Chaos Theory
Order hidden in disorder — the science of the butterfly effect. From Poincaré and Lorenz to fractals, strange attractors and the Mandelbrot set: how simple rules produce endless, beautiful unpredictability.
A chronological documentary of 169 moments spanning 1890–2026 on Loreline.
last updated 2026-07-22
Eras
- The Pioneers — The minds who found order in disorder — Poincaré and the three-body problem, Edward Lorenz and the weather, Mandelbrot, Feigenbaum, Yorke and James Gleick, whose 1987 book gave chaos its name in the public mind.
- The Butterfly Effect — Sensitive dependence on initial conditions — Lorenz's discovery that a tiny change can utterly reshape the future, and the question that named it: does a butterfly's wings in Brazil set off a tornado in Texas?
- Strange Attractors — Order hidden inside chaos — the Lorenz, Rössler and other strange attractors, the beautiful shapes that chaotic systems trace in phase space.
- The Logistic Map & Bifurcation — How one simple equation breaks into chaos — the logistic map, the period-doubling route, and Feigenbaum's universal constant 4.669… that appears again and again in nature.
- Fractals & the Mandelbrot Set — The geometry of roughness — Mandelbrot's fractals, the infinite detail of the Mandelbrot and Julia sets, Koch snowflakes and the self-similar patterns of nature.
- Chaos in Nature — Where chaos lives in the real world — the double pendulum, turbulence, weather, populations, heartbeats and the three-body problem.
- Chaos in Culture — Chaos beyond the lab — Ian Malcolm's monologue in Jurassic Park, the butterfly effect in film and art, and the Santa Fe Institute's science of complexity.
- — Henri Poincaré. The French mathematician who, studying the three-body problem in 1890, first glimpsed that simple deterministic systems could be wildly unpredictable.
- — The Koch snowflake. A curve of infinite length enclosing a finite area — an early fractal that defied ordinary geometry.
- — The Sierpiński triangle. A self-similar fractal made of ever-smaller copies of itself.
- — A Julia set. A member of the family of fractals closely tied to the Mandelbrot set, each point of which spawns its own intricate world.
- — The Lorenz attractor. The butterfly-shaped strange attractor Edward Lorenz found in 1963 — order hidden inside chaotic weather equations.
- — James A. Yorke. The mathematician whose 1975 paper 'Period Three Implies Chaos' gave the field its name.
- — The bifurcation diagram. The logistic maps route to chaos — one equation splitting into a fractal fog.
- — The Rössler attractor. Another strange attractor — Otto Rössler's simpler chaotic system, folding trajectories into an endless ribbon.
- — The Mandelbrot set. The most famous fractal — infinitely detailed, self-similar, and generated by one tiny equation iterated over the complex plane.
- — Jurassic Park - Lunch - Great Scenes. One of the greatest scenes in film history. Disclaimer: I don't own any of the footage presented here, this video was made merely to pay homage to this film and not for any profit or commercial reasons. No copyright infringement intended, video is for entertainment purposes ONLY.
- — Ian Malcolm Chaos Theory | Jurassic Park | DINOSAUR Movie. Boxoffice Movie Scenes
- — Jurassic Park (1993) - Chaos Theory Scene | Movieclips. Movieclips
- — La théorie du chaos d'après Ian Malcolm | Jurassic Park | Extrait VF. Boxoffice | Les Grands Moments de Cinéma
- — Arthur Clarke - Fractals - The Colors Of Infinity 1 of 6. do5e
- — CHAOS. fractalgod
- — Benoit Mandelbrot Hunting the Hidden Dimension Nova 2008. Equations of the matrix
- — Benoit Mandelbrot: Fractals and the art of roughness. TED
- — Fractals: The geometry of Nature? - Benoit Mandelbrot. An enquiry into the Nature of Fractal Geometry. Includes an interview with Benoît Mandelbrot, the father of Fractals, who died 17th October 2010.
- — Benoit Mandelbrot - (full) The Nature of Roughness in Mathematics, Science and Art.. fractal
- — Lorenz Attractor - Physics 123 demo with Paul Horowitz. Prof. Paul Horowitz is Professor of Physics and of Electrical Engineering at Harvard University's Dept. of Physics and principal investigator on the Harvard SETI project. He is the co- author, along with Winfield Hill, of "The Art of Electronics".
