MANY-DIMENSIONAL LORENTZ CELLULAR AUTOMATA AND TURING MACHINES

1996 ◽  
Vol 06 (06) ◽  
pp. 1127-1135 ◽  
Author(s):  
LEONID A. BUNIMOVICH
Keyword(s):  
Cellular Automata ◽  
Artificial Life ◽  
Lattice Gases ◽  
Square Lattice ◽  
Turing Machines ◽  
Natural Conditions ◽  
Vortex Sheets ◽  
Cubic Lattices ◽  
Higher Dimensional ◽  
Lorentz Lattice Gases

We study the class of cellular automata that generalizes the Lorentz lattice gases in statistical mechanics, the models of industrious ants in the theory of an artificial life and the so-called Tur-mites (many-dimensional Turing machines). We prove that on the square lattice ℤd, d = 2, the existence of a bounded orbit of a particle (ant, machine) determines all nondegenerate local scattering rules (states of a machine). For higher dimensional (d ≥ 3) cubic lattices we show that under some natural conditions all possible bounded orbits (vortices) can live only in some “vortex sheets” that have a dimension strictly less than d.

Lorentz Lattice Gases and Many-Dimensional Turing Machines

2002 ◽  
pp. 443-467 ◽  
Author(s):  
Leonid A. Bunimovich ◽  
Milena A. Khlabystova
Keyword(s):  
Lattice Gases ◽  
Turing Machines ◽  
Lorentz Lattice Gases

MODELING THE SINOATRIAL NODE BY CELLULAR AUTOMATA WITH IRREGULAR TOPOLOGY

2010 ◽  
Vol 21 (01) ◽  
pp. 107-127 ◽  
Author(s):  
DANUTA MAKOWIEC
Keyword(s):  
Cellular Automata ◽  
Sinoatrial Node ◽  
Single Cells ◽  
Square Lattice ◽  
Proper Function ◽  
System Control ◽  
Cyclic Activity ◽  
Cellular Dynamics ◽  
Horizontal Connections ◽  
Intercellular Connections

The role of irregularity in intercellular connections is studied in the first natural human pacemaker called the sinoatrial node by modeling with the Greenberg–Hastings cellular automata. Facts from modern physiology about the sinoatrial node drive modeling. Heterogeneity between cell connections is reproduced by a rewiring procedure applied to a square lattice. The Greenberg–Hastings rule, representing the intrinsic cellular dynamics, is modified to imitate self-excitation of each pacemaker cell. Moreover, interactions with nearest neighbors are changed to heterogeneous ones by enhancing horizontal connections. Stationary states of the modeled system emerge as self-organized robust oscillatory states. Since the sinoatrial node role relies on a single cell cyclic activity, properties of single cells are studied. It appears that the strength and diversity of cellular oscillations depend directly on properties of intrinsic cellular dynamics. But these oscillations also depend on the underlying topology. Moderate nonuniformity of intercellular connections are found vital for proper function of the sinoatrial node, namely, for producing robust oscillatory states that are able to respond effectively to the autonomic system control.

Computational Foundations of the Anticipatory Artificial Autopoietic Cellular Automata

2021 ◽  
pp. 289-307
Author(s):  
Daniel M. Dubois ◽  
Stig C. Holmberg
Keyword(s):  
Artificial Intelligence ◽  
Cellular Automata ◽  
Living Cell ◽  
Artificial Life ◽  
Initial Conditions ◽  
Living Cells ◽  
Asymmetric Membrane

A survey of the Varela automata of autopoiesis is presented. The computation of the Varela program, with initial conditions given by a living cell, is not able to self-maintain the membrane of the living cell. In this chapter, the concept of anticipatory artificial autopoiesis (AAA) is introduced. In this chapter, the authors present a new algorithm of the anticipatory artificial autopoiesis, which extend the Varela automata. The main enhancement consists in defining an asymmetric membrane of the artificial lining cell. The simulations show the anticipatory generation of artificial living cells starting with any initial conditions. The new concept of anticipatory artificial autopoiesis is related to artificial life (Alife) and artificial intelligence (AI). This is a breakthrough in the computational foundation of autopoiesis.

scholarly journals Complexity-theoretic aspects of expanding cellular automata

2020 ◽  
Author(s):  
Augusto Modanese
Keyword(s):  
Cellular Automata ◽  
Polynomial Time ◽  
Time Complexity ◽  
Truth Table ◽  
Decision Problems ◽  
Turing Machines ◽  
One Dimensional ◽  
Alternative Characterization ◽  
Time Class ◽  
Theoretical Standpoint

Abstract The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between existing ones. The respective polynomial-time complexity class is shown to coincide with $${\le _{tt}^p}(\textsf {NP})$$ ≤ tt p ( NP ) , that is, the class of decision problems polynomial-time truth-table reducible to problems in $$\textsf {NP}$$ NP . An alternative characterization based on a variant of non-deterministic Turing machines is also given. In addition, corollaries on select XCA variants are proven: XCAs with multiple accept and reject states are shown to be polynomial-time equivalent to the original XCA model. Finally, XCAs with alternative acceptance conditions are considered and classified in terms of $${\le _{tt}^p}(\textsf {NP})$$ ≤ tt p ( NP ) and the Turing machine polynomial-time class $$\textsf {P}$$ P .

Theoretical Models of Cooperative Dynamics Near the Glass Transition

1990 ◽  
Vol 215 ◽  
Author(s):  
Josef Jäckle
Keyword(s):  
Glass Transition ◽  
Lattice Gas ◽  
Finite Size ◽  
Theoretical Models ◽  
Lattice Gases ◽  
Bootstrap Percolation ◽  
Square Lattice ◽  
High Particle Concentration ◽  
High Particle ◽  
Percolation Problem

AbstractIt is shown that diffusion in the hard-square and hard-octahedron lattice gases at high particle concentration has cooperative properties resembling molecular relaxation in undercooled liquids near the glass transition. For these models a characteristic length of cooperativity is introduced by an underlying percolation problem, which determines whether permanently blocked particles exist in lattices of finite size. The percolation problem belongs to a general class of bootstrap percolation models. Salient Monte Carlo results for the concentration and size dependence of self diffusion in the hard-square lattice gas are presented. Similarities with the n-spin facilitated kinetic Ising models are also pointed out.

Sign in / Sign up

Export Citation Format

Share Document