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

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.

Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

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.)

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.

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 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.

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.

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.

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

Within quantum physics, the order of events across time may not follow causality

Although time is considered a fixed, ordered mapping of events, where the past affects the future, quantum superposition breaks down causality, suggesting that future events can occur simultaneously with past ones. Within the quantum model, the notion of cause and effect is not a fundamental feature of our universe.

Chaos gardening involves scattering seeds without any planning

The trend is intended to produce colorful, dense gardens by mixing various seeds. While encouraging experimentation and lower stakes, the success of these gardens depends on choosing plants with similar needs and incorporating native, nectar-rich flowers.

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

Butterfly populations have declined by 22% from 2000 to 2020

Research suggests that one in every five butterflies is lost due to pesticide use, habitat loss, and climate change. Playing a vital role in pollination, their declining populations threaten plant reproduction and the health of ecosystems.

Bomb cyclones can produce heavy rain, blizzard conditions, and intense winds

Known as "bombogenesis" in meteorology, these systems get their colloquial name from their rapid intensification over a 24-hour period—a phenomenon seen in some tropical cyclones. They occur most commonly along the coasts of the Northeast and Northwest US when there is a severe temperature difference between colliding air masses.

How upheavals in accepted scientific theories helped popularize the term 'paradigm'

When Thomas Kuhn published "The Structure of Scientific Revolutions" in 1962, he described the history of science as comprising periods of "normal science" where these accepted frameworks—paradigms—gradually accumulate anomalies until they cannot describe nature. Revolutionary science, such as the development of a new theory, results in a paradigm shift, another term Kuhn helped popularize. (Some readers may experience a paywall.)

Classical mechanics describes the motion of and forces on everyday objects

Newton's laws form the core of classical mechanics, suitable for everyday objects and speeds. The term is relatively new, distinguishing the branch of physics from quantum and relativistic mechanics.

The greenhouse effect was discovered by analyzing Earth's temperature

Using mathematical techniques developed to analyze heat transfer, Jean-Baptiste Joseph Fourier showed that Earth should be significantly cooler if solar radiation were the only contributor to its surface temperature. By considering that the atmosphere could amplify the sun's warming effect, he formulated what became known as the greenhouse effect.

Fearology, or the study of fear, explores the difference between stress and fear

Our brains involuntarily respond to our environment and signal alarm when that isn’t always needed, triggering responses that include goose bumps. But understanding fear and how to talk our brains into calming down can improve daily life.

The ultraviolet catastrophe is the infinite energy prediction of classical physics

When scientists first tried calculating the radiation emitted by a heated object, their assumption was that energy was equally distributed across wavelengths and produced infinite energy at low wavelengths. This contradicted observations, which showed near-zero energy intensity at those values.

Chronobiologists study the effect of time on biological cycles

Circadian rhythms were first observed in the 1700s, when French astronomer Jean-Jacques D'Ortous de Mairan put a plant in a dark room and watched it still respond to day and night cycles, setting off further studies about specific light-dark biological cycles, an area of inquiry that continues today with the human "clock proteins" at the molecular level.

Is ice slippery because of amorphization—a chaos of molecules caused by sliding?

Traditional explanations cite three factors that make ice slippery: pressure, friction and so-called premelting. A fourth has been proposed in recent years: amorphization, that sliding along some surfaces creates molecular disorder, causing liquid-like behavior.

The Big Bang theory explains the expanding universe and its fiery early origins

The term “Big Bang” was initially coined by a skeptic of the theory, but the name stuck despite the theory not depicting a "bang." The event took place everywhere in the universe at once, and the theory explains the abundance of hydrogen and helium in the universe.

The science of optical illusions

The human brain has developed cognitive shortcuts to help us navigate in a world where our visual senses are constantly bombarded of information. But these shortcuts can also be exploited, tricking the brain into telling us something is happening when it really isn't. This short video unpacks the neuroscience behind some of the most common (but perplexing) optical illusions.

The terms 'bug' and 'debugging' were popularized by Grace Hopper's team

Engineers working on the Mark II computer at Harvard University identified a moth in one of its components in 1947, which caused it to malfunction. Describing the incident as the "first actual case of bug being found," the term first used by Thomas Edison in 1878 to describe faults in an apparatus caught on.

What is a reply all email storm?

When 30,000 people receive an email, to which anyone can "reply all," a spontaneous chain reaction of many more messages can be sparked, producing what's known as an "email storm." This has happened at a large scale in several high-profile cases, most notably in Thomson Reuter's email database. Check out Know Your Meme's breakdown of this phenomenon and description of several major examples.

Stars appear to twinkle because turbulence in the motion of molecules in Earth's atmosphere causes light to bend and wiggle rapidly on its way to the surface—a phenomenon called scintillation.

Dirty lightning is a thunderstorm created from friction between rising and falling flows of ash and smoke during volcanic eruptions.

How Amazon operates a 'flywheel' business model, a self-reinforcing cycle that drives continuous growth

According to the physics of black holes, our 4D reality may be a hologram—a projection of information coded on a 2D surface on the edge of the universe.

Radioactive elements can introduce software errors because the ionizing radiation they produce can detach electrons from atoms, and computer code relies on the distribution of electrons.

Some Pokémon have been named after real and fictional organisms, while some real-world species have been named after Pokémon, such as Chilicola charizard and Binburrum zapdos.

While the sun's gravity keeps the planets in orbit, their gravity also pulls on the sun, causing it and everything else in the solar system to orbit around a mutual balance point called the barycenter—the true center of the solar system.

El Niño, Spanish for 'the boy,' was named after Jesus Christ because the phenomenon resembled the weather changes observed around Christmastime.

The name 'Silicon Valley' arose from the founding of Shockley Semiconductor Laboratory in Fairchild Semiconductor in 1956-57, founded near Stanford University in Palo Alto

The term 'algorithm' originated from the Latinized name of al-Khwārizmī, a 9th-century mathematician whose works introduced Arabic numerals and the decimal-based numeral system to Europe and whose treatise 'Al-Jabr' gave algebra its name.

Exploring the Larry Bird punch that almost changed March Madness

About 12.5% of US adults experience a phobia in their lifetime, a diagnosis that hinges on the intense fear interfering with daily life and persisting for at least six months.

Clever Hans was a 1900s horse that was believed to be able to solve math equations, tell time, and read and comprehend German, until a psychology student discovered how he got his answers.

The word 'jazz' evolved from 'jasm,' 19th-century American slang for 'energy'

Studies suggest when you sleep is as important as how much you get, and syncing with your circadian rhythms may lead to less fatigue and improved long-term health outcomes

Ebola is a filovirus, meaning it resembles a thread under a microscope, though it sometimes twists and can resemble a bowl of spaghetti.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

Warren Buffett's former professor Benjamin Graham is known as the 'father of value investing,' a strategy in which investors seek to buy stocks trading below their intrinsic worth.

Georgia O'Keeffe's flower paintings are often assumed to be sexual, though the artist claimed she was simply interested in highlighting the beauty of flowers that most people neglect

Scientists testing how climate change affects plants found, in a years-long simulation study, that poison ivy grew 70% faster with the resulting extra carbon dioxide.

SpongeBob exemplifies Aristotle's philosophy for living well because he understands that happiness doesn't come from external factors like money, recognition, or power.

The power and influence of the American presidency have expanded significantly over time—far beyond what the founders envisioned.

The first horror movie is believed to be George Méliès' 1986 short 'The Haunted Castle,' which pioneered the use of special effects