Garden of Eden (cellular automaton) (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Garden of Eden (cellular automaton)" in English language version.

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17doi.org

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8ams.org

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3harvard.edu

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2maa.org

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2semanticscholar.org

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1conwaylife.com

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1uni-bielefeld.de

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1complex-systems.com

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ams.org

mathscinet.ams.org

Toffoli & Margolus (1990). Note however that Toffoli and Margolus refer to the transition function as the global map. Toffoli, Tommaso; Margolus, Norman (1990), "Invertible cellular automata: a review", Physica D: Nonlinear Phenomena, 45 (1–3): 229–253, Bibcode:1990PhyD...45..229T, doi:10.1016/0167-2789(90)90185-R, MR 1094877
Kari (1990); Kari (1994). Kari's main result is that it is undecidable to test whether a cellular automaton is reversible, but he also shows the undecidability of testing whether a Garden of Eden exists. Kari, Jarkko (1990), "Reversibility of 2D cellular automata is undecidable", Physica D, 45 (1–3): 379–385, Bibcode:1990PhyD...45..379K, doi:10.1016/0167-2789(90)90195-U Kari, Jarkko (1994), "Reversibility and surjectivity problems of cellular automata", Journal of Computer and System Sciences, 48 (1): 149–182, doi:10.1016/S0022-0000(05)80025-X, MR 1259654
Toffoli & Margolus (1990): "Even if one were willing to fall back on a brute-force search, a long search time would generate only a few items, and even those would be for the most part quite uninteresting." Toffoli, Tommaso; Margolus, Norman (1990), "Invertible cellular automata: a review", Physica D: Nonlinear Phenomena, 45 (1–3): 229–253, Bibcode:1990PhyD...45..229T, doi:10.1016/0167-2789(90)90185-R, MR 1094877
Sutner (1991). Sutner, Klaus (1991), "De Bruijn graphs and linear cellular automata" (PDF), Complex Systems, 5: 19–30, MR 1116419
Ceccherini-Silberstein, Machì & Scarabotti (1999); Capobianco, Guillon & Kari (2013); Bartholdi2019. Ceccherini-Silberstein, T. G.; Machì, A.; Scarabotti, F. (1999), "Amenable groups and cellular automata", Annales de l'Institut Fourier, 49 (2): 673–685, doi:10.5802/aif.1686, MR 1697376 Capobianco, Silvio; Guillon, Pierre; Kari, Jarkko (2013), "Surjective cellular automata far from the Garden of Eden", Discrete Mathematics & Theoretical Computer Science, 15 (3): 41–60, MR 3141826 Bartholdi, Laurent (2019), "Amenability of groups is characterized by Myhill's theorem", Journal of the European Mathematical Society, 21 (10), with an appendix by Dawid Kielak: 3191–3197, arXiv:1605.09133, doi:10.4171/JEMS/900, MR 3994103
Gromov (1999). Gromov, M. (1999), "Endomorphisms of symbolic algebraic varieties", Journal of the European Mathematical Society, 1 (2): 109–197, doi:10.1007/PL00011162, MR 1694588, Zbl 0998.14001
Gottschalk (1973). Gottschalk, Walter (1973), "Some general dynamical notions", Recent Advances in Topological Dynamics (Proc. Conf. Topological Dynamics, Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund), Lecture Notes in Mathematics, vol. 318, Springer-Verlag, pp. 120–125, doi:10.1007/BFb0061728, ISBN 978-3-540-06187-8, MR 0407821
Ceccherini-Silberstein & Coornaert (2010). Ceccherini-Silberstein, Tullio; Coornaert, Michel (2010), "Surjunctive groups", Cellular automata and groups, Springer Monographs in Mathematics, Springer-Verlag, pp. 57–75, doi:10.1007/978-3-642-14034-1_3, ISBN 978-3-642-14033-4, MR 2683112

