Explainer: What is chaos theory?

Using math, scientists show that chaos is not really random

a satellite image showing Hurrican Ian from space

Here’s Hurricane Ian on September 28, 2022, as photographed by a U.S. weather satellite. It caused more than $1 billion in damage. Chaos in the data used to predict the hurricane’s path limited how early scientists knew where Ian would slam Cuba and Florida (outlined above).


It’s common to hear the term chaos used to describe seemingly random, unpredictable events. The energetic behavior of kids on a bus ride home from a field trip might be one example. But to scientists, chaos means something else. It refers to a system that is not totally random but still cannot be easily predicted. There’s a whole area of science devoted to this. It’s known as chaos theory.

In a non-chaotic system, it’s easy to measure the details of the starting environment. A ball rolling down a hill is one example. Here, the ball’s mass and the hill’s height and angle of decline are the starting conditions. If you know these starting conditions, you can predict how fast and far the ball will roll.

A chaotic system is similarly sensitive to its initial conditions. But even tiny changes to those conditions can lead to huge changes later. So, it’s hard to look at a chaotic system at any given time and know exactly what its initial conditions were.

For example, have you ever wondered why predictions of the weather one to three days from now can be horribly wrong? Blame chaos. In fact, weather is the poster child of chaotic systems.

The origin of chaos theory

Mathematician Edward Lorenz developed modern chaos theory in the 1960s. At the time, he was a meteorologist at the Massachusetts Institute of Technology in Cambridge. His work involved using computers to predict weather patterns. That research turned up something strange. A computer could predict very different weather patterns from almost the same set of starting data.

But those starting data weren’t exactly the same. Small variations in the initial conditions led to wildly different outcomes.

To explain his findings, Lorenz likened the subtle differences in starting conditions to the impacts of the flapping wings of some distant butterfly. Indeed, by 1972 he called this the “butterfly effect.” The idea was that the flap of an insect’s wings in South America might set up conditions that led to a tornado in Texas. He suggested that even subtle air movements — such as those caused by butterfly wings — could create a domino effect. Over time and distance, those effects might add up and intensify winds.

Does a butterfly really affect the weather? Probably not. Bo-Wen Shen is a mathematician at San Diego State University in California. This idea is an oversimplification, he argues. In fact, “the concept … has been generalized mistakenly,” Shen says. It’s led to a belief that even small human actions could lead to huge unintended impacts. But the general idea — that tiny changes to chaotic systems can have huge effects — still holds up.

Maren Hunsberger, a scientist and actress, explains how chaos is not some random behavior, but instead describes things that are hard to predict well. This video shows why.

Studying chaos

Chaos is difficult to predict, but not impossible. From the outside, chaotic systems appear to have traits that are semi-random and unpredictable. But even though such systems are more sensitive to their initial conditions, they do still follow all the same laws of physics as simple systems. So the motions or events of even chaotic systems progress with almost clock-like precision. As such, they can be predictable — and largely knowable — if you can measure enough of those initial conditions.

One way scientists predict chaotic systems is by studying what’s known as their strange attractors. A strange attractor is any underlying force that controls the overall behavior of a chaotic system.

Shaped like swirling ribbons, these attractors work somewhat like wind picking up leaves. Like leaves, chaotic systems are drawn to their attractors. Similarly, a rubber ducky in the ocean will be drawn to its attractor — the ocean surface. This is true no matter how waves, winds and birds may jostle the toy. Knowing the shape and position of an attractor can help scientists predict the path of something (such as storm clouds) in a chaotic system.

Chaos theory can help scientists better understand many different processes besides weather and climate. For instance, it can help explain irregular heartbeats and the motions of star clusters.

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