presence of a plant root at a given site symbolises the logical {\sc True}, an absence the logical {\sc False}. Logical functions are calculated via interaction between roots. Two types of two-inputs-two-outputs gates are proposed: a gate $\langle x, y \rangle \rightarrow \langle xy, x+y \rangle$ where root apexes are guided by gravity and a gate $\langle x, y \rangle \rightarrow \langle \overline{x}y, x \rangle$ where root apexes are guided by humidity. We propose a design of binary half-adder based on the gates.

cs.ET↗

arXiv2016

A Computation in a Cellular Automaton Collider Rule 110

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.

nlin.CG↗

arXiv2014

Designing Complex Dynamics in Cellular Automata with Memory

Since their inception at {\it Macy conferences} in later 1940s complex systems remain the most controversial topic of inter-disciplinary sciences. The term `complex system' is the most vague and liberally used scientific term. Using elementary cellular automata (ECA), and exploiting the CA classification, we demonstrate elusiveness of `complexity' by shifting space-time dynamics of the automata from simple to complex by enriching cells with {\it memory}. This way, we can transform any ECA class to another ECA class --- without changing skeleton of cell-state transition function --- and vice versa by just selecting a right kind of memory. A systematic analysis display that memory helps `discover' hidden information and behaviour on trivial --- uniform, periodic, and non-trivial --- chaotic, complex --- dynamical systems.

nlin.CG↗

arXiv2013

A Note on Elementary Cellular Automata Classification

We overview and compare classifications of elementary cellular automata, including Wolfram's, Wuensche's, Li and Packard, communication complexity, power spectral, topological, surface, compression, lattices, and morphological diversity classifications. This paper summarises several classifications of elementary cellular automata (ECA) and compares them with a newly proposed one, that induced by endowing rules with memory.

nlin.CG↗

arXiv2013

Bio-imitaiton of Mexican migration routes to the USA with slime mould on 3D terrains

Plasmodium of Physarum polycephalum is a large single cell visible by unaided eye. It shows sophisticated behavioural traits in foraging for nutrients and developing an optimal transport network of protoplasmic tubes spanning sources of nutrients. When placed in an environment with distributed sources of nutrients the cell 'computes' an optimal graph spanning the nutrients by growing a network of protoplasmic tubes. P. polycephalum imitates development of man-made transport networks of a country when configuration of nutrients represents major urban areas. We employ this feature of the slime mould to imitate mexican migration to USA. The Mexican migration to USA is the World's largest migration system. We bio-physically imitate the migration using slime mould P. polycephalum. In laboratory experiments with 3D Nylon terrains of USA we imitated development of migratory routes from Mexico-USA border to ten urban areas with high concentration of Mexican migrants. From results of laboratory experiments we extracted topologies of migratory routes, and highlighted a role of elevations in shaping the human movement networks.

cs.ET↗