Mechanical mechanism for self-replication
Author:
Ralph P. Lano
Journal:
Quart. Appl. Math.
MSC (2020):
Primary 92C40; Secondary 92B05
DOI:
https://doi.org/10.1090/qam/1709
Published electronically:
February 6, 2025
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Additional Information
Abstract: This study presents a theoretical model for a self-replicating mechanical system inspired by biological processes within living cells and supported by computer simulations. The model breaks down self-replication into a few core components, each constructed from a small set of fundamental building blocks. Two models are proposed: one inspired by additive manufacturing techniques and the other by protein folding, both leading to similar results. Key functionalities, such as sorting, copying, building, and computing, are demonstrated. These models provide valuable insights into the constraints of self-replicating systems. This work offers a foundational framework for future research on self-replicating mechanisms and their information-processing applications.
References
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- Emil L. Post, Formal reductions of the general combinatorial decision problem, Amer. J. Math. 65 (1943), 197–215. MR 7893, DOI 10.2307/2371809
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- H. A. Simon, The architecture of complexity, Proceedings of the American Philosophical Society 106 (1962), no. 6, 467.
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- J. von Neumann and A. W. Burks, Theory of self-reproducing automata, University of Illinois Press, 1966.
- Stephen Wolfram, A new kind of science, Wolfram Media, Inc., Champaign, IL, 2002. MR 1920418
- Y. Zhang, Z. Qian, J. Zhuang, S. Fan, H. Wei, and N. Yang, Mechanical system with soft modules and rigid frames realizing logic gates and computation, Advanced Intelligent Systems 5 (2023), no. 2, 2200374.
References
- B. Alberts, R. Heald, A. Johnson, D. Morgan, M. Raff, K. Roberts, and P. Walter, Molecular biology of the cell, W.W. Norton & Company, 2022.
- Y. Benenson, Biomolecular computing systems: principles, progress and potential, Nature Reviews Genetics 13 (2012), no. 7, 455–468.
- S. Brenner, Life’s code script, Nature 482 (2012), no. 7386, 461.
- John Cocke and Marvin Minsky, Universality of Tag systems with $P=2$, J. Assoc. Comput. Mach. 11 (1964), 15–20. MR 175709, DOI 10.1145/321203.321206
- C. M. Collins, Self reproducing fundamental fabricating machine system, June 9, 1998, US Patent 5,764,518.
- K. E. Drexler, Nanosystems: molecular machinery, manufacturing, and computation, John Wiley & Sons, 1992.
- R. A. Freitas and R. C. Merkle, Kinematic self-replicating machines, Landes Bioscience, 2004.
- H. Jacobson, Information, reproduction and the origin of life, American Scientist 43 (1955), no. 1, 119.
- E. L. Kristoffersen, M. Burman, A. Noy, and P. Holliger, Rolling circle RNA synthesis catalyzed by RNA, eLife 11 (2022).
- W. K. Langford, A. Ghassaei, and N. Gershenfeld, Self-assembling assemblers and manipulators built from a set of primitive blocks, December 18, 2018, US Patent 10,155,314.
- R. P. Lano, Towards a self-replicating Turing machine, arXiv preprint arXiv:2306.16872 (2023).
- R. P. Lano, Mechanical self-replication, arXiv preprint arXiv:2407.14556 (2024).
- R. P. Lano, Self-replicating mechanical universal Turing machine, arXiv preprint arXiv:2409.19037 (2024).
- A. Lindenmayer, Mathematical models for cellular interactions in development II. Simple and branching filaments with two-sided inputs, Journal of Theoretical Biology 18 (1968), no. 3, 300.
- R. C. Merkle, Convergent assembly, Nanotechnology 8 (1997), no. 1, 18.
- Marvin L. Minsky, Computation: finite and infinite machines, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1967. MR 356580
- D. L. Nelson and M. M. Cox, Lehninger principles of biochemistry, W. H. Freeman, 2008.
- M. O’Donnell, L. Langston, and B. Stillman, Principles and concepts of DNA replication in bacteria, archaea, and eukarya, Cold Spring Harbor Perspectives in Biology 5 (2013), no. 7.
- L. S. Penrose, Self-reproducing machines, Scientific American 200 (1959), no. 6, 105.
- Emil L. Post, Formal reductions of the general combinatorial decision problem, Amer. J. Math. 65 (1943), 197–215. MR 7893, DOI 10.2307/2371809
- Y. Ren, R. Jamagne, D. J. Tetlow, and D. A. Leigh, A tape-reading molecular ratchet, Nature 612 (2022), no. 7938, 78.
- H. A. Simon, The architecture of complexity, Proceedings of the American Philosophical Society 106 (1962), no. 6, 467.
- A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem, Proc. London Math. Soc. (2) 42 (1936), no. 3, 230–265. MR 1577030, DOI 10.1112/plms/s2-42.1.230
- S. Varghese, J. A. A. W. Elemans, A. E. Rowan, and R. J. M. Nolte, Molecular computing: paths to chemical Turing machines, Chemical Science 6 (2015), no. 11, 6050.
- John von Neumann, The general and logical theory of automata, Cerebral Mechanisms in Behavior. The Hixon Symposium, Wiley, New York, 1951, pp. 1–31; discussion, pp. 32–41. MR 45446
- John von Neumann, First draft of a report on the EDVAC, edited and with an introduction by Michael D. Godfrey, IEEE Ann. Hist. Comput. 15 (1993), no. 4, 27–75. MR 1241101, DOI 10.1109/85.238389
- J. von Neumann and A. W. Burks, Theory of self-reproducing automata, University of Illinois Press, 1966.
- Stephen Wolfram, A new kind of science, Wolfram Media, Inc., Champaign, IL, 2002. MR 1920418
- Y. Zhang, Z. Qian, J. Zhuang, S. Fan, H. Wei, and N. Yang, Mechanical system with soft modules and rigid frames realizing logic gates and computation, Advanced Intelligent Systems 5 (2023), no. 2, 2200374.
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Additional Information
Ralph P. Lano
Affiliation:
Technische Hochschule Nürnberg Georg Simon Ohm, Keßlerplatz 12, 90489 Nürnberg, Germany
MR Author ID:
324107
ORCID:
0009-0007-6981-8168
Email:
ralph.lano@th-nuernberg.de
Received by editor(s):
December 10, 2024
Received by editor(s) in revised form:
January 2, 2025
Published electronically:
February 6, 2025
Article copyright:
© Copyright 2025
by the author
