Greetings everyone,
I was wondering whether there are any interesting aspects of cellular automata as computational models in the strict(er) sense of the term:
For example: a 2D cellular automaton sorting an array of numbers or so, or something more complicated. Note: I am not referring for example to a Turing Machine designed in the Game of Life where the gliders can be seen as bits/wires etc, but rather a rule that has been designed for such purposes.
Are there any interesting works/papers you could suggest?
I understand that using CA as models for simulation is kind of what I am describing, but I am interested in a purely computational sense.
You might check this Conference Paper Computational Aspects of Cellular Automata on Countable Sofic Shifts
Chapter Cellular Automata – A Computational Point of View
You may refer following papers:
Conference Paper Computational Aspects of Asynchronous Cellular Automata
Conference Paper Computational Aspects of Cellular Automata on Countable Sofic Shifts
You might find interesting the review paper written by a collective of researchers using cellular automata to model laser dynamics, chemical catalization processes, and dynamic recrystallization. One topic offers open source software written in C++ and using the visualization library Qt.
https://www.researchgate.net/publication/338019707_BUILDING_EFFICIENT_COMPUTATIONAL_CELLULAR_AUTOMATA_MODELS_OF_COMPLEX_SYSTEMS_BACKGROUND_APPLICATIONS_RESULTS_SOFTWARE_AND_PATHOLOGIES
In 2010, I edited a book with colleagues that has an introduction chapter describing CA basics, which is followed by a number of applications provided by different authors. It might be of interest too.
It is always good to study open source codes of CAs in order to learn their design fast and be effective.
I'm working on the application of CA in cryptography, I think these papers can be interested for you :
Article A design of a new hash function based on cellular automata
Chapter A Lightweight Cellular Automata-Based Cryptosystem Evaluated...
Chapter A New Secure Cellular Automata Cryptosystem for Embedded Devices
There is already one answer on computational aspects of CA dealing with a publication (there are more of them) made by myself. In this answer, I would like to share with those who might be interested in the Python software that simulates John Conway's 'Game of the Life'. Everyone can download it and play with it. By making our hands 'dirty' with programming, we learn a lot. Enjoy.
At the bottom of the software page are more animations for those who would like to play around with the software and want to know what they might to do with it:
https://www.researchgate.net/publication/355043921_The_simplest_Python_program_simulating_a_cellular_automaton_model_of_a_complex_system_the_'Game_of_Life'/stats
As an example, one animation of AND logic gate is here:
https://www.researchgate.net/publication/355043921_The_simplest_Python_program_simulating_a_cellular_automaton_model_of_a_complex_system_the_'Game_of_Life'/stats
Software will get an upgrade in the future and more animations will be shared. Stay tuned when interested.
Hi,
I also recommend to have a look to our research. It is interesting to see how can you use the theory of automata to generate random numbers :
"A FULL CYCLE LENGTH PSEUDORANDOM NUMBER GENERATOR BASED ON COMPOSITIONS OF AUTOMATA"
https://www.informatica.si/index.php/informatica/article/view/3109
Regards,
Norbert
There is existing a very important source of various models, approaches, and theory on cellular automata, which is provided in the book:
Andrew Ilachinski: "Cellular Automata: A Discrete Universe", WORLD SCIENTIFIC (July 2001) DOI: 10.1142/4702,
https://www.worldscientific.com/worldscibooks/10.1142/4702
I do recommend to read this book as it serves as a very well written advanced introduction into cellular automata.
S. Wolfram - A New Kind Of Science - https://www.wolframscience.com/nks/
Dear Nikolaos Kyparissas,
Your question triggered the work on this paper of which main idea was hovering in the air quite some time. Thank you for triggering it 🙏
Quite a few citations and very interesting links are provided in the paper. I recommend you to read as much of those citation as you can. Very important are are the first two on GoL!
This stream of research on emergent properties of computation is highly exciting and will eventually lead to better understanding of biology.
https://www.researchgate.net/publication/358446061_Why_Do_Biology_and_Medicine_Need_to_Study_Robust_Massive_Parallel_Information_Processing_Environments_Explained_on_the_Game_of_Life_and_Its_Generalization
This paper provide relevant reviews and research to this question. Additionally, it contains introductory research on error-resistant emergents. Might be interesting to some.
[1] Jiri Kroc: "Robust massive parallel information processing environments in biology and medicine: case study", Problems of Information Society 13:2 (2022) 12-22, DOI : 10.25045/jpis.v13.i2.02
Those who want to try to compute Game of Live CA with various neighborhoods can download open-source code (load, save functionality is being tested now, release in a few weeks).
[2] Jiri Kroc: "Python program GoL-N24 simulating the 'Game of Life' with variable neighborhood using eight neighbors from 24 possible", open-source Python software, ResearchGate (November 2022).
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