Polyominoes on a multicolored infinite grid

2020 ◽  
pp. 25-31
Keyword(s):  
Infinite Grid

Introduction

2019 ◽  
pp. 1-12
Author(s):  
Richard Evan Schwartz
Keyword(s):  
Vertical Line ◽  
Absolute Value ◽  
Light Point ◽  
Infinite Grid

This introductory chapter provides an overview of the book, which deals with the plaid model. The plaid model is a rule for assigning a square tiling of the plane to each parameter A = p/q ɛ (0, 1) with pq even. Such parameters are called even rational. Based on the parameter A, even integers are assigned to the lines of the usual infinite grid of integer-spaced vertical and horizontal lines. These integers are called capacities. At the same time, a second grid of slanting lines is defined and odd integers are assigned to these lines. These odd integers are called masses. Then, a light point is placed at every intersection of the form σ‎ ∩ τ‎ where σ‎ is a slanting line, τ‎ is a horizontal or vertical line, and the mass of σ‎ has the same sign as the capacity of τ‎ and smaller absolute value.

scholarly journals Infinite Grid Exploration by Disoriented Robots

2021 ◽  
pp. 129-145
Author(s):  
Quentin Bramas ◽  
Stéphane Devismes ◽  
Pascal Lafourcade
Keyword(s):  
Infinite Grid

scholarly journals INFINITE NETWORKS OF IDENTICAL CAPACITORS

2010 ◽  
Vol 24 (07) ◽  
pp. 695-705 ◽  
Author(s):  
J. H. ASAD ◽  
R. S. HIJJAWI ◽  
A. J. SAKAJI ◽  
J. M. KHALIFEH
Keyword(s):  
Lattice Site ◽  
Superposition Principle ◽  
Square Lattice ◽  
Simple Cubic ◽  
Infinite Grid ◽  
Infinite Networks

The capacitance between the origin and any other lattice site in an infinite square lattice of identical capacitors each of capacitance C is calculated. The method is generalized to infinite Simple Cubic (SC) lattice of identical capacitors each of capacitance C. We make use of the superposition principle and the symmetry of the infinite grid.

Linkage on the infinite grid

2018 ◽  
Vol 137 ◽  
pp. 51-56 ◽  
Author(s):  
Adam S. Jobson ◽  
André E. Kézdy ◽  
Jenő Lehel
Keyword(s):  
Infinite Grid

scholarly journals Optimal (t,r) broadcasts on the infinite grid

2019 ◽  
Vol 255 ◽  
pp. 183-197 ◽  
Author(s):  
Benjamin F. Drews ◽  
Pamela E. Harris ◽  
Timothy W. Randolph
Keyword(s):  
Infinite Grid

scholarly journals Circle formation by asynchronous opaque robots on infinite grid

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Ranendu Adhikary ◽  
Manash Kumar Kundu ◽  
Buddhadeb Sau
Keyword(s):  
Communication System ◽  
Distributed Algorithm ◽  
Line Formation ◽  
Grid Environment ◽  
External Communication ◽  
Formation Problem ◽  
Infinite Grid ◽  
Circle Formation

This paper presents a distributed algorithm for circle formation problem under the infinite grid environment by asynchronous mobile opaque robots. Initially all the robots are acquiring distinct positions and they have to form a circle over the grid. Movements of the robots are restricted only along the grid lines. They do not share any global co-ordinate system. Robots are controlled by an asynchronous adversarial scheduler that operates in Look-Compute-Move cycles. The robots are indistinguishable by their nature, do not have any memory of their past configurations and previous actions. We consider the problem under luminous model, where robots communicate via lights, other than that they do not have any external communication system. Our protocol solves the  circle formation problem using seven colors. A subroutine of our algorithm also solves the line formation problem using three colors.

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