archive.org

Blackford, Ikin & McMullen (1999); Hayles (2005). Blackford, Russell; Ikin, Van; McMullen, Sean (1999), "Greg Egan", Strange constellations: a history of Australian science fiction, Contributions to the study of science fiction and fantasy, vol. 80, Greenwood Publishing Group, pp. 190–200, ISBN 978-0-313-25112-2 Hayles, N. Katherine (2005), "Subjective cosmology and the regime of computation: intermediation in Greg Egan's fiction", My mother was a computer: digital subjects and literary texts, University of Chicago Press, pp. 214–240, ISBN 978-0-226-32147-9

arxiv.org

Ceccherini-Silberstein, Machì & Scarabotti (1999); Capobianco, Guillon & Kari (2013); Bartholdi2019. Ceccherini-Silberstein, T. G.; Machì, A.; Scarabotti, F. (1999), "Amenable groups and cellular automata", Annales de l'Institut Fourier, 49 (2): 673–685, doi:10.5802/aif.1686, MR 1697376 Capobianco, Silvio; Guillon, Pierre; Kari, Jarkko (2013), "Surjective cellular automata far from the Garden of Eden", Discrete Mathematics & Theoretical Computer Science, 15 (3): 41–60, MR 3141826 Bartholdi, Laurent (2019), "Amenability of groups is characterized by Myhill's theorem", Journal of the European Mathematical Society, 21 (10), with an appendix by Dawid Kielak: 3191–3197, arXiv:1605.09133, doi:10.4171/JEMS/900, MR 3994103

complex-systems.com

Sutner (1991). Sutner, Klaus (1991), "De Bruijn graphs and linear cellular automata" (PDF), Complex Systems, 5: 19–30, MR 1116419

conwaylife.com

In Lifeline Vol. 3 (September 1971), editor Robert T. Wainwright announced that Roger Banks and Steve Ward had proven the existence of a Garden of Eden whose live cells fit into a $9 \times 33$ rectangle, and presented a configuration believed by Banks to be a Garden of Eden. In Lifeline Vol. 4 (December 1971), Wainwright reported that a group at Honeywell using software by Don Woods had verified Banks' configuration to be a Garden of Eden. See also Gardner (1983). Gardner, Martin (1983), "Chapters 20 and 21: The Game of Life, Parts I and II" (PDF), Wheels, Life, and Other Mathematical Amusements, W. H. Freeman, pp. 214–258; see in particular pp. 230 and 248

