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Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps

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Classification of cellular automata based on the Hamming distance.

Gaspar Alfaro¹, Miguel A F Sanjuán¹

¹Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, Móstoles, 28933 Madrid, Spain.

Chaos (Woodbury, N.Y.)

|August 21, 2024

Summary

This study introduces a new algorithm for classifying elementary cellular automata using Hamming distance, enhancing Wolfram

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Area of Science:

* Computational theory
* Complex systems science
* Discrete mathematics

Background:

* Elementary cellular automata (ECAs) exhibit complex behaviors.
* Wolfram's 1980s research classified ECAs based on observed patterns.
* Existing classification methods may lack detailed differentiation.

Purpose of the Study:

* To develop an effective algorithm for classifying elementary cellular automata.
* To refine existing classification schemes with more granular subclasses.
* To provide heuristic reasoning for the emergence of fractal patterns in ECAs.

Main Methods:

* Development of a novel algorithm for ECA classification.
* Utilizing Hamming distance to measure difference patterns between ECA states.
* Comparison and alignment with Wolfram's established classification.

Main Results:

* The proposed algorithm effectively classifies ECAs.
* The classification aligns with Wolfram's phenomenology.
* Identified additional subclasses within ECA rules.
* Discovered heuristic reasoning explaining fractal pattern formation.

Conclusions:

* The Hamming distance-based algorithm offers a more effective classification of ECAs.
* This refined classification provides deeper insights into ECA behavior.
* The heuristic reasoning contributes to understanding the origins of fractal patterns in these systems.