Tools for devising cellular automata in the hyperbolic 3D space

被引：0
|
作者：
Margenstern, M
Skordev, G
机构：
[1] Univ Metz, LITA, EA 3097, F-57045 Metz, France
[2] Univ Bremen, CeVis, Fachbereich Math, D-28359 Bremen, Germany
来源：
FUNDAMENTA INFORMATICAE | 2003年 / 58卷 / 3-4期
关键词：
cellular automata; hyperbolic geometry; tilings; combinatorial geometry;
D O I：
暂无
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
The study of cellular automata (CA) on tilings of hyperbolic plane was initiated in [13]. Appropriate tools were developed which allow linear algorithms to implement cellular automata on the tiling of the hyperbolic plane with the regular rectangular pentagon. In this paper we tackle the problem of devising similar tools in the case of the 3D hyperbolic space. The tools are given for the rectangular dodecahedral tiling of the 3D hyperbolic space. We give an algorithm which computes all needed information from the number of a cell. The algorithm is cubic in time and quadratic in space.
引用
收藏
页码：369 / 398
页数：30
相关论文
共 50 条
  • [1] Tools for devising cellular automata in the 3D hyperbolic space, II - The numeric algorithms
    Margenstern, M
    Skordev, G
    6TH WORLD MULTICONFERENCE ON SYSTEMICS, CYBERNETICS AND INFORMATICS, VOL XI, PROCEEDINGS: COMPUTER SCIENCE II, 2002, : 548 - 552
  • [2] Tools for devising cellular automata in the 3D hyperbolic space, I - The geometric algorithm
    Margenstern, M
    Skordev, G
    6TH WORLD MULTICONFERENCE ON SYSTEMICS, CYBERNETICS AND INFORMATICS, VOL XI, PROCEEDINGS: COMPUTER SCIENCE II, 2002, : 542 - 547
  • [3] Simulating 3D cellular automata with 2D cellular automata
    Poupet, V
    MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE 2004, PROCEEDINGS, 2004, 3153 : 439 - 450
  • [4] A universal cellular automaton with five states in the 3D hyperbolic space
    Margenstern, Maurice
    JOURNAL OF CELLULAR AUTOMATA, 2006, 1 (04) : 317 - 351
  • [5] Cyclic cellular automata in 3D
    Reiter, Clifford A.
    CHAOS SOLITONS & FRACTALS, 2011, 44 (09) : 764 - 768
  • [6] 3D surface cellular automata and their applications
    Gobron, S
    Chiba, N
    JOURNAL OF VISUALIZATION AND COMPUTER ANIMATION, 1999, 10 (03): : 143 - 158
  • [7] Time and space complexity classes of hyperbolic cellular automata
    Iwamoto, C
    Margenstern, M
    IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS, 2004, E87D (03): : 700 - 707
  • [8] 3D AUTOCUT: a 3D segmentation algorithm based on cellular automata
    Neto, E. C.
    Cortez, P. C.
    Rodrigues, V. E.
    Cavalcante, T. S.
    Valente, I. R. S.
    ELECTRONICS LETTERS, 2017, 53 (25) : 1640 - 1641
  • [9] A New Weakly Universal Cellular Automaton in the 3D Hyperbolic Space with Two States
    Margenstern, Maurice
    REACHABILITY PROBLEMS, 2011, 6945 : 205 - 217
  • [10] NONLINEAR WAVES ON 3D HYPERBOLIC SPACE
    Metcalfe, Jason
    Taylor, Michael
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (07) : 3489 - 3529
12345