doi.org

Moore (1962). Moore, E. F. (1962), "Machines models of self-reproduction", Mathematical Problems in the Biological Sciences, Proceedings of Symposia in Applied Mathematics, vol. 14, pp. 17–33, doi:10.1090/psapm/014/9961, ISBN 9780821813140 {{citation}}: ISBN / Date incompatibility (help); reprinted in Burks, Arthur W. (1970), Essays on Cellular Automata, University of Illinois Press, pp. 187–203.
Kari (2012), Section 2.1, "Basic Definitions", pp. 5–6. Kari, Jarkko J. (2012), "Basic Concepts of Cellular Automata", in Rozenberg, Grzegorz; Bäck, Thomas; Kok, Joost N. (eds.), Handbook of Natural Computing, Springer, pp. 3–24, doi:10.1007/978-3-540-92910-9_1, ISBN 978-3-540-92909-3
Toffoli & Margolus (1990). Note however that Toffoli and Margolus refer to the transition function as the global map. Toffoli, Tommaso; Margolus, Norman (1990), "Invertible cellular automata: a review", Physica D: Nonlinear Phenomena, 45 (1–3): 229–253, Bibcode:1990PhyD...45..229T, doi:10.1016/0167-2789(90)90185-R, MR 1094877
Kari (2012), p. 10. Kari, Jarkko J. (2012), "Basic Concepts of Cellular Automata", in Rozenberg, Grzegorz; Bäck, Thomas; Kok, Joost N. (eds.), Handbook of Natural Computing, Springer, pp. 3–24, doi:10.1007/978-3-540-92910-9_1, ISBN 978-3-540-92909-3
Kari (2012), p. 11. Kari, Jarkko J. (2012), "Basic Concepts of Cellular Automata", in Rozenberg, Grzegorz; Bäck, Thomas; Kok, Joost N. (eds.), Handbook of Natural Computing, Springer, pp. 3–24, doi:10.1007/978-3-540-92910-9_1, ISBN 978-3-540-92909-3
Kari (1990); Kari (1994). Kari's main result is that it is undecidable to test whether a cellular automaton is reversible, but he also shows the undecidability of testing whether a Garden of Eden exists. Kari, Jarkko (1990), "Reversibility of 2D cellular automata is undecidable", Physica D, 45 (1–3): 379–385, Bibcode:1990PhyD...45..379K, doi:10.1016/0167-2789(90)90195-U Kari, Jarkko (1994), "Reversibility and surjectivity problems of cellular automata", Journal of Computer and System Sciences, 48 (1): 149–182, doi:10.1016/S0022-0000(05)80025-X, MR 1259654
Toffoli & Margolus (1990): "Even if one were willing to fall back on a brute-force search, a long search time would generate only a few items, and even those would be for the most part quite uninteresting." Toffoli, Tommaso; Margolus, Norman (1990), "Invertible cellular automata: a review", Physica D: Nonlinear Phenomena, 45 (1–3): 229–253, Bibcode:1990PhyD...45..229T, doi:10.1016/0167-2789(90)90185-R, MR 1094877
Kari (2012), Proposition 2, p. 11. Kari, Jarkko J. (2012), "Basic Concepts of Cellular Automata", in Rozenberg, Grzegorz; Bäck, Thomas; Kok, Joost N. (eds.), Handbook of Natural Computing, Springer, pp. 3–24, doi:10.1007/978-3-540-92910-9_1, ISBN 978-3-540-92909-3
The one-dimensional case of this result is Theorem 5.1 of Hedlund (1969). As in the simpler proof given here, it uses compactness of the configuration space. In their earlier work, Moore and Myhill did not distinguish orphans from Gardens of Eden, and proved their results only in terms of orphans. Hedlund, G. A. (1969), "Endomorphisms and Automorphisms of the Shift Dynamical Systems", Mathematical Systems Theory, 3 (4): 320–375, doi:10.1007/BF01691062, S2CID 21803927
Hedlund (1969), Theorem 3.4. Hedlund, G. A. (1969), "Endomorphisms and Automorphisms of the Shift Dynamical Systems", Mathematical Systems Theory, 3 (4): 320–375, doi:10.1007/BF01691062, S2CID 21803927
Myhill (1963). Myhill, J. (1963), "The converse of Moore's Garden-of-Eden theorem", Proceedings of the American Mathematical Society, 14 (4): 685–686, doi:10.1090/S0002-9939-1963-0155764-9, JSTOR 2034301; reprinted in Burks, Arthur W. (1970), Essays on Cellular Automata, University of Illinois Press, pp. 204–205.
Amoroso & Cooper (1970); Skyum (1975). Skyum, Sven (1975), "Confusion in the Garden of Eden", Proceedings of the American Mathematical Society, 50 (1): 332–336, doi:10.1090/S0002-9939-1975-0386350-1
Margenstern (2009). Margenstern credits the result jointly to himself and Jarkko Kari. Margenstern, Maurice (2009), "About the Garden of Eden theorems for cellular automata in the hyperbolic plane", 15th International Workshop on Cellular Automata and Discrete Complex Systems, Electronic Notes in Theoretical Computer Science, vol. 252, pp. 93–102, doi:10.1016/j.entcs.2009.09.016
Ceccherini-Silberstein, Machì & Scarabotti (1999); Capobianco, Guillon & Kari (2013); Bartholdi2019. Ceccherini-Silberstein, T. G.; Machì, A.; Scarabotti, F. (1999), "Amenable groups and cellular automata", Annales de l'Institut Fourier, 49 (2): 673–685, doi:10.5802/aif.1686, MR 1697376 Capobianco, Silvio; Guillon, Pierre; Kari, Jarkko (2013), "Surjective cellular automata far from the Garden of Eden", Discrete Mathematics & Theoretical Computer Science, 15 (3): 41–60, MR 3141826 Bartholdi, Laurent (2019), "Amenability of groups is characterized by Myhill's theorem", Journal of the European Mathematical Society, 21 (10), with an appendix by Dawid Kielak: 3191–3197, arXiv:1605.09133, doi:10.4171/JEMS/900, MR 3994103
Gromov (1999). Gromov, M. (1999), "Endomorphisms of symbolic algebraic varieties", Journal of the European Mathematical Society, 1 (2): 109–197, doi:10.1007/PL00011162, MR 1694588, Zbl 0998.14001
Gottschalk (1973). Gottschalk, Walter (1973), "Some general dynamical notions", Recent Advances in Topological Dynamics (Proc. Conf. Topological Dynamics, Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund), Lecture Notes in Mathematics, vol. 318, Springer-Verlag, pp. 120–125, doi:10.1007/BFb0061728, ISBN 978-3-540-06187-8, MR 0407821
Ceccherini-Silberstein & Coornaert (2010). Ceccherini-Silberstein, Tullio; Coornaert, Michel (2010), "Surjunctive groups", Cellular automata and groups, Springer Monographs in Mathematics, Springer-Verlag, pp. 57–75, doi:10.1007/978-3-642-14034-1_3, ISBN 978-3-642-14033-4, MR 2683112

