Elementary cellular automata are the simplest form of cellular automata, studied extensively by Wolfram in the 1980s. He discovered complex behavior in some of these automata and developed a classification for all cellular automata based on their phenomenology. In this paper, we present an algorithm to classify them more effectively by measuring difference patterns using the Hamming distance. Our classification aligns with Wolfram’s and further categorizes them into additional subclasses. Finally, we have found a heuristic reasoning providing and explanation about why some rules evolve into fractal patterns.
REFERENCES
1.
2.
S.
Wolfram
, Theory and Applications of Cellular Automata
(World Scientific Press
, Singapore
, 1986
).3.
D.
Chowdhury
, L.
Santen
, and A.
Schadschneider
, Phys. Rep.
329
, 199
(2000
). 4.
C.
Burstedde
, K.
Klauck
, A.
Schadschneider
, and J.
Zittartz
, Physica A
295
, 507
(2001
). 5.
S.
Carrasco
, P.
Medina
, J.
Rogan
, and J. A.
Valdivia
, Chaos
30
, 063148
(2020
). 6.
D. H.
Rothman
and J. M.
Keller
, J. Stat. Phys.
52
, 1119
(1988
). 7.
V. R.
Unni
, C. K.
Law
, and A.
Saha
, Chaos
30
, 113141
(2020
). 8.
L.
Kadanoff
, S. R.
Nagel
, L.
Wu
, and S.
Zhou
, Phys. Rev. A
39
, 6524
(1989
). 9.
10.
P.
Tougaw
, L.
Douglas
, and S.
Craig
, J. Appl. Phys.
75
, 1818
(1994
). 11.
S.
Nandi
, B. K.
Kar
, and P.
Pal Chaudhuri
, IEEE Trans. Comput.
43
, 1346
(1994
). 12.
J.
Machiacao
, A. G.
Marco
, and O. M.
Bruno
, Expert Syst. Appl.
39
, 12626
(2012
).13.
J.
Lechleiter
, S.
Girard
, E.
Peralta
, and D.
Clapham
, Science
252
, 123
(1991
). 14.
K. C.
De Carvalho
and T.
Tomé
, Mod. Phys. Lett. B
18
, 873
(2004
). 15.
M.
Redeker
, A.
Adamatzky
, and G. J.
Martínez
, Int. J. Mod. Phys. C
24
, 1350010
(2013
). 16.
17.
K.
Taga
, Y.
Kato
, Y.
Kawahara
, Y.
Yamazaki
, and H.
Nakao
, Chaos
31
, 103121
(2021
). 18.
19.
W.
Li
, N. H.
Packard
, and C. G.
Langton
, Physica D
45
, 77
(1990
). 20.
A.
Wuesche
and M.
Lesser
, “The global dynamics of cellular automata; An atlas of basin of attraction fields of one-dimensional cellular automata,” in The Santa Fe Institute Studies in the Sciences of Complexity
(Addison-Wesley, Reading, MA, 1992).21.
22.
H.-P.
Stricker
, Complex Syst.
32
, 229–251
(2023
).23.
Q.
Lei
, J.
Lee
, X.
Huang
, and S.
Kawasaki
, Entropy
23
, 209
(2021
). 24.
M.
Freedman
and M. B.
Hastings
, Commun. Math. Phys.
376
, 1171
(2020
). 25.
M.
Vispoel
, A. J.
Daly
, and J. M.
Baetens
, Physica D
432
, 133074
(2022
). 26.
See https://www.wolframalpha.com for WolframAlpha computational engine of knowledge .
27.
R.
Hamming
, Bell Syst. Tech. J.
29
, 147
(1950
). 28.
D.
Bazeia
, M. B. P. N.
Pereira
, A. V.
Brito
, B. F.
Oliveira
, and J. G. G. S.
Ramos
, Sci. Rep.
7
, 44900
(2017
). 29.
D.
Bazeia
, J.
Menezes
, B. F.
De Oliveira
, and J. G. G. S.
Ramos
, Europhys. Lett.
119
, 58003
(2017
). 30.
Gaspar
Alfaro
and Miguel A. F.
Sanjuán
, Phys. Rev. E
109
, 014203
(2024
). © 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