- — James Gleick on Chaos: Making a New Science. Open Road Media
- — James Gleick extended interview. ABC News (Australia)
- — Chaos and Butterfly Effect - Sixty Symbols. Sixty Symbols
- — Koch snowflake fractal | Perimeter, area, and volume | Geometry | Khan Academy. Khan Academy
- — What Is The Coastline Paradox?. Veritasium
- — Principles of Complexity - Overview. Santa Fe Institute
- — Complexity: Life, Scale, & Civilization. Santa Fe Institute
- — James Gleick Interview and Reading. The Royal Society
- — Awesome Prime Number Constant (Mills' Constant) - Numberphile. Numberphile
- — Chaos | Chapter 7 : Strange Attractors - The butterfly effect. It's so blatant
- — Measuring Coastline - Numberphile. Numberphile
- — Carbon Maestro - Chaos Theory (feat. Forest Rain and MEMJ0123). Carbon Maestro
- — MAE5790-1 Course introduction and overview. Cornell MAE
- — MAE5790-4 Model of an insect outbreak. Cornell MAE
- — MAE5790-2 One dimensional Systems. Cornell MAE
- — MAE5790-18 Strange attractor for the Lorenz equations. Cornell MAE
- — The Joy of x: A Guided Tour of Math. Santa Fe Institute
- — Fractals The Hidden Dimension HD 1080p Nova. Universe TV
- — Filled Julia Set. Numberphile2
- — Patterns of Life – Edward Lorenz and Chaos Theory (#5/5). OpenLearn from The Open University
- — What is chaos, by James Yorke. Modesto Montoya
- — What Is A Fractal (and what are they good for)?. MITK12Videos
- — The Neutral Theory of Ecology. MIT OpenCourseWare
- — Ecosystem Stability, Critical Transitions, and Biodiversity. MIT OpenCourseWare
- — ChaosBook.org chapter Go with the flow: Strange attractors - Lorenz again. birdtracks
- — K4 M Illuminating the Genesis of Chaos - Mitchell Feigenbaum's Journey of Discovery #SCCS2015. icmReporting
- — Social Attractors & Chaos. Systems Innovation Network
- — Tien-Yien Li. If you find our videos helpful you can support us by buying something from amazon.
- — Deterministic Nonperiodic Flow: Chaos Theory. BK Teach
- — Lorenz Attractor and Chaos. MIT OpenCourseWare
- — Double Pendulum Chaos Demonstration. lalaithion
- — The Mandelbrot Set: How it Works, and Why it's Amazing!. Jimi Sol
- — The mystery of 0.577 - Numberphile. Numberphile
- — The Butterfly Effect | This Video Will Change Your Life | Documentary. Top5s
- — The Feigenbaum Constant (4.669) - Numberphile. Numberphile
- — Fractals are typically not self-similar. 3Blue1Brown
- — The Julia Sets: How it Works, and Why it's Amazing!. Jimi Sol
- — The Coastline Paradox & Fractals. This video explains what the Coastline Paradox and Fractlas are.
- — The Butterfly Effect - What Does It Really Signify?. Oxford Mathematics
- — CET OBJET EST CHAOTIQUE ! (double pendule). Dr Nozman
- — Can BUTTERFLIES Cause TORNADOES? The Butterfly Effect Explained. Ancient Mysteries
- — Double pendulum | Chaos | Butterfly effect | Computer simulation. Think Twice
- — Beyond Chaos: The Continuing Enigma of Turbulence ▸ KITP Public Lecture by Nigel Goldenfeld. Kavli Institute for Theoretical Physics
- — 3D Strange Attractors. Softology
- — Celebrating the Science of Jule Charney and Ed Lorenz. Born 100 years ago, MIT professors Jule Charney and Ed Lorenz profoundly shaped the field of meteorology during their lifetimes. Charney laid the groundwork for numerical weather prediction and saw it transform nearly every aspect of the field, while Lorenz changed our conception of weather from deterministic phenomena to chaos. Their stories are intertwined with the evolution of meteorological research at MIT, which is continued today in the Program for Oceans, Atmospheres, and Climate within the Department of…
- — MIT on Chaos and Climate: Edward N. Lorenz and the End of the Cartesian Universe. Earth, Atmospheric and Planetary Sciences at MIT
- — MIT on Chaos and Climate: Biological Population Dynamics. Earth, Atmospheric and Planetary Sciences at MIT
- — MIT on Chaos and Climate: From Determinism to Probability in Numerical Weather Prediction. Earth, Atmospheric and Planetary Sciences at MIT
- — Fractals Documentary - The Colours Of Infinity (1995) -. Quixotic Psychotic
- — Introduction to Complexity: Period Doubling Route to Chaos Part 2. Complexity Explorer
- — BUTTERFLY EFFECT: How THIS Butterfly Caused a Tornado!. Arvin Ash
- — Why 5/3 is a fundamental constant for turbulence. 3Blue1Brown
- — High Detail Slow Mandelbrot Zoom (2160p/4k). Lazy Ape
- — The Lorenz Attractor Explained. Josh Kastorf
- — Dynamical Systems And Chaos: Strange Attractors Summary. Complexity Explorer
- — Are there other Chaotic Attractors?. Orfeas Liossatos
- — What's so special about the Mandelbrot Set? - Numberphile. Numberphile
- — How a Butterfly’s Wingbeat CAN Change the Weather. SciShow
- — How fractals can help you understand the universe | BBC Ideas. What is a fractal, and how can fractals help us understand the universe? Classic examples of fractals in nature are broccoli and snowflakes. They can offer a fascinating explanation for how the world works!
