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Morphogenesis and form  ·  Article

Neural cellular automata and multi-scale competency architecture

Neural cellular automata (NCAs) are grids of cells in which each cell updates its state from its neighbours' states using a trained neural network67. Hartl, Risi and Levin note that NCAs have been proposed by others as toy models for morphogenesis7. Hartl, Risi and Levin use them to ask how the competency of decision-making centers at different scales affects evolution6.

Earliest held
2012, Craddock TJ, Tuszynski JA…
Most discussed in
Evolutionary Implications of Self-Assembling…, 2024
In the library
158 passages in 24 works
Rewritten
2026-10-25
18501875190019251950197520002025Craddock TJ, Tuszynski JA, Hameroff S, 20121Bessonov N, Levin M, Morozova N…, 20152Evangelidis V, Jones J, Dourvas N…, 20173Pio-Lopez L, Bischof J, LaPalme JV…, 20234Pio-Lopez L, Bischof J, LaPalme JV…, 20235Hartl B, Risi S, Levin M, 20246Hartl B, Risi S, Levin M, 20247Shreesha L, Levin M, 20248Pio-Lopez L, Hartl B, Levin M, 20259
01

Cellular automata as models

Craddock, Tuszynski and Hameroff (2012) described cellular automata as lattices of interacting units. They noted that simple rule-based interactions among neighbouring states, updated at discrete time steps, can give complex patterns, computation and self-organization1. Cellular automata are widely used to model growth of biological tissues. Bessonov, Levin and colleagues (2015) built a regeneration model on a square grid of cells that exchange signals and divide. Their aim was a minimal model that explains exact regeneration of an amputated part2. Evangelidis and colleagues (2017) presented a model based on cellular automata agents that gave a fair match with their 3D experimental results on Physarum networks imitating Roman roads3.

02

From fixed rules to networks

Hartl, Risi and Levin (2024) place cellular automata within Artificial Life. Cells on a grid change in time through local update rules6. Their NCAs replace the fixed rule with a trainable neural network, meant to model the decision-making machinery inside a biological cell. Such NCAs have been trained to form patterns, and the authors liken this to development from a single egg cell to an anatomical form7. Pio-Lopez and colleagues (2023) tie the approach to growing neural cellular automata. They call neural networks a convenient formalism for cell behaviour, equal in power to gene-regulatory networks5.

03

Goals, stress and aging

Pio-Lopez and colleagues (2023) said that the neural cellular automata of one earlier work they discuss include no cellular signalling and no use of stress to link homeostatic levels4. Shreesha and Levin (2024) compared several development modes in simulation. They report that stress sharing helps collective problem-solving8. Pio-Lopez, Hartl and Levin (2025) trained NCAs with an evolutionary algorithm to form a 16 by 16 smiley-face pattern. Each cell's network reads its neighbours' states and sets its own state9. Their keywords tie this work to aging and cognition.

