Skip to main content
SpringerLink
Log in

Genealogy Interceded Phenotypic Analysis (GIPA) of ECA Rules

  • Conference paper
  • First Online:
Proceedings of Second Asian Symposium on Cellular Automata Technology (ASCAT 2023)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1443))

Included in the following conference series:

  • 71 Accesses

Abstract

This study demonstrates an alternative ECA rules classification using information-theoretic measures with 88 minimal representatives of ECA rules. It proposes using entropy-time diagrams (variation in BiEntropy values with time) to compare ECAs behavior, where two configurations may correspond to the same approximate information content despite their visual differences in the space-time diagrams. The genotype of an ECA rule, which is perceived as the amount of information processed, is captured through four proposed measures, i.e., DiffEntropy (DE), SimConfigOrdered (SCO), SimConfigImmediate (SCI), and SimConfigFluctuation (SCF). By clustering the temporal sequences of entropy values of different rules using dynamic time warping (DTW), a Genealogy Interceded Phenotypic Analysis (GIPA) of 88 ECA rules is proposed. This study is restricted to synchronous ECA with periodic boundary conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Al-Emam, M., Kaurov, V.: Cellular automata complexity threshold and classification: a geometric perspective. Complex Syst. 23(4), 355–376 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bhattacharjee, K., Naskar, N., Roy, S., Das, S.: A survey of cellular automata: types, dynamics, non-uniformity and applications. Nat. Comput. 19(2), 433–461 (2020)

    Article  MathSciNet  Google Scholar 

  3. Croll, G.J.: Bientropy—the approximate entropy of a finite binary string (2013). https://doi.org/10.48550/ARXIV.1305.0954, arXiv:1305.0954

  4. Croll, G.J.: Bientropy, trientropy and primality. Entropy 22(3), 311 (2020)

    Article  MathSciNet  Google Scholar 

  5. Culik, K., Yu, S.: Undecidability of CA classification schemes. Complex Syst. 2(2), 177–190 (1988)

    MathSciNet  MATH  Google Scholar 

  6. Gold, O., Sharir, M.: Dynamic time warping and geometric edit distance. ACM Trans. Algorithms (TALG) 14, 1–17 (2018)

    Article  MATH  Google Scholar 

  7. Grattarola, D., Livi, L., Alippi, C.: Learning graph cellular automata. Adv. Neural. Inf. Process. Syst. 34, 20983–20994 (2021)

    Google Scholar 

  8. Kari, J.: Theory of cellular automata: a survey. Theor. Comput. Sci. 334(1–3), 3–33 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Martinez, G.J.: A note on elementary cellular automata classification (2013). arXiv:1306.5577

  10. Sutner, K.: Computational classification of cellular automata. Int. J. Gen. Syst. 41(6), 595–607 (2012). https://doi.org/10.1080/03081079.2012.695899

    Article  MathSciNet  MATH  Google Scholar 

  11. Tavenard, R., Faouzi, J., Vandewiele, G., Divo, F., Androz, G., Holtz, C., Payne, M., Yurchak, R., Rußwurm, M., Kolar, K., Woods, E.: Tslearn, a machine learning toolkit for time series data. J. Mach. Learn. Res. 21(118), 1–6 (2020). http://jmlr.org/papers/v21/20-091.html

  12. Vispoel, M., Daly, A.J., Baetens, J.M.: Progress, gaps and obstacles in the classification of cellular automata. Phys. D: Nonlinear Phenom. 432, 133074 (2022). https://doi.org/10.1016/j.physd.2021.133074, https://www.sciencedirect.com/science/article/pii/S0167278921002311

Download references

Acknowledgements

(i) This work is done as a project in the Indian Summer School on Cellular Automata 2022. (ii) The author would like to acknowledge Dr. Sukanta Das, Associate Professor, IIEST, Shibpur, for his gracious support and guidance in completing this project at the online Indian Summer School on Cellular Automata 2022, and Dr. Kamalika Bhattacharjee, Assistant Professor, NIT Tiruchirappalli, for her immense help in improving the quality of this manuscript and valuable discussions on cellular automata.

Author information

Authors and Affiliations

  1. University School of Information, Communication and Technology, Guru Gobind Singh (GGS) Indraprastha University, New Delhi, 110078, India

    Rinkaj Goyal

Authors
  1. Rinkaj Goyal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rinkaj Goyal .

Editor information

Editors and Affiliations

  1. Department of Information Technology, Indian Institute of Engineering Science and Technology, Shibpur, West Bengal, India

    Sukanta Das

  2. National Polytechnic Institute, Mexico City, Mexico

    Genaro Juarez Martinez

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Goyal, R. (2023). Genealogy Interceded Phenotypic Analysis (GIPA) of ECA Rules. In: Das, S., Martinez, G.J. (eds) Proceedings of Second Asian Symposium on Cellular Automata Technology. ASCAT 2023. Advances in Intelligent Systems and Computing, vol 1443. Springer, Singapore. https://doi.org/10.1007/978-981-99-0688-8_14

Download citation

Publish with us

Policies and ethics

Search

Navigation