- — Chaos: The Science of the Butterfly Effect. Veritasium
- — The Real Butterfly Effect. Sabine Hossenfelder
- — Solving the Three Body Problem. PBS Space Time
- — This equation will change how you see the world (the logistic map). The logistic map connects fluid convection, neuron firing, the Mandelbrot set and so much more. Fasthosts Techie Test competition is now closed! Learn more about Fasthosts here: Code for interactives is available below...
- — The Chaotic Pendulum. The Cardboard Channel
- — Inside Out: James Gleick Turns Chaos, Genius & Information into Best Sellers | Event - Nov 21, 2013. NYU Arthur L. Carter Journalism Institute
- — Julia Sets, and how they relate to The Mandelbrot Set. The Mathemagicians' Guild
- — W. Brian Arthur (Part 1) on The History of Complexity Economics. From its beginnings as a discipline nearly 150 years ago, economics rested on assumptions that don’t hold up when studied in the present day. The notion that our economic systems are in equilibrium, that they’re made of actors making simple rational and self-interested decisions with perfect knowledge of society— these ideas prove about as useful in the Information Age as Newton’s laws of motion are to quantum physicists. A novel paradigm for economics, borrowing insights from ecology and evolutionary biology,…
- — Turbulent Flow is MORE Awesome Than Laminar Flow. Everyone loves laminar flow but turbulent flow is the real MVP. A portion of this video was sponsored by Cottonelle. Purchase Cottonelle Flushable Wipes and try them for yourself:
- — Koch Snowflake Fractal: Area and Perimeter Calculation. Tom Rocks Maths
- — Does the flap of butterfly's wings cause tornado ? (weather prediction and butterfly effect). The Flocking Mind
- — The Beauty of Chaos - Strange Attractors. morn1415
- — Bifurcation and Chaos: Population Distributions under the Logistic Map. What you're seeing here are probability distributions of a population after 30 years, assuming the population was initially uniformly distributed and the population next year is given by the logistic map:
- — 2.920050977316 - Numberphile. Numberphile
- — Nonlinear Dynamics and Chaos: Introduction (Strogatz Ch. 1) | Lecture 1. Dr. Shane Ross
- — What Is Turbulence? Turbulent Fluid Dynamics are Everywhere. Steve Brunton
- — Turbulence: Reynolds Averaged Navier-Stokes (Part 1, Mass Continuity Equation). Steve Brunton
- — Highlight - Mandelbrot Fractal Zoom. Maths Town
- — Logistic Map Explained (Strogatz Ch. 10): Period-Doubling Route to Chaos | Part 1. Dr. Shane Ross
- — Period-Doubling Route to Chaos & Universality: Feigenbaum Constants in Experiments | Strogatz Ch. 10. Dr. Shane Ross
- — Strange Attractors Explained (Strogatz Ch. 12): Stretching and Folding in Phase Space. Dr. Shane Ross
- — Chaos Theory: the language of (in)stability. The field of study of chaos has its roots in differential equations and dynamical systems, the very language that is used to describe how any physical system evolves in the real world. This video aims to tell the story of chaos step by step, from simple non-chaotic systems, to different types of attractors, to fractal spaces and the language of unpredictability.
