DOI: 10.1038/311419a0. Cellular automata as models of complexity

Cellular automata as models of complexity

10.1038/311419a0

Crossref journal-article

Springer Science and Business Media LLC

Nature (297)

Bibliography

Wolfram, S. (1984). Cellular automata as models of complexity. Nature, 311(5985), 419â424.

Authors 1

Stephen Wolfram (first)

References 24 Referenced 1,081

Wolfram, S. Rev. Mod. Phys. 55, 601–644 (1983). (10.1103/RevModPhys.55.601) / Rev. Mod. Phys. by S Wolfram (1983)
Wolfram, S. Physica 10 D, 1–35 (1984). / Physica by S Wolfram (1984)
Wolfram, S. Commun. Math. Phys. (in the press).
Wolfram, S. Cellular Automata (Los Alamos Science, Autumn, 1983). / Cellular Automata by S Wolfram (1983)
Mandelbrot, B. The Fractal Geometry of Nature (Freeman, San Francisco, 1982). / The Fractal Geometry of Nature by B Mandelbrot (1982)
Packard, N., Preprint Cellular Automaton Models for Dendritic Growth (Institute for Advanced Study, 1984). / Cellular Automaton Models for Dendritic Growth by N Packard (1984)
Madore, B. & Freedman, W. Science 222, 615–616 (1983). (10.1126/science.222.4624.615) / Science by B Madore (1983)
Greenberg, J. M., Hassard, B. D. & Hastings, S. P. Bull. Amer. Math. Soc. 84, 1296–1327 (1978). (10.1090/S0002-9904-1978-14560-1) / Bull. Amer. Math. Soc. by JM Greenberg (1978)
Vichniac, G. Physica 10 D, 96–116 (1984). / Physica by G Vichniac (1984)
Domany, E. & Kinzel, W. Phys. Rev. Lett. 53, 311–314 (1984). (10.1103/PhysRevLett.53.311) / Phys. Rev. Lett. by E Domany (1984)
Waddington, C. H. & Cowe, R. J. J. theor. Biol. 25, 219–225 (1969). (10.1016/S0022-5193(69)80060-3) / J. theor. Biol. by CH Waddington (1969)
Lindsay, D. T. Veliger 24, 297–299 (1977). / Veliger by DT Lindsay (1977)
Young, D. A. A Local Activator–Inhibitor Model of Vertebrate Skin Patterns (Lawrence Livermore National Laboratory Rep., 1983). / A Local Activator–Inhibitor Model of Vertebrate Skin Patterns by DA Young (1983)
Guckenheimer, J. & Holmes, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin, 1983). (10.1007/978-1-4612-1140-2) / Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by J Guckenheimer (1983)
Hopcroft, J. E. & Ullman, J. D. Introduction to Automata Theory, Languages, and Computation (Addison-Wesley, New York, 1979). / Introduction to Automata Theory, Languages, and Computation by JE Hopcroft (1979)
Packard, N. Preprint, Complexity of Growing Patterns in Cellular Automata (Institute for Advanced Study, 1983). / Complexity of Growing Patterns in Cellular Automata by N Packard (1983)
Martin, O, Odlyzko, A. & Wolfram, S. Commun. Math. Phys. 93, 219–258 (1984). (10.1007/BF01223745) / Commun. Math. Phys. by O Martin (1984)
Grassberger, P. Physica 10 D, 52–58 (1984). / Physica by P Grassberger (1984)
Lind, D. Physica 10 D, 36–44 (1984). / Physica by D Lind (1984)
Margolus, N. Physica 10 D, 81–95 (1984). / Physica by N Margolus (1984)
Smith, A. R. Journal of the Association for Computing Machinery 18, 339–353 (1971). (10.1145/321650.321652) / Journal of the Association for Computing Machinery by AR Smith (1971)
Berlekamp, E. R., Conway, J. H. & Guy, R. K. Winning Ways for your Mathematical Plays Vol. 2, Ch. 25 (Academic, New York, 1982). / Winning Ways for your Mathematical Plays by ER Berlekamp (1982)
Gardner, M. Wheels, Life and other Mathematical Amusements (Freeman, San Francisco, 1983). / Wheels, Life and other Mathematical Amusements by M Gardner (1983)
Wolfram, S. SMP Reference Manual (Computer Mathematics Group, Inference Corporation, Los Angeles, 1983). / SMP Reference Manual by S Wolfram (1983)

Dates

Type	When
Created	20 years, 9 months ago (Nov. 17, 2004, 10:03 p.m.)
Deposited	2 years, 3 months ago (May 16, 2023, 8:58 p.m.)
Indexed	1 day, 18 hours ago (Aug. 22, 2025, 12:46 a.m.)
Issued	40 years, 10 months ago (Oct. 1, 1984)
Published	40 years, 10 months ago (Oct. 1, 1984)
Published Print	40 years, 10 months ago (Oct. 1, 1984)

