Skip to main content

Chaotic Fractals with Multivalued Logic in Cellular Automata

  • Conference paper

Abstract

This report deals with the application of multi-valued logic in cellular automata. A four valued logic system with dibit representation has been considered in this case. The general properties and their relations to build such logical systems are also investigated and the question of implementation of this logical system in cellular automata environment has also been studied. It is shown, that chaotic fractals i.e, fractals as function of initial conditions are formed in such cases. It is interesting to note also that fractals so formed are multifractals and thus may have applications in analyzing natural fractal formation. Subject. terms: Multivalued Logic, Cellular Automata, Fractals.

Keywords

  • Cellular Automaton
  • Logic System
  • Truth Table
  • Logical System
  • Fractal Formation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (Canada)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Zinovev, A, A : Philosophical problems of many valued logic [A revised edition] edited and translated by Guido Kung and David Dinsmore comey, D. Reidle publishing company dordrecht-Holland,(1963).

    Google Scholar 

  2. Lukasiewicz , J : O logice trojwartosciowej, Ruch filozoficzny,5,169-170 (1920).

    Google Scholar 

  3. Lukasiewicz, J: Aristotles Syllogistic from the stand point of modern formal logic, Oxford, London, 1951.

    Google Scholar 

  4. Wolfram Stephen : Statistical mechanics of cellur automata, Review of mod. Phys. 55 pp. 601-694 (1983).

    Google Scholar 

  5. Stanffer Dietrich : Cellur Automata from the book Fractals and Disordered Systems edited by Arumin Bunde and Sholmo Havlin, Springer-Verlag, Berlin Heidelberg 298-321(1991).

    Google Scholar 

  6. J.Taboury, J.M.Wang, P.Chavel, F.Devos and P.Garda, Optical Cellular processor architecture 1: Principles , App. Opt. Vol 9, pp 1643-1650(1988).

    Google Scholar 

  7. J. Taboury, J. M. Wang, Pchavel, F. Devos Optical Cellular processor architecture, 2: Illustration and system considerations , App. Optics, Vol 28, pp 3138(1989).

    Google Scholar 

  8. P. Chapel, A Cavrineli and I. Glasv, Opto electronic cellular automata for video real time vision Optics in computing OC’ 2000 Canada, Ouebec 18-23 June 2000, SPIE, 2000 pp 374-381(2000).

    Google Scholar 

  9. Lin, Shu and Costello, D. J. JR. “Error Control Coding: Fundamentals and Applications ”, Prentice –Hall, New Jersy (1983).

    Google Scholar 

  10. Stanley, H.E : Fractals and multifractals: The interplay of Physics and Geometry from the book ‘Fractals and Disordered Systems’ edited by Arumin Bunde and Sholmo Havlin, Springer-Verlag, Berlin Heidelberg 1- 50(1991).

    Google Scholar 

  11. Amal K. Ghosh and A. Basuray, “Trinary optical logic processors using shadow casting with polarized light”, Optics Communications, vol.79,number 1,2 , October 1990, pp 11 – 14.

    Google Scholar 

  12. A. Basuray, S. Mukhopadhyay, Hirak K. Ghosh, A. K. Dutta, “ A tristate optical logic system”, Optics Comm.,vol.85, Sept.1991, pp 167 -170.

    CrossRef  Google Scholar 

  13. P. Pal Chaudhury, D. R. Chowdhury, S. Nandi and S. Chatterjee “ Additive Cellular Automata – Theory and applications:Vol.1”,IEEE Computer press, California, USA(1997).

    Google Scholar 

  14. M. A. Hasan and M. Ebledaei “Efficient architectures for computations over variable dimensional Galois fields”, IEEE Trans. Circuits and Systems – I Fundamental theory and applications, Vol.45 no. 11 1205-1211(1998).

    CrossRef  Google Scholar 

  15. M. A. Hasan and A. G. Warsal “VLSI algorithms, architectures and implementation of a versatile GF(2m) processor ”, IEEE Trans. on Computers, Vol.49, 1064-1073(2000).

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2007 Springer

About this paper

Cite this paper

Ghosh, A.K., Choudhury, P.P., Basuray, A. (2007). Chaotic Fractals with Multivalued Logic in Cellular Automata. In: Sobh, T. (eds) Innovations and Advanced Techniques in Computer and Information Sciences and Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6268-1_15

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-6268-1_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-6267-4

  • Online ISBN: 978-1-4020-6268-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics