‘C (language)ellular-automaton’ directory
- See Also
- Gwern
- Links
- “Active Surface Waves Drive Rippling in Myxococcus Xanthus Colonies”, Bourque et al 2025
- “Aging As a Loss of Goal-Directedness: An Evolutionary Simulation and Analysis Unifying Regeneration With Anatomical Rejuvenation”, Pio-Lopez et al 2025
- “‘Next-Level’ Chaos Traces the True Limit of Predictability”
- “What Can We Learn about Engineering and Innovation from Half a Century of the Game of Life Cellular Automaton?”, Wolfram 2025
- “Autoregressive Large Language Models Are Computationally Universal”, Schuurmans et al 2024
- “The Patterns of Nils Aall Barricelli”, Agaram 2024
- “A Minimal Scenario for the Origin of Non-Equilibrium Order”, Ravasio et al 2024
- “Emergence of Large-Scale Mechanical Spiral Waves in Bacterial Living Matter”, Liu et al 2024
- “Classical Sorting Algorithms As a Model of Morphogenesis: Self-Sorting Arrays Reveal Unexpected Competencies in a Minimal Model of Basal Intelligence”, Zhang et al 2023
- “Conway’s Game of Life Is Omniperiodic”, Brown et al 2023
- “The Penrose Tiling Is a Quantum Error-Correcting Code”, Li & Boyle 2023
- “Machine Learning Without a Processor: Emergent Learning in a Nonlinear Electronic Metamaterial”, Dillavou et al 2023
- “How to Build a Computer Using Origami”, Green 2023
- “Flat Origami Is Turing Complete”, Hull & Zakharevich 2023
- “Self-Replicating Hierarchical Structures Emerge in a Binary Cellular Automaton”, Yang 2023
- “Flow-Lenia: Towards Open-Ended Evolution in Cellular Automata through Mass Conservation and Parameter Localization”, Plantec et al 2022
- “Grokking Phase Transitions in Learning Local Rules With Gradient Descent”, Žunkovič & Ilievski 2022
- “Living Material Assembly of Bacteriogenic Protocells”, Xu et al 2022b
- “Studying Growth With Neural Cellular Automata”, Greydanus 2022
- “Variational Neural Cellular Automata”, Palm et al 2022
- “Fundamental Behaviors Emerge from Simulations of a Living Minimal Cell”, Thornburg et al 2022
- “Collective Intelligence for Deep Learning: A Survey of Recent Developments”, Ha & Tang 2021
- “𝜇NCA: Texture Generation With Ultra-Compact Neural Cellular Automata”, Mordvintsev & Niklasson 2021
- “JPEG XL Would Be Turing-Complete”, Bohdan 2021
- “Texture Generation With Neural Cellular Automata”, Mordvintsev et al 2021
- “Synthetic Living Machines: A New Window on Life”, Ebrahimkhani & Levin 2021
- “A Cellular Platform for the Development of Synthetic Living Machines”, Blackiston et al 2021
- “Cells Form Into ‘Xenobots’ on Their Own: Embryonic Cells Can Self-Assemble into New Living Forms That Don’t Resemble the Bodies They Usually Generate, Challenging Old Ideas of What Defines an Organism”, Ball 2021
- “Growing 3D Artefacts and Functional Machines With Neural Cellular Automata”, Sudhakaran et al 2021
- “Nothing in Evolution Makes Sense except in the Light of Parasites”, Hickinbotham et al 2021
- “Regenerating Soft Robots through Neural Cellular Automata”, Horibe et al 2021
- “An Antiviral Self-Replicating Molecular Heterotroph”, Shapiro et al 2020
- “Conway’s Gradient of Life: Approximate Atavising With Differentiable Automata”, Chandra 2020
- “The Recursive Universe”, Ghassaei 2020
- “Growing Neural Cellular Automata: Differentiable Model of Morphogenesis”, Mordvintsev et al 2020
- “Finding Mona Lisa in the Game of Life: Using a SAT Solver to Find Game of Life States That Turn into Pictures”, Gal 2020
- “Intrinsically Motivated Discovery of Diverse Patterns in Self-Organizing Systems”, Reinke et al 2019
- “Going Critical”, Simler 2019
- “Honeybees’ Mesmerizing Defensive Wave”, ViralHog 2019
- “Lenia—Biology of Artificial Life”, Chan 2018
- “Cellular Automata As Convolutional Neural Networks”, Gilpin 2018
- “The Simple Algorithm That Ants Use to Build Bridges”
- “Now What?”, Hopfield 2018
- “Altering the Threshold of an Excitable Signal Transduction Network Changes Cell Migratory Modes”, Miao et al 2017
- Advances in Physarum Machines: Sensing and Computing With Slime Mould, Adamatzky 2016
- “Is Spearman’s Law of Diminishing Returns (SLODR) Meaningful for Artificial Agents?”, Hernandez-Orallo 2016
- “Life’s Information Hierarchy: The Explanation for the Complex, Multi-Scale Structure of Biological and Social Systems Lies in Their Manipulation of Space and Time to Reduce Uncertainty about the Future”, Flack 2014
- “Birds of a Feather … Track 7 Neighbors to Flock Together”, Azvolinsky 2013
- “Starling Flock Networks Manage Uncertainty in Consensus at Low Cost”, Young et al 2013
- “The Complexity of Small Universal Turing Machines: a Survey”, Neary & Woods 2011
- “Mathematical Marbling”, Lu et al 2011
- “Implications of the Turing Completeness of Reaction-Diffusion Models, Informed by GPGPU Simulations on an XBox 360: Cardiac Arrhythmias, Re-Entry and the Halting Problem”, Scarle 2009
- “Small Universal Turing Machines”, Neary 2008
- “Time-Reversal in Conway’s Life As SAT”, Bain 2007
- “Complexity of Langton’s Ant”, Gajardo et al 2003
- “Reliable Cellular Automata With Self-Organization”, Gacs 2000
- “Emergence of Self-Replicating Structures in a Cellular Automata Space”, Chou & Reggia 1997
- “Turing Patterns in CNNs, I: Once over Lightly”, Goras et al 1995
- “Unpredictability and Undecidability in Dynamical Systems”, Moore 1990
- “Cellular Neural Networks: Theory”, Chua & Yang 1988b
- “Cellular Neural Networks: Applications”, Chua & Yang 1988
- “Studying Artificial Life With Cellular Automata”, Langton 1986
- “Hashlife: Exploiting Regularities in Large Cellular Spaces”, Gosper 1984
- “The Determination of the Value of Rado’s Noncomputable Function Σ(𝑘) for Four-State Turing Machines”, Brady 1983
- “Automaton Models of Reproduction by Self-Inspection”, Laing 1977
- “The Next Industrial Revolution”, Dyson 1977
- “The Checkerboard Model of Social Interaction”, Sakoda 1971
- “Tag Systems and Lag Systems”, Wang 1963
- “Artificial Living Plants: Proposed Here Is a Design for Self-Reproducing Machines That Would Be Harvested for the Materials from Which They Construct Themselves. They Might Prove More Feasible Than Spaceships and More Profitable”, Moore 1956
- “DLA—Diffusion Limited Aggregation”
- “CSS3 Proven to Be Turing Complete”
- “Building a Working Game of Tetris in Conway’s Game of Life”
- “OTCA Metapixel”, Wiki 2026
- “29-Year-Old Conway Conjecture Settled”
- “Self-Classifying MNIST Digits”
- “Adversarial Reprogramming of Neural Cellular Automata”
- “Self-Organising Textures”
- “Computing in Dwarf Fortress”
- “Experimentations With Abstract Machines”
- “Grey-Area/rps-Automata”
- “From Brainfuck to Domino Computers: A Trip into Esoteric Languages, Turing Machines, Cellular Automata and the Nature of Computation”
- “Cirkoban: Sokoban Meets Cellular Automata Written in Scheme”
- “Tables of Soyga: the First Cellular Automaton?”
- “ControlNet Game of Life”
- “Is Bioelectricity the Key to Limb Regeneration?”
- “An Account of Electricity and the Body, Reviewed”
- “The Lasting Lessons of John Conway’s Game of Life”
- “The JPEG XL Image Format Has Demo Potential”
- “‘Amazing Science’: Researchers Find Xenobots Can Give Rise to Offspring Science”
- “Living Robots Made from Frog Cells Can Replicate Themselves in a Dish”
- “Rule 110 Train Turing Machine Explained”
- Sort By Magic
- Wikipedia (22)
- Miscellaneous
- Bibliography
See Also
Gwern
“Surprisingly Turing-Complete”, Gwern 2012
Links
“Active Surface Waves Drive Rippling in Myxococcus Xanthus Colonies”, Bourque et al 2025
Active surface waves drive rippling in Myxococcus xanthus colonies
“Aging As a Loss of Goal-Directedness: An Evolutionary Simulation and Analysis Unifying Regeneration With Anatomical Rejuvenation”, Pio-Lopez et al 2025
“‘Next-Level’ Chaos Traces the True Limit of Predictability”
“What Can We Learn about Engineering and Innovation from Half a Century of the Game of Life Cellular Automaton?”, Wolfram 2025
“Autoregressive Large Language Models Are Computationally Universal”, Schuurmans et al 2024
Autoregressive Large Language Models are Computationally Universal
“The Patterns of Nils Aall Barricelli”, Agaram 2024
“A Minimal Scenario for the Origin of Non-Equilibrium Order”, Ravasio et al 2024
“Emergence of Large-Scale Mechanical Spiral Waves in Bacterial Living Matter”, Liu et al 2024
Emergence of large-scale mechanical spiral waves in bacterial living matter
“Classical Sorting Algorithms As a Model of Morphogenesis: Self-Sorting Arrays Reveal Unexpected Competencies in a Minimal Model of Basal Intelligence”, Zhang et al 2023
“Conway’s Game of Life Is Omniperiodic”, Brown et al 2023
“The Penrose Tiling Is a Quantum Error-Correcting Code”, Li & Boyle 2023
“Machine Learning Without a Processor: Emergent Learning in a Nonlinear Electronic Metamaterial”, Dillavou et al 2023
Machine Learning Without a Processor: Emergent Learning in a Nonlinear Electronic Metamaterial
“How to Build a Computer Using Origami”, Green 2023
“Flat Origami Is Turing Complete”, Hull & Zakharevich 2023
“Self-Replicating Hierarchical Structures Emerge in a Binary Cellular Automaton”, Yang 2023
Self-Replicating Hierarchical Structures Emerge in a Binary Cellular Automaton
“Flow-Lenia: Towards Open-Ended Evolution in Cellular Automata through Mass Conservation and Parameter Localization”, Plantec et al 2022
“Grokking Phase Transitions in Learning Local Rules With Gradient Descent”, Žunkovič & Ilievski 2022
Grokking phase transitions in learning local rules with gradient descent
“Living Material Assembly of Bacteriogenic Protocells”, Xu et al 2022b
“Studying Growth With Neural Cellular Automata”, Greydanus 2022
Studying Growth with Neural Cellular Automata
View External Link:
“Variational Neural Cellular Automata”, Palm et al 2022
“Fundamental Behaviors Emerge from Simulations of a Living Minimal Cell”, Thornburg et al 2022
Fundamental behaviors emerge from simulations of a living minimal cell
“Collective Intelligence for Deep Learning: A Survey of Recent Developments”, Ha & Tang 2021
Collective Intelligence for Deep Learning: A Survey of Recent Developments
“𝜇NCA: Texture Generation With Ultra-Compact Neural Cellular Automata”, Mordvintsev & Niklasson 2021
𝜇NCA: Texture Generation with Ultra-Compact Neural Cellular Automata
“JPEG XL Would Be Turing-Complete”, Bohdan 2021
“Texture Generation With Neural Cellular Automata”, Mordvintsev et al 2021
“Synthetic Living Machines: A New Window on Life”, Ebrahimkhani & Levin 2021
“A Cellular Platform for the Development of Synthetic Living Machines”, Blackiston et al 2021
A cellular platform for the development of synthetic living machines
“Cells Form Into ‘Xenobots’ on Their Own: Embryonic Cells Can Self-Assemble into New Living Forms That Don’t Resemble the Bodies They Usually Generate, Challenging Old Ideas of What Defines an Organism”, Ball 2021
“Growing 3D Artefacts and Functional Machines With Neural Cellular Automata”, Sudhakaran et al 2021
Growing 3D Artefacts and Functional Machines with Neural Cellular Automata
“Nothing in Evolution Makes Sense except in the Light of Parasites”, Hickinbotham et al 2021
Nothing in evolution makes sense except in the light of parasites
“Regenerating Soft Robots through Neural Cellular Automata”, Horibe et al 2021
“An Antiviral Self-Replicating Molecular Heterotroph”, Shapiro et al 2020
“Conway’s Gradient of Life: Approximate Atavising With Differentiable Automata”, Chandra 2020
Conway’s Gradient of Life: Approximate Atavising with Differentiable Automata
“The Recursive Universe”, Ghassaei 2020
“Growing Neural Cellular Automata: Differentiable Model of Morphogenesis”, Mordvintsev et al 2020
Growing Neural Cellular Automata: Differentiable Model of Morphogenesis
“Finding Mona Lisa in the Game of Life: Using a SAT Solver to Find Game of Life States That Turn into Pictures”, Gal 2020
“Intrinsically Motivated Discovery of Diverse Patterns in Self-Organizing Systems”, Reinke et al 2019
Intrinsically Motivated Discovery of Diverse Patterns in Self-Organizing Systems
“Going Critical”, Simler 2019
“Lenia—Biology of Artificial Life”, Chan 2018
“Cellular Automata As Convolutional Neural Networks”, Gilpin 2018
“The Simple Algorithm That Ants Use to Build Bridges”
“Now What?”, Hopfield 2018
“Altering the Threshold of an Excitable Signal Transduction Network Changes Cell Migratory Modes”, Miao et al 2017
Altering the threshold of an excitable signal transduction network changes cell migratory modes
Advances in Physarum Machines: Sensing and Computing With Slime Mould, Adamatzky 2016
Advances in Physarum Machines: Sensing and Computing with Slime Mould
“Is Spearman’s Law of Diminishing Returns (SLODR) Meaningful for Artificial Agents?”, Hernandez-Orallo 2016
Is Spearman’s law of diminishing returns (SLODR) meaningful for artificial agents?
“Life’s Information Hierarchy: The Explanation for the Complex, Multi-Scale Structure of Biological and Social Systems Lies in Their Manipulation of Space and Time to Reduce Uncertainty about the Future”, Flack 2014
“Birds of a Feather … Track 7 Neighbors to Flock Together”, Azvolinsky 2013
“Starling Flock Networks Manage Uncertainty in Consensus at Low Cost”, Young et al 2013
Starling Flock Networks Manage Uncertainty in Consensus at Low Cost
“The Complexity of Small Universal Turing Machines: a Survey”, Neary & Woods 2011
“Mathematical Marbling”, Lu et al 2011
“Implications of the Turing Completeness of Reaction-Diffusion Models, Informed by GPGPU Simulations on an XBox 360: Cardiac Arrhythmias, Re-Entry and the Halting Problem”, Scarle 2009
“Small Universal Turing Machines”, Neary 2008
“Time-Reversal in Conway’s Life As SAT”, Bain 2007
“Complexity of Langton’s Ant”, Gajardo et al 2003
“Reliable Cellular Automata With Self-Organization”, Gacs 2000
“Emergence of Self-Replicating Structures in a Cellular Automata Space”, Chou & Reggia 1997
Emergence of self-replicating structures in a cellular automata space
“Turing Patterns in CNNs, I: Once over Lightly”, Goras et al 1995
“Unpredictability and Undecidability in Dynamical Systems”, Moore 1990
“Cellular Neural Networks: Theory”, Chua & Yang 1988b
“Cellular Neural Networks: Applications”, Chua & Yang 1988
“Studying Artificial Life With Cellular Automata”, Langton 1986
“Hashlife: Exploiting Regularities in Large Cellular Spaces”, Gosper 1984
“The Determination of the Value of Rado’s Noncomputable Function Σ(𝑘) for Four-State Turing Machines”, Brady 1983
The determination of the value of Rado’s noncomputable function Σ(𝑘) for four-state Turing machines
“Automaton Models of Reproduction by Self-Inspection”, Laing 1977
“The Next Industrial Revolution”, Dyson 1977
“The Checkerboard Model of Social Interaction”, Sakoda 1971
“Tag Systems and Lag Systems”, Wang 1963
“Artificial Living Plants: Proposed Here Is a Design for Self-Reproducing Machines That Would Be Harvested for the Materials from Which They Construct Themselves. They Might Prove More Feasible Than Spaceships and More Profitable”, Moore 1956
“DLA—Diffusion Limited Aggregation”
“CSS3 Proven to Be Turing Complete”
“Building a Working Game of Tetris in Conway’s Game of Life”
“OTCA Metapixel”, Wiki 2026
“29-Year-Old Conway Conjecture Settled”
“Self-Classifying MNIST Digits”
View External Link:
“Adversarial Reprogramming of Neural Cellular Automata”
Adversarial Reprogramming of Neural Cellular Automata
View External Link:
“Self-Organising Textures”
View External Link:
“Computing in Dwarf Fortress”
View External Link:
“Experimentations With Abstract Machines”
“Grey-Area/rps-Automata”
“From Brainfuck to Domino Computers: A Trip into Esoteric Languages, Turing Machines, Cellular Automata and the Nature of Computation”
View PDF (108MB):
/doc/www/seriot.ch/daf930a6edf6f54b36ac0ade4e4286aa1692b780.pdf
“Cirkoban: Sokoban Meets Cellular Automata Written in Scheme”
“Tables of Soyga: the First Cellular Automaton?”
“ControlNet Game of Life”
“Is Bioelectricity the Key to Limb Regeneration?”
“An Account of Electricity and the Body, Reviewed”
“The Lasting Lessons of John Conway’s Game of Life”
“The JPEG XL Image Format Has Demo Potential”
“‘Amazing Science’: Researchers Find Xenobots Can Give Rise to Offspring Science”
‘Amazing science’: researchers find xenobots can give rise to offspring Science
“Living Robots Made from Frog Cells Can Replicate Themselves in a Dish”
Living robots made from frog cells can replicate themselves in a dish
“Rule 110 Train Turing Machine Explained”
Sort By Magic
Annotations sorted by machine learning into inferred 'tags'. This provides an alternative way to browse: instead of by date order, one can browse in topic order. The 'sorted' list has been automatically clustered into multiple sections & auto-labeled for easier browsing.
Beginning with the newest annotation, it uses the embedding of each annotation to attempt to create a list of nearest-neighbor annotations, creating a progression of topics. For more details, see the link.
network-consensus
universal-turing
emergent-learning
self-organization
Wikipedia (22)
Miscellaneous
/doc/cs/cellular-automaton/2012-05-13-phillipbradbury-otcametapixel-lifeinlife.webmhttps://a.tulv.in/algorithms/programming/2021/02/19/finding-mona-lisa-in-the-game-of-life.htmlhttps://blog.otoro.net/2022/10/01/collectiveintelligence/View External Link:
https://btm.qva.mybluehost.me/building-arbitrary-life-patterns-in-15-gliders/https://spritely.institute/news/hoot-wireworld-live-in-browser.htmlhttps://www.quantamagazine.org/flying-fish-and-aquarium-pets-yield-secrets-of-evolution-20220105/-
View External Link:
Bibliography
https://arxiv.org/abs/2410.03170#deepmind: “Autoregressive Large Language Models Are Computationally Universal”,https://arxiv.org/abs/2210.15435: “Grokking Phase Transitions in Learning Local Rules With Gradient Descent”,2022-xu-2.pdf: “Living Material Assembly of Bacteriogenic Protocells”,2011-lu.pdf: “Mathematical Marbling”,1990-moore.pdf: “Unpredictability and Undecidability in Dynamical Systems”,1986-langton.pdf: “Studying Artificial Life With Cellular Automata”,