Alexander Mordvintsev showed me two clumps of pixels on his screen. They pulsed, grew and blossomed into monarch butterflies. As the two butterflies grew, they smashed into each other, and one got the worst of it; its wing withered away. But just as it seemed like a goner, the mutilated butterfly did a kind of backflip and grew a new wing like a salamander regrowing a lost leg.
Mordvintsev, a research scientist at Google Research in Zurich, had not deliberately bred his virtual butterflies to regenerate lost body parts; it happened spontaneously. That was his first inkling, he said, that he was onto something. His project built on a decades-old tradition of creating cellular automata: miniature, chessboard-like computational worlds governed by bare-bones rules. The most famous, the Game of Life, first popularized in 1970, has captivated generations of computer scientists, biologists and physicists, who see it as a metaphor for how a few basic laws of physics can give rise to the vast diversity of the natural world.
In 2020, Mordvintsev brought this into the era of deep learning by creating neural cellular automata, or NCAs. Instead of starting with rules and applying them to see what happened, his approach started with a desired pattern and figured out what simple rules would produce it. “I wanted to reverse this process: to say that here is my objective,” he said. With this inversion, he has made it possible to do “complexity engineering,” as the physicist and cellular-automata researcher Stephen Wolfram proposed in 1986 — namely, to program the building blocks of a system so that they will self-assemble into whatever form you want. “Imagine you want to build a cathedral, but you don’t design a cathedral,” Mordvintsev said. “You design a brick. What shape should your brick be that, if you take a lot of them and shake them long enough, they build a cathedral for you?”
Such a brick sounds almost magical, but biology is replete with examples of basically that. A starling murmuration or ant colony acts as a coherent whole, and scientists have postulated simple rules that, if each bird or ant follows them, explain the collective behavior. Similarly, the cells of your body play off one another to shape themselves into a single organism. NCAs are a model for that process, except that they start with the collective behavior and automatically arrive at the rules.
Alexander Mordvintsev created complex cell-based digital systems that use only neighbor-to-neighbor communication.
Courtesy of Alexander Mordvintsev
The possibilities this presents are potentially boundless. If biologists can figure out how Mordvintsev’s butterfly can so ingeniously regenerate a wing, maybe doctors can coax our bodies to regrow a lost limb. For engineers, who often find inspiration in biology, these NCAs are a potential new model for creating fully distributed computers that perform a task without central coordination. In some ways, NCAs may be innately better at problem-solving than neural networks.
Life’s Dreams
Mordvintsev was born in 1985 and grew up in the Russian city of Miass, on the eastern flanks of the Ural Mountains. He taught himself to code on a Soviet-era IBM PC clone by writing simulations of planetary dynamics, gas diffusion and ant colonies. “The idea that you can create a tiny universe inside your computer and then let it run, and have this simulated reality where you have full control, always fascinated me,” he said.
He landed a job at Google’s lab in Zurich in 2014, just as a new image-recognition technology based on multilayer, or “deep,” neural networks was sweeping the tech industry. For all their power, these systems were (and arguably still are) troublingly inscrutable. “I realized that, OK, I need to figure out how it works,” he said.
He came up with “deep dreaming,” a process that takes whatever patterns a neural network discerns in an image, then exaggerates them for effect. For a while, the phantasmagoria that resulted — ordinary photos turned into a psychedelic trip of dog snouts, fish scales and parrot feathers — filled the internet. Mordvintsev became an instant software celebrity.
Among the many scientists who reached out to him was Michael Levin of Tufts University, a leading developmental biologist. If neural networks are inscrutable, so are biological organisms, and Levin was curious whether something like deep dreaming might help to make sense of them, too. Levin’s email reawakened Mordvintsev’s fascination with simulating nature, especially with cellular automata.
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