SourcesEach quotation was checked word for word against the passage it opens.
  1. Simple rule-based interactions among neighbor cell states updating at discrete time steps can lead to complex patterns, computation and self-organization in cellular automata.Craddock TJ, Tuszynski JA, Hameroff S, 2012 · Cytoskeletal signaling: is memory encoded in microtubule lattices by CaMKII… · open at passage 37
  2. The implementation of the model is based on the method of cellular automata where cells are located at the nodes of a square grid.Bessonov N, Levin M, Morozova N, Reinberg N, Tosenberger A…, 2015 · On a model of pattern regeneration based on cell memory · open at passage 9
  3. Moreover, a model based on Cellular Automata Agents is presented to provide fair match with the introduced experimental results in 3D.Evangelidis V, Jones J, Dourvas N, Tsompanas MA, Sirakoulis…, 2017 · Physarum machines imitating a Roman road network: the 3D approach · open at passage 3
  4. However, their neural cellular automata do not include any cellular signalling or any use of stress capable of linking the different homeostatic levelsPio-Lopez L, Bischof J, LaPalme JV, Levin M, 2023 · The scaling of goals from cellular to anatomical homeostasis: an evolutionary… · open at passage 17
  5. The general approach is related to cellular neural networks [54] and more particularly to the growing neural cellular automata [48] where each cell has access to the states of its neighbours and contains a neural network to drive actionsPio-Lopez L, Bischof J, LaPalme JV, Levin M, 2023 · The scaling of goals from cellular to anatomical homeostasis: an evolutionary… · open at passage 21
  6. In such CAs, the (numerical) states of localized cells, organized on a discrete spatial grid, change in time via local update rules.Hartl B, Risi S, Levin M, 2024 · Evolutionary Implications of Self-Assembling Cybernetic Materials with… · open at passage 8
  7. Such self-orchestrated pattern formation is reminiscent of the self-regulated development of a biological organism, from a single fertilized egg cell to a complex anatomical form.Hartl B, Risi S, Levin M, 2024 · Evolutionary Implications of Self-Assembling Cybernetic Materials with… · open at passage 19
  8. By comparing the data, we find interesting and important roles of stress sharing as a dynamic that facilitates collective problem-solving.Shreesha L, Levin M, 2024 · Stress sharing as cognitive glue for collective intelligences: A computational… · open at passage 12
  9. which perceive the numerical states of their direct cellular neighbors on the grid of the NCA to regulate their own cell state individually.Pio-Lopez L, Hartl B, Levin M, 2025 · Aging as a Loss of Goal-Directedness: An Evolutionary Simulation and Analysis… · open at passage 95
Linked ideas
The NCA studies treat patterning as a goal pursued by cells, and the aging paper frames its simulation as loss of that goal-directedness.
Hartl and colleagues say plain cellular automata are not known to show closed-loop homeostatic activity, which trained NCAs are meant to add.
Pio-Lopez and colleagues call the neural network in each cell a formalism equal in power to a gene-regulatory network.
Gap junctionspart of / contains
In the 2023 model, each cell's network can control gap junctions to pass morphogen and stress to other cells.
The 2015 cellular automaton model of regeneration on a square grid is an earlier Levin collaboration using the same grid-of-cells method.
Shreesha and Levin report that stress sharing between cells helps collective problem-solving in their simulations.
Evolvabilityrelated to
Hartl et al. use NCA models of morphogenesis with evolutionary algorithms to test how multi-scale cellular competency affects evolution itself, so NCAs serve as the tool for studying evolvability.
Another simulation approach in which local units give rise to tissue-level goal-directed behaviour.
Where it is discussedPassages matching neural cellular automata, NCA, cellular automata, multi-scale competency architecture
2024Evolutionary Implications of Self-Assembling Cybernetic Materials with… · Hartl B, Risi S, Levin M60
2025Aging as a Loss of Goal-Directedness: An Evolutionary Simulation and Analysis… · Pio-Lopez L, Hartl B, Levin M53
2019The Computational Boundary of a "Self": Developmental Bioelectricity Drives… · Levin M8
2023The scaling of goals from cellular to anatomical homeostasis: an evolutionary… · Pio-Lopez L, Bischof J, LaPalme JV…7
2024Embryos assist morphogenesis of others through calcium and ATP signaling… · Tung A, Sperry MM, Clawson W, Pavuluri…3
2012Modeling planarian regeneration: a primer for reverse-engineering the worm · Lobo D, Beane WS, Levin M3
2023There's Plenty of Room Right Here: Biological Systems as Evolved, Overloaded… · Bongard J, Levin M3
2022Counting with Cilia: The Role of Morphological Computation in Basal Cognition… · Rorot W2
2023Bioelectric networks: the cognitive glue enabling evolutionary scaling from… · Levin M2
2022Technological Approach to Mind Everywhere: An Experimentally-Grounded Framework… · Levin M2