The 'butterfly effect' is the informal name for chaos theory

In mathematics, chaos theory involves complex systems that are highly sensitive to their initial conditions. Originally discovered when analyzing weather data, slight variations in the data input into such systems create drastically different results, despite following known physical laws.

The origin of chaos theory, colloquially known as the 'butterfly effect'

The theory explains that systems following well-understood physical laws can still produce unpredictable outcomes due to small variations in their initial conditions. Originally identified in weather data, elements of chaos have been observed in stock market fluctuations, cardiac arrhythmias, and the evolution of online social movements.

The life of Edward Lorenz, who originally used a seagull in his 'butterfly effect' metaphor

By accidentally finding that rounding one variable to its third decimal place and re-running a weather simulation produced a drastically different two-month forecast, the American mathematician established the field of chaos theory. His paper—"Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas?"—introduced the well-known metaphor for the behavior of chaotic systems. (Some readers may experience a paywall.)

Learn how natural systems exhibit characteristics of chaos theory

In biology, some mathematical models of ecosystem populations and heart irregularities show strong sensitivity to initial conditions, which scientists can simulate to determine quantitative tipping points at which these systems become unstable. Within the social sciences, crowd behavior and the virality of social media posts have shown how human behavior fits within the framework of chaos theory.

View the Lorenz attractor, a graphical solution to chaotic equations that resembles a butterfly

The discovery of chaos theory came from Edward Lorenz's computer model of the atmosphere, which used three equations to quantify atmospheric circulation. However, the chaotic evolution of this system creates wandering figure-8-like shapes—some resembling butterfly wings—as it repeatedly attempts to settle on one of two values along unique trajectories.

An explanation distinguishing the butterfly effect from causality, necessity, and sufficiency

In pop culture, the analogy has conveyed the impression that the flapping of a butterfly's wings has a cascading effect that directly produces a tornado somewhere else on Earth. However, butterfly-wing flapping alone is insufficient to cause tornadoes, as the complexity of atmospheric systems requires many more conditions to produce them, any of which can be the tipping point to initiate tornadogenesis.

Mathematics proves turbulence's chaos creates super diffusion

Turbulent flow is responsible for the rapid scattering of dandelion seeds, volcanic ash, and untied balloons. Its swirling behavior accelerates particle scattering faster than other mixing methods, as particles acquire energy from the interactions of eddies.

How chaos helps explain why small market corrections can produce major economic instability

Oxford University complex systems professor Doyne Farmer discusses how predictions from many economic models are overly weighted toward simple relationships, such as supply and demand, and external shocks, such as the COVID-19 pandemic. However, real-world macroeconomic systems involve public and private actors interacting, producing feedback loops and cascading effects that resemble the oscillatory behavior seen in chaotic systems.

Understanding turbulence, which is characterized by growing chaos at multiple scales

As energy is lost in fluids undergoing turbulent, non-linear flow, particles will collectively form eddies, or whirlpools, of various sizes that mix together. The energy cascade of larger eddies becoming smaller ones before dissipating completely varies based on the initial conditions of the fluid, a characteristic feature of chaotic systems.

Climate models use complex equations and supercomputers to predict future climate

The equations apply the laws of thermodynamics, fluid motion, and radiative transfer to a 3D grid along Earth's surface. After solving them for each cell in the grid over a time interval, the results carry over to neighboring cells, and the process repeats into the future.

Accurate climate models incorporate calculus to account for complex feedback loops

The simplest models assume uniformity across the Earth, with incoming energy from the sun being offset by the planet's albedo, or reflectiveness, which prevents the radiation from being fully absorbed. Incorporating elements such as atmospheric layers, latitude bands, geographic variability, and emissivity yields coupled differential equations quantifying Earth's interconnected systems.

A mathematical and visual analysis distinguishing chaos from randomness

Random systems lack any underlying pattern or causal relationships, while chaos is mathematically deterministic because the behavior follows established laws of nature. In 3D plots, chaotic systems produce outputs that approximate a mathematical function, while random points appear as statistical noise.

Turbulence has been called the most important unsolved problem in classical physics

Despite being the most common type of fluid flow in our world, scientists have struggled to model turbulent flow accurately. Though behaving unpredictably, understanding inertia and viscosity can help determine whether turbulence will occur.

An interview with James Yorke, the man who coined the mathematical term 'chaos'

Along with co-author Tien-Yien Li, the former University of Maryland mathematics department chair published the paper, "Period Three Implies Chaos" in 1975. "Chaos" then became the terminological placeholder for systems with sensitive dependence on initial conditions, which had been well known to mathematicians for over a decade.

The turbulence experienced in airplanes results from unexpected changes in airflow

Pilots rely on forecasts, onboard tools, and air traffic control to avoid regions of severe turbulence during flight. Turbulence is generally weaker for those sitting in the front of the main cabin and for morning flights that follow cooler nighttime temperatures.

Atmospheric processes amplify the strength of storms by coalescing clouds

Research has shown that turbulent mixing of air at the edges of clouds and other small-scale thermal activity beneath them help clouds group together, intensifying short bursts of rainfall, especially in tropical regions. Simulations reveal this produces more powerful storms than predicted by older models, though they may occur less frequently.

