184規則
184規則 是種一維二進制細胞自動機規則, 在解決多數問題(majority problem)以及同時描述幾個看似完全不同的粒子系統時有着應用：
- 184規則可以用來簡單模擬一條單向車道上的車流，並形成了描述更複雜交通流量模型的細胞自動機模型的基礎。[1]
- 184規則還可以用於模擬顆粒沉積到不規則表面上的過程，每個步驟中都會有表面的局部最小值被顆粒填充。在執行模擬的每個步驟時，顆粒的數量是不斷增加的。 一旦放置，粒子就不再移動。
- 184規則還可以根據彈道湮滅的概念來理解，系統中不同的粒子通過一維介質向左向右移動。當兩個移動方向不同的粒子碰撞時，它們彼此湮滅，使得在執行完每個步驟後，粒子數只能保持不變或者減少。
以上描述雖然有着的明顯矛盾，但是可以通過設置不同的自動機狀態與粒子的相關關係來描述不同的問題。
定義
[編輯]184規則的自動機狀態由一維的單元陣列組成，每個單元包含二進制值（0或1）。其中0可以表示道路可以可用，1可以表示車輛。 在其演化的每個步驟中，184規則自動機同時對所有細胞使用以下規則生成下一個陣列中的每個細胞，以確定每個細胞的新狀態：[2]
| 當前狀態 | 111 | 110 | 101 | 100 | 011 | 010 | 001 | 000 |
|---|---|---|---|---|---|---|---|---|
| 中心細胞的新狀態 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 |
此規則的；之所以命名為184規則，是因為描述上述狀態表的Wolfram代碼的最後三行：10111000，由二進制轉換為十進制時是數字184。
有好幾種不同的方式直觀地描述184規則：
交通流量
[編輯]
表面沉積
[編輯]
彈道湮滅
[編輯]
參見
[編輯]註釋
[編輯]- ^ E.g. see Fukś (1997).
- ^ This rule table is already given in a shorthand form in the name "Rule 184", but it can be found explicitly e.g. in Fukś (1997).
參考文獻
[編輯]- Alonso-Sanz, Ramon. Number-preserving rules. Discrete Systems with Memory. World Scientific series on nonlinear science, Ser. A 75. World Scientific. 2011: 55–57 [2017-02-02]. ISBN 9789814343633. （原始內容存檔於2020-09-20）.
- Belitsky, Vladimir; Ferrari, Pablo A. Ballistic annihilation and deterministic surface growth. Journal of Statistical Physics. 1995, 80 (3–4): 517–543. Bibcode:1995JSP....80..517B. doi:10.1007/BF02178546.
- Biham, Ofer; Middleton, A. Alan; Levine, Dov. Self-organization and a dynamic transition in traffic-flow models. Physical Review A. 1992, 46 (10): R6124–R6127. Bibcode:1992PhRvA..46.6124B. PMID 9907993. arXiv:cond-mat/9206001
. doi:10.1103/PhysRevA.46.R6124. - Boccara, Nino; Fukś, Henryk. Cellular automaton rules conserving the number of active sites. Journal of Physics A: Math. Gen. 1998, 31 (28): 6007–6018. Bibcode:1998JPhA...31.6007B. arXiv:adap-org/9712003 . doi:10.1088/0305-4470/31/28/014.
- Capcarrere, Mathieu S.; Sipper, Moshe; Tomassini, Marco. Two-state, r = 1 cellular automaton that classifies density (PDF). Physical Review Letters. 1996, 77 (24): 4969–4971. Bibcode:1996PhRvL..77.4969C. PMID 10062680. doi:10.1103/PhysRevLett.77.4969.
- Chopard, Bastien; Droz, Michel. Cellular Automata Modeling of Physical Systems. Cambridge University Press. 1998. ISBN 0-521-67345-3.
- Chowdhury, Debashish; Santen, Ludger; Schadschneider, Andreas. Statistical physics of vehicular traffic and some related systems. Physics Reports. 2000, 329 (4): 199–329. Bibcode:2000PhR...329..199C. arXiv:cond-mat/0007053 . doi:10.1016/S0370-1573(99)00117-9.
- Fukś, Henryk. Solution of the density classification problem with two similar cellular automata rules. Physical Review E. 1997, 55 (3): R2081–R2084. Bibcode:1997PhRvE..55.2081F. doi:10.1103/PhysRevE.55.R2081.
