This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: Predicting a system's final outcome from its initial state is the ultimate goal for many physicists. In certain complex systems, however, this goal is thwarted by chaos, where even the subtlest tweaks to the initial state can lead to completely different fates, making the system almost impossible to predict.
In research published in Nature Communications, Illinois physicists developed a model showing that unpredictability can also arise in nonchaotic systems. Despite being fully deterministic, the team's model resists computational attempts to predict its final state based on its initial configuration. Remarkably, however, the scientists found that the model's dynamics give rise to topological structure that can eventually be used as a reliable predictor of final fate, demonstrating that predictability itself can emerge over time.
Push a block of known mass with a known force. As any physics student knows, the block's initial position allows us to predict its final position at some specified time. In deterministic systems such as this one, the final outcome is predetermined by the initial configuration and the rules governing its evolution through time.
In practice, however, things aren't always so simple. In chaotic deterministic systems, for instance, although the governing rules may be known exactly, minuscule deviations in the systems' initial configurations can become magnified, leading to different final states than one might have expected. But it seems chaos isn't the only source of unpredictability, an idea Illinois physics professor Hyun Youk stumbled across some years back.
"When I started my group 11 years ago," he said, "we started working on models of living systems to understand how complex dynamics can arise from simple deterministic rules, specifically systems of living cells that interact with each other to form spatial patterns. "In 2020, we computationally searched for ways that cells could communicate by secreting molecules and sensing those from other cells. We found communication modes that matched how cells in nature form the very same types of spatial patterns." The model Youk's team focused on was a cellular automaton (CA), a discrete grid of individual cells, each of which is in one of a finite number of possible states and can change its state according to fixed update rules.
Although these rules are often very simple, CAs can develop remarkably sophisticated patterns that appear to move, interact and even self-replicate, behaviors that have inspired their use as models for pattern formation within the fields of physics, computer science and biology. In the 2020 work, Youk's team defined their own CA, one whose cells resemble those found in living tissues. Each cell takes on one of four states, visualized as a color, and after every time step, changes its state according to a special gene circuit, mimicking how real cells secrete and sense molecules around them.
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