Clouds' subtle climate effects require significant computational power to simulate

Responsible for reflecting sunlight and preventing thermal energy from entering the Earth system while also trapping energy and keeping it in the system, clouds are understood to substantially influence climate predictions. Because even supercomputers struggle to accurately model their dynamic behavior, researchers have used AI to indirectly incorporate clouds into climate models.

Unlike quantum mechanics, classical physics suggests free will does not exist

Models based on Newton's laws of motion suggest all actions are predetermined and must follow specific trajectories and outcomes, such that everything that will ever occur in the future has already been set in motion by past causes. However, quantum mechanics challenges determinism because it is based on probability, where no outcome is certain.

Climatologists use past data and advanced models to forecast future climate trends

Unlike meteorology, which focuses on weather forecasting over several days, climatology identifies trends in data over periods of 30 or more years. This data can go back millions of years and help refine models to forecast centuries into the future.

Fast-changing conditions during their formation make tornado forecasting difficult

The final steps of tornadogenesis—the process of forming a tornado—depend on near-surface details, such as local geography, which are difficult for radar to observe and affect how funnel clouds make contact with the ground. Inconsistencies in storm behavior have limited the amount of advance warning people receive before tornadoes touch down.

Explore interactive simulations of strange attractors, the graphs that help visualize chaos

Although simple, linear equations reach an explicit value for a given input, such as *f(x) \= x* + 1 equaling 4 when *x* equals 3, some chaotic, nonlinear systems tend to evolve towards multiple values simultaneously. These simulations allow users to observe the unusual mathematical artifacts created by systems as their outputs evolve toward these distinct values.

Learn why modern scientific patterns have been described as theories rather than laws

After confirming that the accuracy of some laws of physics is limited to certain domains, science became more hesitant to categorize identified mathematical relationships, such as quantum mechanics, as unchanging laws. Instead, these recent, complex frameworks are designated as theories to acknowledge that they are conditional and may be part of a larger, more complete future framework.

Because some models of the universe do not incorporate time, it may be an emergent property born from our limited perception of the universe, rather than a fundamental property of reality.

The field of attribution science seeks to determine whether specific phenomena, such as melting glaciers, droughts, and hurricanes, are driven by Earth's natural climate cycles or by human-caused climate change.

Probability waves govern particles like electrons in the quantum space

Just as waves are extended objects whose heights change across space, quantum waves dictate that the probability of an object existing in different locations across space varies. Like water waves, the probability waves can combine, changing the heights—and therefore probabilities—in different locations.

The ingredients that make up severe weather

A seven-minute video illustrating how a storm is made. These factors—moisture, instability, lift, and shear—are explained through a series of data sets and creative, descriptive diagrams.

In a tornado outbreak, a single severe weather system can spawn multiple twisters

By maintaining the ingredients for tornadoes—differences in wind speed and direction across altitudes, moisture, and rising air—for long periods of time as it moves across a region, a severe thunderstorm can continuously produce tornadoes by lifting multiple columns of horizontally rotating air.

The story of two female programmers running the simulations behind chaos theory's discovery

Margaret Hamilton and Ellen Fetter worked on MIT's 800-pound Royal McBee LGP-30 computer, which was fed binary code on paper tape to perform computations. Among the computations performed were those involving equations describing the motion of gas in a circulating fluid for Edward Lorenz, widely considered the father of chaos theory.

Tornado chasers include scientists conducting field projects

Research teams use drones, mobile weather stations, and radar systems to capture real-time meteorological data, better understand conditions that favor tornado formation, and improve forecasting models. As of 2022, model limitations result in roughly 70% of tornado warnings being false alarms.

Meteorological v. astronomical seasons, explained

Meteorologists and climatologists define seasons differently from “regular” or astronomical spring, summer, fall, and winter. Traditional seasons reflect the movement of celestial objects, known as the astronomical seasons; meteorologists mark seasonal change based on temperature averages.

Global climate models simulate Earth system interactions and how human activity impacts climate

By splitting the planet into tiny 3D grid cells, supercomputers can run thousands of equations for each cell to determine the movement of energy, moisture, and other elements across Earth. The equations can also incorporate greenhouse gases to determine how humans affect the climate.

Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

Climate change is increasing the frequency and intensity of severe turbulence

Severe turbulence over the North Atlantic has increased by 55% over the past 40 years, driven by strengthened jet streams and storm systems. Ongoing increases in global temperatures, which fuel these changes, may triple severe turbulence incidents in the coming decades.

View the 55 ECVs used to describe Earth's atmospheric conditions

Essential climate variables include physical, chemical, and biological variables that meaningfully contribute to Earth's climate and how it changes with time. Many of these variables influence one another through feedback mechanisms across Earth's atmosphere, hydrosphere, cryosphere, biosphere, and geosphere.

The arrow of time—the concept that time only moves in the forward direction—is thought to result from the universe progressing toward greater disorder, or entropy.

What's the difference between weather and climate?

A five-minute TedEd video exploring the differences between weather and climate – what they are, how we predict them, and what those predictions can tell us.

Within quantum mechanics, the Heisenberg uncertainty principle limits how precisely one can simultaneously know the values of pairs of complementary properties for an object, such as position and momentum.

AI-powered models can provide low-cost, localized and accurate weather forecasting

These models can run on standard laptops, reducing the need for expensive supercomputers and expanding access to developing regions. AI forecasts can help farmers make informed planting decisions, improving crop yields and reducing costs.