- — Chaos discrete logistic map. CBlissMath
- — Fractals in Nature || Chaos. Chaos and Cryptography
- — The Rössler attractor. PhySim
- — Exploring The Bleak Chaos of THE BUTTERFLY EFFECT. Ryan Hollinger
- — The Anatomy of a Dynamical System. Steve Brunton
- — [TSUCS2] Three-Scroll Unified Chaotic System|Chaotic attractor | Chaos Theory. Three-Scroll Unified Chaotic System (TSUCS2) results into a chaotic attractor - This nonlinear system (known as TSUCS2) with specific initial conditions is solved numerically and the resulting trajectory is shown through a 3 dimensional animation.
- — J. Doyne Farmer on The Complexity Economics Revolution. Santa Fe Institute
- — Foundational Concepts In Chaos Theory: An Explanation of Veritasium's Logistic Map Video. In This video I'll go over the foundations of chaos theory to and you'll learn how to prove and predict certain aspects of the Logistic Map.
- — Beyond the Mandelbrot set, an intro to holomorphic dynamics. 3Blue1Brown
- — The Problem With The Butterfly Effect. minutephysics
- — Bifurcation Diagram Live Geogebra Build (as seen on Numberphile). SparksMaths
- — The Colours Of Infinity (2010 version). William Rood
- — The Beauty of the Butterfly Effect. Science Marshall
- — Infinite Relaxation [Part 1] - A Mandelbrot Fractal Zoom (3e3284). A relaxing full colour 4-hour journey into the deep depths of the Mandelbrot. This is now the deepest zoom on this channel, going to a magnifiction of 3e3284. That is 3 with 3284 zeros after it! (Try zooming in that far on your phone).
- — James Gleick at Nobel Conference XXVI. Gustavus Adolphus College
- — Logistic Map Bifurcation Diagram (An Introduction). Jonathan Mitchell
- — Chaos Theory. Met Office - Learn About Weather
- — Chaos and the Three Body Problem. Eliza Diggins
- — Chaotic Dynamical Systems. Steve Brunton
- — Complexity Explorer Lecture: David Krakauer • What is Complexity?. To celebrate Complexity Explorer's 10th anniversary, we're excited to share a lecture from SFI President David Krakauer sectioning the concept of complexity and exploring complexity epistemology and emergence.
- — The Chaos Theory - Fractal Foundation. Sir JPagdilao Classroom
- — Chaotic Systems Simulation | Rössler Attractor. SlowWave
- — Chaos theory and geometry: can they predict our world? – with Tim Palmer. The Royal Institution
- — Is the Logistic Map hiding in the Mandelbrot Set? | #SoME3. Desdenova
- — The Butterfly Effect: How a Flutter in Brazil Causes Tornadoes in Texas!. Think tiny actions don't matter? Think again! Learn how the flap of a butterfly's wings can set off a chain of events leading to massive storms halfway across the world. Uncover the chaos theory in 3 minutes!
- — Chaos Theory and The Butterfly Effect - Predicting The Unpredictable. University of Bristol
- — Period 3 Implies Chaos - Dynamical Systems | Lecture 32. In this lecture we learn about one of the most famous results in all of chaos theory: "Period 3 Implies Chaos." This incredible result is due to Li and Yorke and was published in 1975. In fact, it is the first occurrence of the word chaos in the mathematics literature to describe the complex dynamics that can arise in discrete-time dynamical systems. In this lecture we state and prove the "Period 3 Theorem." Interestingly, one needs little more than basic calculus to arrive at the result. Towards the end of the…
- — Explaining the Bifurcation Diagram for the Lorenz Chaotic System. Lazaros Moysis
- — Decoding Math’s Famed Fractal: The Mandelbrot Set. Quanta Magazine
- — Explaining the Bifurcation Diagram for the Logistic Map. Lazaros Moysis
- — Beautiful Chaos Based on Langford Attractor. Ohtou Nao
- — Unlocking the Mystery of the Feigenbaum Constant. Word Mastery Channel
- — Sensitive dependence on initial conditions. Active Math
- — A simple guide to chaos theory - BBC World Service. BBC World Service
- — The REAL Three Body Problem in Physics. Up and Atom
- — Unlocking The Mystery Of The Coastline Paradox Through Fractals. Seven Liu
- — Making Sense of Chaos: A Better Economics for a Better World. Santa Fe Institute