harvard.edu

ui.adsabs.harvard.edu

Toffoli & Margolus (1990). Note however that Toffoli and Margolus refer to the transition function as the global map. Toffoli, Tommaso; Margolus, Norman (1990), "Invertible cellular automata: a review", Physica D: Nonlinear Phenomena, 45 (1–3): 229–253, Bibcode:1990PhyD...45..229T, doi:10.1016/0167-2789(90)90185-R, MR 1094877
Kari (1990); Kari (1994). Kari's main result is that it is undecidable to test whether a cellular automaton is reversible, but he also shows the undecidability of testing whether a Garden of Eden exists. Kari, Jarkko (1990), "Reversibility of 2D cellular automata is undecidable", Physica D, 45 (1–3): 379–385, Bibcode:1990PhyD...45..379K, doi:10.1016/0167-2789(90)90195-U Kari, Jarkko (1994), "Reversibility and surjectivity problems of cellular automata", Journal of Computer and System Sciences, 48 (1): 149–182, doi:10.1016/S0022-0000(05)80025-X, MR 1259654
Toffoli & Margolus (1990): "Even if one were willing to fall back on a brute-force search, a long search time would generate only a few items, and even those would be for the most part quite uninteresting." Toffoli, Tommaso; Margolus, Norman (1990), "Invertible cellular automata: a review", Physica D: Nonlinear Phenomena, 45 (1–3): 229–253, Bibcode:1990PhyD...45..229T, doi:10.1016/0167-2789(90)90185-R, MR 1094877

inria.fr

hal.inria.fr

Ceccherini-Silberstein, Machì & Scarabotti (1999); Capobianco, Guillon & Kari (2013); Bartholdi2019. Ceccherini-Silberstein, T. G.; Machì, A.; Scarabotti, F. (1999), "Amenable groups and cellular automata", Annales de l'Institut Fourier, 49 (2): 673–685, doi:10.5802/aif.1686, MR 1697376 Capobianco, Silvio; Guillon, Pierre; Kari, Jarkko (2013), "Surjective cellular automata far from the Garden of Eden", Discrete Mathematics & Theoretical Computer Science, 15 (3): 41–60, MR 3141826 Bartholdi, Laurent (2019), "Amenability of groups is characterized by Myhill's theorem", Journal of the European Mathematical Society, 21 (10), with an appendix by Dawid Kielak: 3191–3197, arXiv:1605.09133, doi:10.4171/JEMS/900, MR 3994103