- Fukś, Henryk; Boccara, Nino. Generalized deterministic traffic rules (PDF). International Journal of Modern Physics C. 1998, 9 (1): 1–12 [2017-02-02]. Bibcode:1998IJMPC...9....1F. doi:10.1142/S0129183198000029. （原始內容存檔 (PDF)於2007-09-27）.
- Fukui, M.; Ishibashi, Y. Traffic flow in 1D cellular automaton model including cars moving with high speed. Journal of the Physical Society of Japan. 1996, 65 (6): 1868–1870. Bibcode:1996JPSJ...65.1868F. doi:10.1143/JPSJ.65.1868.
- Gaylord, Richard J.; Nishidate, Kazume. Traffic Flow. Modeling Nature: Cellular Automata Simulations with Mathematica. Springer-Verlag. 1996: 29–34. ISBN 978-0-387-94620-7.
- Krug, J.; Spohn, H. Universality classes for deterministic surface growth. Physical Review A. 1988, 38 (8): 4271–4283. Bibcode:1988PhRvA..38.4271K. PMID 9900880. doi:10.1103/PhysRevA.38.4271.
- Land, Mark; Belew, Richard. No perfect two-state cellular automata for density classification exists. Physical Review Letters. 1995, 74 (25): 1548–1550. Bibcode:1995PhRvL..74.5148L. PMID 10058695. doi:10.1103/PhysRevLett.74.5148.
- Li, Wentian. Power spectra of regular languages and cellular automata (PDF). Complex Systems. 1987, 1: 107–130 [2017-02-02]. （原始內容 (PDF)存檔於2007-10-07）.
- Li, Wentian. Phenomenology of nonlocal cellular automata. Journal of Statistical Physics. 1992, 68 (5–6): 829–882. Bibcode:1992JSP....68..829L. doi:10.1007/BF01048877.
- Maerivoet, Sven; De Moor, Bart. Cellular automata models of road traffic. Physics Reports. 2005, 419 (1): 1–64. Bibcode:2005PhR...419....1M. arXiv:physics/0509082 . doi:10.1016/j.physrep.2005.08.005.
- Moreira, Andres. Universality and decidability of number-conserving cellular automata. Theoretical Computer Science. 2003, 292 (3): 711–721. arXiv:nlin.CG/0306032 . doi:10.1016/S0304-3975(02)00065-8.
- Nagel, Kai. Particle hopping models and traffic flow theory. Physical Review E. 1996, 53 (5): 4655–4672. Bibcode:1996PhRvE..53.4655N. arXiv:cond-mat/9509075 . doi:10.1103/PhysRevE.53.4655.
- Nagel, Kai; Schreckenberg, Michael. A cellular automaton model for freeway traffic. Journal de Physique I. 1992, 2 (12): 2221–2229. Bibcode:1992JPhy1...2.2221N. doi:10.1051/jp1:1992277.
- Pivato, M. Defect particle kinematics in one-dimensional cellular automata. Theoretical Computer Science. 2007, 377 (1–3): 205–228. arXiv:math.DS/0506417 . doi:10.1016/j.tcs.2007.03.014.
- Redner, Sidney. 8.5 Ballistic Annihilation. A Guide to First-Passage Processes. Cambridge University Press. 2001: 288 [2017-02-02]. ISBN 9780521652483. （原始內容存檔於2020-09-14）.
- Sukumar, N. Effect of boundary conditions on cellular automata that classify density. 1998. arXiv:comp-gas/9804001 .
- Tadaki, Shin-ichi; Kikuchi, Macato. Jam phases in a two-dimensional cellular automaton model of traffic flow. Physical Review E. 1994, 50 (6): 4564–4570. Bibcode:1994PhRvE..50.4564T. doi:10.1103/PhysRevE.50.4564.
- Wang, Bing-Hong; Kwong, Yvonne-Roamy; Hui, Pak-Ming. Statistical mechanical approach to Fukui-Ishibashi traffic flow models. Physical Review E. 1998, 57 (3): 2568–2573. Bibcode:1998PhRvE..57.2568W. doi:10.1103/PhysRevE.57.2568.
- Wolfram, Stephen. A New Kind of Science. Wolfram Media. 2002.
