Universal Cellular Automata in the Hyperbolic Spaces
نویسنده
چکیده
This paper introduces several cellular automata in hyperbolic spaces which are able to simulate any computational device, as they are universal. We sketchily present five universal cellular automata, four of them on two grids of the hyperbolic plane and one in a grid of the hyperbolic 3D space. Key–Words: Theory of Computation, Cellular Automata, universality, hyperbolic geometry.
منابع مشابه
About Strongly Universal Cellular Automata
In this paper, we construct a strongly universal cellular automaton on the line with 11 states and the standard neighbourhood. We embed this construction into several tilings of the hyperbolic plane and of the hyperbolic 3D space giving rise to strongly universal cellular automata with 10 states.
متن کاملCellular Automata and Combinatoric Tilings in Hyperbolic Spaces. A Survey
The first paper on cellular automata in the hyperbolic plane appeared in [37], based on the technical report [35]. Later, several papers appeared in order to explore this new branch of computer science. Although applications are not yet seen, they may appear, especially in physics, in the theory of relativity or for cosmological researches.
متن کاملModeling Urban Sprawling of Tehran Metropolitan Area Based on PSO
The main goal of the present study was to implement a hybrid pattern of cellular automata model and particle swarm optimization algorithm based on TM and ETM+ imagery of landsat satellite from 1988 to 2010 for simulating the urban sprawling. In this study, an alternative model was implemented in two ways: the first method was based on two images (1988 and 2010) and the second one was based on t...
متن کاملUrban Growth Modeling using Integrated Cellular Automata and Gravitational Search Algorithm (Case Study: Shiraz City, Iran)
Cities are growing and encountering many changes over time due to population growth and migration. Identification and detection of these changes play important roles in urban management and sustainable development. Urban growth models are divided into two main categories: first cellular models which are further divided into experimental, dynamic, and integrated models and second vector models. ...
متن کاملUniversal Approximator Property of the Space of Hyperbolic Tangent Functions
In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.
متن کامل