Previously on Knowing Neurons, we considered self-organized criticality (SOC) and network science (AKA graph theory) as two possible sources of complex behavior in the brain and other physiological systems. As discussed in that piece, complex behavior as observed in quantifiable, physiological signals appears healthy, motivating the question of what gives rise to such behavior. In two prior posts, we established that studying individual parts per se in a physiological system will never yield a complete understanding of the system.

Complex behavior in physiological systems like the brain often arises from complex interactions between simple parts. Consider a checker board of two colors in which each square, or cell, changes according to the colors of neighboring cells. Cells of one color are considered to be alive, while cells of the other color are considered to be dead. A live cell with too many neighbors, over-crowded, will die in the next generation, as will a live cell with too few neighbors. Reproduction is simulated by allowing dead cells with exactly three neighbors each to become live cells in the next generation. Such is John Conway’s Game of Life, a “game” developed to simulate life using simple rules applied to cellular automata. The cellular automata evolve each generation to produce frighteningly sophisticated and dynamic patterns with whimsical names, such as glider, blinker, and pulsar. Self-replicating patterns have also been reported. As with the brain, a complete understanding of the system cannot be obtained by studying individual parts or cells.


But it’s not all fun and games. An interesting property of cellular automata is that logic gates can be constructed from dynamic patterns to perform logical operations such as and, or, and not. In principle, cellular automata can solve any problem solvable by a computer. In his book A New Kind of Science, physicist Stephan Wolfram proposes that the mathematical equations, which set the foundation for modern physics, may eventually give way to non-mathematical rules, like those governing Conway’s Game of Life, applied to particles. Wolfram even proposes that there is one such ultimate rule governing everything in the Universe. Wolfram is hardly the only physicist to become interested in cellular automata. Physicist John Crutchfield has noted that boundaries between cells of the same color, mapped over time, resemble traces of charged particles in a bubble chamber, further underscoring the universality of cellular automata to computation.


While most scholars accept cellular automataas an abstract, simplified model for understanding complexity in the brain, two maverick theoreticians have taken the concept somewhat more literally. Collaborating with anesthesiologist Stuart Hammeroff, Roger Penrose–author of The Emperor’s New Mind–has proposed that computations in the brain might be carried out in microtubules with cellular automata-like properties. Microtubules are generally considered as long filaments, formed from numerous tubulin proteins, which form the cytoskeleton of the neuron. The tubulin proteins themselves are dimers composed of two subunits, alpha and beta. An electron that oscillates between the two subunits might allow subunits to alternate between two states–on and off–depending on the electron’s presence or absence. Consequently, the microtubule itself might behave as a wrapped cellular automata grid, with tubulin subunits switching between states each generation depending on the states of neighboring subunits. Furthermore, the exotic quantum properties of electrons would actually allow such a cellular automata to behave as a quantum computer, i.e., a computer which is not limited by the classical physics governing macroscopic objects.


It should be emphasized that the above model is still highly theoretical with little empirical evidence supporting the existence of such microtubule computations. However, Hammeroff and Penrose argue that such a theory might explain everything from certain aspects of human consciousness to the ability of unicellular organisms such as the paramecium (whose cytoskeleton includes microtubules) to “think” without actually possessing a brain.

While this theoretical work remains controversial, direct evidence of cellular automata-like behavior in the brain has been observed in the form of intercellular calcium waves. While poorly understood, these propagating waves of calcium—which strongly resemble the glider patterns from Conway’s Game of Life—are initiated by astrocytes in the hippocampus and retina and are believed to be a form of intercellular communication which may modulate synaptic function. Moreover, intercellular calcium waves are a likely example the of complex interactions between parts (neurons) which must be studied to obtain a complete understanding of the brain as a complex system.

The ability of cellular automata to elegantly model complex phenomena remains a simple proof of principle that interactions between simple parts can explain many behaviors often attributed to living systems. Moreover, such behavior can never be fully understood by studying individual parts. While the “neighbor rules” of the brain remain a mystery, a new generation of physiologists, thinking outside the box (or grid, as it were) will be required to understand the brain in the context of Wolfram’s “new kind of science.”

Taken together, SOC, network science, and cellular automata are powerful tools for understanding complexity in the brain. Which model do you think gives the greatest insight into the brain’s complex behavior? Let us know in the comments.



Mitchell, Melanie. Complexity: A guided tour. Oxford University Press, 2009.

Wolfram, Stephen. A new kind of science. Vol. 5. Champaign: Wolfram media, 2002.

Hameroff, Stuart. “Quantum computation in brain microtubules? The Penrose-Hameroff’Orch OR’model of consciousness.” PHILOSOPHICAL TRANSACTIONS-ROYAL SOCIETY OF LONDON SERIES A MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (1998): 1869-1895.

Scemes, Eliana, and Christian Giaume. “Astrocyte calcium waves: what they are and what they do.” Glia 54.7 (2006): 716-725.

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