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Evolutionary Trajectories by Recursive Analysis of 1D Cellular Automata.

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Title: Evolutionary Trajectories by Recursive Analysis of 1D Cellular Automata.
Authors: Ghosh, Arijit1,2 (AUTHOR) arijit.maths@gmail.com, Sahoo, Sudhakar1 (AUTHOR) sudhakar.sahoo@gmail.com
Source: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Sep2026, Vol. 36 Issue 11, p1-24. 24p.
Subjects: Cellular automata, Boolean expressions, Mathematical logic, Mathematical analysis
Abstract: In this paper, extensive analysis has been done using the recursive evaluation technique on One-Dimensional Cellular Automata (1D CA). This approach focuses on tracking the formation of cell values and identifying the contributing cells from the initial configuration at a given generation. Coining the new naming convention of fundamental rules in 1D CA, along with their groups and different Boolean operators, the closed-form formula has been derived for certain CA. Cell values at the nth generation without even explicitly computing the intermediate iteration steps have been attempted. These are derived through nested symbolic expressions that trace back to the initial state, enabling both symbolic and visual analysis of rule evolution. Our approach accommodates both uniform rules, characterized by a common update function applied to all cells and nonuniform rule sets, in which individual cells evolve under distinct logical functions. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 194674185
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  Data: Evolutionary Trajectories by Recursive Analysis of 1D Cellular Automata.
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  Data: <searchLink fieldCode="AR" term="%22Ghosh%2C+Arijit%22">Ghosh, Arijit</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> arijit.maths@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Sahoo%2C+Sudhakar%22">Sahoo, Sudhakar</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sudhakar.sahoo@gmail.com</i>
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  Data: <searchLink fieldCode="DE" term="%22Cellular+automata%22">Cellular automata</searchLink><br /><searchLink fieldCode="DE" term="%22Boolean+expressions%22">Boolean expressions</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+logic%22">Mathematical logic</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink>
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  Label: Abstract
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  Data: In this paper, extensive analysis has been done using the recursive evaluation technique on One-Dimensional Cellular Automata (1D CA). This approach focuses on tracking the formation of cell values and identifying the contributing cells from the initial configuration at a given generation. Coining the new naming convention of fundamental rules in 1D CA, along with their groups and different Boolean operators, the closed-form formula has been derived for certain CA. Cell values at the nth generation without even explicitly computing the intermediate iteration steps have been attempted. These are derived through nested symbolic expressions that trace back to the initial state, enabling both symbolic and visual analysis of rule evolution. Our approach accommodates both uniform rules, characterized by a common update function applied to all cells and nonuniform rule sets, in which individual cells evolve under distinct logical functions. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1142/S0218127426501488
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      – Code: eng
        Text: English
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        PageCount: 24
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    Subjects:
      – SubjectFull: Cellular automata
        Type: general
      – SubjectFull: Boolean expressions
        Type: general
      – SubjectFull: Mathematical logic
        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
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      – TitleFull: Evolutionary Trajectories by Recursive Analysis of 1D Cellular Automata.
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            NameFull: Ghosh, Arijit
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            NameFull: Sahoo, Sudhakar
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              M: 09
              Text: Sep2026
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              Y: 2026
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              Value: 36
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              Value: 11
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            – TitleFull: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
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