Funders 0

None

BibTeX

@article{Wolfram_1984, title={Cellular automata as models of complexity}, volume={311}, ISSN={1476-4687}, url={http://dx.doi.org/10.1038/311419a0}, DOI={10.1038/311419a0}, number={5985}, journal={Nature}, publisher={Springer Science and Business Media LLC}, author={Wolfram, Stephen}, year={1984}, month=oct, pages={419–424} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        22
      ]
    ],
    "date-time": "2025-08-22T04:46:24Z",
    "timestamp": 1755837984516
  },
  "reference-count": 24,
  "publisher": "Springer Science and Business Media LLC",
  "issue": "5985",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1984,
            10,
            1
          ]
        ],
        "date-time": "1984-10-01T00:00:00Z",
        "timestamp": 465436800000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "http://www.springer.com/tdm"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1984,
        10
      ]
    ]
  },
  "DOI": "10.1038/311419a0",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2004,
        11,
        18
      ]
    ],
    "date-time": "2004-11-18T03:03:19Z",
    "timestamp": 1100746999000
  },
  "page": "419-424",
  "source": "Crossref",
  "is-referenced-by-count": 1081,
  "title": "Cellular automata as models of complexity",
  "prefix": "10.1038",
  "volume": "311",
  "author": [
    {
      "given": "Stephen",
      "family": "Wolfram",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "297",
  "reference": [
    {
      "key": "BF311419a0_CR1",
      "doi-asserted-by": "publisher",
      "first-page": "601",
      "DOI": "10.1103/RevModPhys.55.601",
      "volume": "55",
      "author": "S Wolfram",
      "year": "1983",
      "unstructured": "Wolfram, S. Rev. Mod. Phys. 55, 601\u2013644 (1983).",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "BF311419a0_CR2",
      "first-page": "1",
      "volume": "10",
      "author": "S Wolfram",
      "year": "1984",
      "unstructured": "Wolfram, S. Physica 10 D, 1\u201335 (1984).",
      "journal-title": "Physica"
    },
    {
      "key": "BF311419a0_CR3",
      "unstructured": "Wolfram, S. Commun. Math. Phys. (in the press)."
    },
    {
      "key": "BF311419a0_CR4",
      "volume-title": "Cellular Automata",
      "author": "S Wolfram",
      "year": "1983",
      "unstructured": "Wolfram, S. Cellular Automata (Los Alamos Science, Autumn, 1983)."
    },
    {
      "key": "BF311419a0_CR5",
      "volume-title": "The Fractal Geometry of Nature",
      "author": "B Mandelbrot",
      "year": "1982",
      "unstructured": "Mandelbrot, B. The Fractal Geometry of Nature (Freeman, San Francisco, 1982)."
    },
    {
      "key": "BF311419a0_CR6",
      "volume-title": "Cellular Automaton Models for Dendritic Growth",
      "author": "N Packard",
      "year": "1984",
      "unstructured": "Packard, N., Preprint Cellular Automaton Models for Dendritic Growth (Institute for Advanced Study, 1984)."
    },
    {
      "key": "BF311419a0_CR7",
      "doi-asserted-by": "publisher",
      "first-page": "615",
      "DOI": "10.1126/science.222.4624.615",
      "volume": "222",
      "author": "B Madore",
      "year": "1983",
      "unstructured": "Madore, B. & Freedman, W. Science 222, 615\u2013616 (1983).",
      "journal-title": "Science"
    },
    {
      "key": "BF311419a0_CR8",
      "doi-asserted-by": "publisher",
      "first-page": "1296",
      "DOI": "10.1090/S0002-9904-1978-14560-1",
      "volume": "84",
      "author": "JM Greenberg",
      "year": "1978",
      "unstructured": "Greenberg, J. M., Hassard, B. D. & Hastings, S. P. Bull. Amer. Math. Soc. 84, 1296\u20131327 (1978).",
      "journal-title": "Bull. Amer. Math. Soc."
    },
    {
      "key": "BF311419a0_CR9",
      "first-page": "96",
      "volume": "10",
      "author": "G Vichniac",
      "year": "1984",
      "unstructured": "Vichniac, G. Physica 10 D, 96\u2013116 (1984).",
      "journal-title": "Physica"
    },
    {
      "key": "BF311419a0_CR10",
      "doi-asserted-by": "publisher",
      "first-page": "311",
      "DOI": "10.1103/PhysRevLett.53.311",
      "volume": "53",
      "author": "E Domany",
      "year": "1984",
      "unstructured": "Domany, E. & Kinzel, W. Phys. Rev. Lett. 53, 311\u2013314 (1984).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF311419a0_CR11",
      "doi-asserted-by": "publisher",
      "first-page": "219",
      "DOI": "10.1016/S0022-5193(69)80060-3",
      "volume": "25",
      "author": "CH Waddington",
      "year": "1969",
      "unstructured": "Waddington, C. H. & Cowe, R. J. J. theor. Biol. 25, 219\u2013225 (1969).",
      "journal-title": "J. theor. Biol."
    },
    {
      "key": "BF311419a0_CR12",
      "first-page": "297",
      "volume": "24",
      "author": "DT Lindsay",
      "year": "1977",
      "unstructured": "Lindsay, D. T. Veliger 24, 297\u2013299 (1977).",
      "journal-title": "Veliger"