jstor.org

Myhill (1963). Myhill, J. (1963), "The converse of Moore's Garden-of-Eden theorem", Proceedings of the American Mathematical Society, 14 (4): 685–686, doi:10.1090/S0002-9939-1963-0155764-9, JSTOR 2034301; reprinted in Burks, Arthur W. (1970), Essays on Cellular Automata, University of Illinois Press, pp. 204–205.

maa.org

In Lifeline Vol. 3 (September 1971), editor Robert T. Wainwright announced that Roger Banks and Steve Ward had proven the existence of a Garden of Eden whose live cells fit into a $9 \times 33$ rectangle, and presented a configuration believed by Banks to be a Garden of Eden. In Lifeline Vol. 4 (December 1971), Wainwright reported that a group at Honeywell using software by Don Woods had verified Banks' configuration to be a Garden of Eden. See also Gardner (1983). Gardner, Martin (1983), "Chapters 20 and 21: The Game of Life, Parts I and II" (PDF), Wheels, Life, and Other Mathematical Amusements, W. H. Freeman, pp. 214–258; see in particular pp. 230 and 248
Gardner (1983). Gardner, Martin (1983), "Chapters 20 and 21: The Game of Life, Parts I and II" (PDF), Wheels, Life, and Other Mathematical Amusements, W. H. Freeman, pp. 214–258; see in particular pp. 230 and 248

numdam.org

Ceccherini-Silberstein, Machì & Scarabotti (1999); Capobianco, Guillon & Kari (2013); Bartholdi2019. Ceccherini-Silberstein, T. G.; Machì, A.; Scarabotti, F. (1999), "Amenable groups and cellular automata", Annales de l'Institut Fourier, 49 (2): 673–685, doi:10.5802/aif.1686, MR 1697376 Capobianco, Silvio; Guillon, Pierre; Kari, Jarkko (2013), "Surjective cellular automata far from the Garden of Eden", Discrete Mathematics & Theoretical Computer Science, 15 (3): 41–60, MR 3141826 Bartholdi, Laurent (2019), "Amenability of groups is characterized by Myhill's theorem", Journal of the European Mathematical Society, 21 (10), with an appendix by Dawid Kielak: 3191–3197, arXiv:1605.09133, doi:10.4171/JEMS/900, MR 3994103

semanticscholar.org

api.semanticscholar.org

The one-dimensional case of this result is Theorem 5.1 of Hedlund (1969). As in the simpler proof given here, it uses compactness of the configuration space. In their earlier work, Moore and Myhill did not distinguish orphans from Gardens of Eden, and proved their results only in terms of orphans. Hedlund, G. A. (1969), "Endomorphisms and Automorphisms of the Shift Dynamical Systems", Mathematical Systems Theory, 3 (4): 320–375, doi:10.1007/BF01691062, S2CID 21803927
Hedlund (1969), Theorem 3.4. Hedlund, G. A. (1969), "Endomorphisms and Automorphisms of the Shift Dynamical Systems", Mathematical Systems Theory, 3 (4): 320–375, doi:10.1007/BF01691062, S2CID 21803927

uni-bielefeld.de

wwwhomes.uni-bielefeld.de

Flammenkamp (2016). Flammenkamp, Achim (April 2016), "Garden of Eden / Orphan", Achim's Game of Life Page

zbmath.org

Gromov (1999). Gromov, M. (1999), "Endomorphisms of symbolic algebraic varieties", Journal of the European Mathematical Society, 1 (2): 109–197, doi:10.1007/PL00011162, MR 1694588, Zbl 0998.14001