- — What Is The ButterFly Effect? | How can Small Changes Lead to Bigger Changes? | The Chaos Theory. Peekaboo Kidz
- — Iterations part 2: period three implies chaos. Mats Vermeeren
- — Fractals Animation | Koch Snowflake - Manim CE, Python. Ptolémé
- — Unlocking Chaos Theory in Weather Prediction-Beginner Guide. ThinkInnovation
- — The Prime Constant - Numberphile. Numberphile
- — Chaos in Nature: How Nature Embraces Complexity. In this captivating episode of "The Chaos Theory," host Rahul delves deep into the heart of nature's complexity, exploring how chaos manifests in various natural systems. From the mesmerizing patterns of fractal geometry to the unpredictable dance of turbulent flows, chaos reminds us of the limits of our understanding and the awe-inspiring beauty of the world around us. Join us as we unravel the mysteries of nonlinear dynamics, emergence, self-organization, chaotic systems, and bifurcations, uncovering the…
- — Population stability, cycles and chaos. Bill Sutherland's Conservation Concepts
- — Phase Space & Attractors ; Visualizing Nature’s Behaviour. Science Hunter
- — Why The Three-Body Problem Is More Relevant Than Ever. 🌌 The Mystery of the Three-Body Problem 🌌 Welcome to our exploration of one of the most fascinating challenges in physics and mathematics: the Three-Body Problem! In this documentary-style video, we delve into the complexities of predicting the movements of three gravitationally interacting bodies, a puzzle that has puzzled scientists for centuries.
- — Reynolds Number & Ocean Turbulence – Predicting Chaotic Ocean Movements. Dive into the captivating world of ocean dynamics with our latest video, "Reynolds Number & Ocean Turbulence: Unraveling Ocean Mysteries!" 🌊✨ Explore how the Reynolds Number—a key concept in fluid dynamics—helps us predict chaotic ocean movements, from hurricanes to swirling whirlpools.
- — Colorful Chaos - A Lorenz Attractor Animation. Timepiece
- — Deterministic Nonperiodic Flow by Edward Lorenz (1963). Daniel Wieser
- — Lorenz Attractor Tutorial: Chaos Theory Visualization with Python (Google Colab). Code of the Future
- — Mitchell Feigenbaum: The Seeds of Chaos | CUNY Laureates. CUNY TV
- — Double Pendulums are Chaoticn't. 2swap
- — The Lorenz Attractor: The Butterfly That Lives in Chaos. LoopyLoops3D
- — Journey Into Chaos!. Mathematics for Machine Learning
- — Mitchell Feigenbaum – The Physicist Who Found Order in Chaos. Atomic Gear
- — ®️ The Mathematics of Sudden Change | Bifurcation Theory Explained. Staiblocks
- — ®️ Who is .. Henri Poincaré? | The Father of Chaos Theory. Staiblocks
- — Pushing Simulations to the LIMIT to Find Order in Chaos. Drew's Campfire
- — Phase Space: the geometry of Hamiltonian mechanics. Dr. Jorge S. Diaz
- — The Beautiful Mathematics of Chaos: Mandelbrot Sets & Fractal Geometry. The Sleepy Computer Scientist
- — How Weather Models Predict (and Fail): Equations, Chaos & the 10-Day Limit Explained!. Mohsin Insights
- — The Butterfly Effect: Why Weather Forecasts Are Fundamentally Unpredictable. The Silent Ledger
- — Magnetic Pendulum — Chaos From 3 Magnets (Python Simulation). myClover
- — The man who changed the way mathematics is perceived forever (Full Documentary) | Benoit Mandelbrot. wocomoDOCS
- — Benoît Mandelbrot: He Saw The Structure Of The World — They Called Him Crazy. Fools!. Rabbi Solomon
- — What happened behind THE BUTTERFLY EFFECT was more DISTURBING than the movie itself. FILM CULT
- — The Mandelbrot Set Explained | Infinite Zoom Into the Most Famous Fractal in Math. Ratan Chavan
- — Lorenz Attractor Animation | Beautiful Chaos Theory in Motion | Strange Attractor Mathematics. This video showcases the Lorenz Attractor, one of the most famous examples of deterministic chaos in mathematics and physics. Starting from a simple initial point, the trajectory gradually evolves into the iconic butterfly-shaped structure, demonstrating how complex and unpredictable patterns can emerge from simple mathematical equations.
Full text archive: /loreline-text/chaos-theory.md