    },
    {
      "key": "BF311419a0_CR13",
      "volume-title": "A Local Activator\u2013Inhibitor Model of Vertebrate Skin Patterns",
      "author": "DA Young",
      "year": "1983",
      "unstructured": "Young, D. A. A Local Activator\u2013Inhibitor Model of Vertebrate Skin Patterns (Lawrence Livermore National Laboratory Rep., 1983)."
    },
    {
      "key": "BF311419a0_CR14",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/978-1-4612-1140-2",
      "volume-title": "Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields",
      "author": "J Guckenheimer",
      "year": "1983",
      "unstructured": "Guckenheimer, J. & Holmes, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin, 1983)."
    },
    {
      "key": "BF311419a0_CR15",
      "volume-title": "Introduction to Automata Theory, Languages, and Computation",
      "author": "JE Hopcroft",
      "year": "1979",
      "unstructured": "Hopcroft, J. E. & Ullman, J. D. Introduction to Automata Theory, Languages, and Computation (Addison-Wesley, New York, 1979)."
    },
    {
      "key": "BF311419a0_CR16",
      "volume-title": "Complexity of Growing Patterns in Cellular Automata",
      "author": "N Packard",
      "year": "1983",
      "unstructured": "Packard, N. Preprint, Complexity of Growing Patterns in Cellular Automata (Institute for Advanced Study, 1983)."
    },
    {
      "key": "BF311419a0_CR17",
      "doi-asserted-by": "publisher",
      "first-page": "219",
      "DOI": "10.1007/BF01223745",
      "volume": "93",
      "author": "O Martin",
      "year": "1984",
      "unstructured": "Martin, O, Odlyzko, A. & Wolfram, S. Commun. Math. Phys. 93, 219\u2013258 (1984).",
      "journal-title": "Commun. Math. Phys."
    },
    {
      "key": "BF311419a0_CR18",
      "first-page": "52",
      "volume": "10",
      "author": "P Grassberger",
      "year": "1984",
      "unstructured": "Grassberger, P. Physica 10 D, 52\u201358 (1984).",
      "journal-title": "Physica"
    },
    {
      "key": "BF311419a0_CR19",
      "first-page": "36",
      "volume": "10",
      "author": "D Lind",
      "year": "1984",
      "unstructured": "Lind, D. Physica 10 D, 36\u201344 (1984).",
      "journal-title": "Physica"
    },
    {
      "key": "BF311419a0_CR20",
      "first-page": "81",
      "volume": "10",
      "author": "N Margolus",
      "year": "1984",
      "unstructured": "Margolus, N. Physica 10 D, 81\u201395 (1984).",
      "journal-title": "Physica"
    },
    {
      "key": "BF311419a0_CR21",
      "doi-asserted-by": "publisher",
      "first-page": "339",
      "DOI": "10.1145/321650.321652",
      "volume": "18",
      "author": "AR Smith",
      "year": "1971",
      "unstructured": "Smith, A. R. Journal of the Association for Computing Machinery 18, 339\u2013353 (1971).",
      "journal-title": "Journal of the Association for Computing Machinery"
    },
    {
      "key": "BF311419a0_CR22",
      "volume-title": "Winning Ways for your Mathematical Plays",
      "author": "ER Berlekamp",
      "year": "1982",
      "unstructured": "Berlekamp, E. R., Conway, J. H. & Guy, R. K. Winning Ways for your Mathematical Plays Vol. 2, Ch. 25 (Academic, New York, 1982)."
    },
    {
      "key": "BF311419a0_CR23",
      "volume-title": "Wheels, Life and other Mathematical Amusements",
      "author": "M Gardner",
      "year": "1983",
      "unstructured": "Gardner, M. Wheels, Life and other Mathematical Amusements (Freeman, San Francisco, 1983)."
    },
    {
      "key": "BF311419a0_CR24",
      "volume-title": "SMP Reference Manual",
      "author": "S Wolfram",
      "year": "1983",
      "unstructured": "Wolfram, S. SMP Reference Manual (Computer Mathematics Group, Inference Corporation, Los Angeles, 1983)."
    }
  ],
  "container-title": "Nature",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "http://www.nature.com/articles/311419a0",
      "content-type": "text/html",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://www.nature.com/articles/311419a0.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://www.nature.com/articles/311419a0.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        5,
        17
      ]
    ],
    "date-time": "2023-05-17T00:58:45Z",
    "timestamp": 1684285125000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://www.nature.com/articles/311419a0"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1984,
        10
      ]
    ]
  },
  "references-count": 24,
  "journal-issue": {
    "issue": "5985",
    "published-print": {
      "date-parts": [
        [
          1984,
          10
        ]
      ]
    }
  },
  "alternative-id": [
    "BF311419a0"
  ],
  "URL": "http://dx.doi.org/10.1038/311419a0",
  "relation": {},
  "ISSN": [
    "0028-0836",
    "1476-4687"
  ],
  "subject": [],
  "container-title-short": "Nature",
  "published": {
    "date-parts": [
      [
        1984,
        10
      ]
    ]
  }
}