Fractals

Articles and videos

Exemple d'une courbe ni classique, ni fractale by Nik Lygerōs (July 1991) ► A continuous curve of finite length and not differentiable in an infinity of points.
The Marriage of Fractals and Splines by Ron Goldman (June 15^th, 2009) ► After looking to analogies between fractals and Bézier curves, Ron Goldman explains how to combine them by using complex numbers in Bézier equations.
Fractals are typically not self-similar by Grant Sanderson (January 27^th, 2017) ► The definition of non-integer dimensions and of fractals.
Festive Fractals - Computerphile↓ by Philip Moriarty (December 22^nd, 2017) ► This presentation of fractals is neither really good nor interesting.
Effet Papillon et Théorie du Chaos by David Louapre (February 16^th, 2018) ► A very classical presentation of chaotic systems.
Fractal dimensions by Dilts (September 15^th, 2018) ► How is defined and computed the dimension of a fractal.
Les trous du cube - Micmaths by Mickaël Launay (February 19^th, 2019) ► Intersecting Menger sponge with a plane.
Rémi Carles - Dimensions bizarres by Rémi Carles (March 27^th, 2019) ► A short video explaining how to define the dimension of a fractal.
Fractales : le diable est dans les détails by Roger Mansuy (April 2019) ► The Hausdorff dimension of the graph of the Weierstrass function has been computed in 2017.
Tribonacci Numbers (and the Rauzy Fractal) - Numberphile by Edmund Harriss (June 3^rd, 2019) ► A presentation of the Rauzy Fractal.
Chaos: The Science of the Butterfly Effect by Derek Muller (December 6^th, 2019) ► The basics of chaos theory.
This equation will change how you see the world (the logistic map) by Derek Muller (January 29^th, 2020) ► The logistic map, the Mandelbrot Set, and Feigenbaum constant.
Sounds of the Mandelbrot Set by "CodeParade" (February 28^th, 2021) ► The music is awful, but some of the fractals are very nice.
Chaotic Balls (and other animations) - Numberphile by Matt Henderson (July 24^th, 2021) ► The simulation of some chaotic systems.
The Problem With The Butterfly Effect by Henry Reich (October 21^st, 2021) ► Henry Reich explains why the butterfly effect is a bad example of a chaotic system: it emphasises too much causality and predictability instead of unpredictability.
How We Can Make Sense of Chaos — Dynamical systems can be chaotic and impossible to predict, but mathematicians have discovered tools to help understand them. by David S. Richeson (March 2^nd, 2022) ► A presentation of Stephen Smale’s horseshoe map.
How Chaos Control Is Changing The World by Sabine Hossenfelder (December 24^th, 2022) ► Some examples of using AI to control some chaotic systems.
La théorie du chaos - De l'ordre dans le désordre (⧉) by Denis van Waerebeke (October 10^th, 2023) ► The history of the chaos theory.
Une fractale dans le sang - Micmaths by Mickaël Launay (November 16^th, 2023) ► The relationship between the Sierpinski triangle and the blood types.
‘Entropy Bagels’ and Other Complex Structures Emerge From Simple Rules — Simple rules in simple settings continue to puzzle mathematicians, even as they devise intricate tools to analyze them. by Jordana Cepelewicz (February 27^th, 2024) ► As usual, this Quanta Magazine article is interesting, but its shallowness is frustrating.
A 1.58-Dimensional Object - Numberphile by Ben Sparks (March 7^th, 2025) ► A fractal can have a Hausdorff dimension which is an integer and 3D fractals that have projections, along the three axes, which are squares.
↪Fractal Dimensions (extra footage) - Numberphile by Ben Sparks (March 6^th, 2025) ► The continuation of the previous video.
Chaos game
- Chaos Game - Numberphile by Ben Sparks (April 27^th, 2017) ► Random paths generating fractals.
- ↪Chaos Game | Fractals emerging from chaos | Computer simulation | by "Think Twice" (November 7^th, 2017) ► Applications of the previous video (but the last example seems buggy).
- Le jeu du chaos - Automaths #08🚫 by Jason Lapeyronnie (October 2^nd, 2018) ► The usual Sierpinski triangle and some other Iterated Function Systems.
Feigenbaum Constant
- A Magic Number - Sixty Symbols by Philip Moriarty and Roger Bowley (May 30^th, 2009) ► A rather abstract explanation of the first Feigenbaum Constant.
- Mandelbrot set - from order to chaos by Michael Hogg (July 22^nd, 2010) ► Displaying side-by-side what happens on the real axis of the Mandelbrot set and on a bifurcation graph.
- The Feigenbaum Constant (4.669) - Numberphile by Ben Sparks (January 16^th, 2017) ► Logistic Maps bifurcations and the first Feigenbaum Constant.
Mandelbrot Set
- The Mandelbrot Set - Numberphile by Holly Krieger (July 25^th, 2014) ► A presentation of the most famous fractal.
- ↪Filled Julia Set by Holly Krieger (September 30^th, 2014) ► The continuation of the previous video: the filled Julia sets and their relationship with the Mandelbrot set.
- Deux (deux ?) minutes pour Mandelbrot by Jérôme Cottanceau (May 6^th, 2015) ► A classical and effective presentation of the Mandelbrot set.
- The dark side of the Mandelbrot set by Burkard Polster (March 4^th, 2016) ► A classical but effective presentation of the Mandelbrot Set.
- Fibonacci Numbers hidden in the Mandelbrot Set - Numberphile by Holly Krieger (October 5^th, 2017) ► The title says it all.
- What's so special about the Mandelbrot Set? - Numberphile↑ by Ben Sparks (April 18^th, 2019) ► Using interactive graphics to explain Julia sets and the Mandelbrot Set.
- À la découverte de l'ensemble de Mandelbrot - Myriogon #6 by Mickaël Launay (March 24^th, 2020) ► A description on how to generate the Mandelbrot Set and a JavaScript program.
- A Long Zoom Into the Mandelbrot Set (January 26^th, 2024) ► A deep dive into the Mandelbrot Set.
- The Quest to Decode the Mandelbrot Set, Math’s Famed Fractal — For decades, a small group of mathematicians has patiently unraveled the mystery of what was once math’s most popular picture. Their story shows how technology transforms even the most abstract mathematical landscapes. by Jordana Cepelewicz (January 26^th, 2024) ► The work of Misha Lyubich, Jeremy Kahn, Dima Dudko, and Alex Kapiamba to prove the MLC (Mandelbrot Local Connectivity) conjecture.
- The Mystery of Hyperbolicity - Numberphile by Holly Krieger (February 21^st, 2024) ► The density of hyperbolicity conjecture.
- The superior fractal no-one has heard of by Matt Parker (June 28^th, 2025) ► A classical presentation of Mandelbrot and Julia Sets.
Space filling curves
- Space-Filling Curves - Numberphile by Henry Segerman (September 26^th, 2016) ► The title says it all.
- ↪Infinite Staircase - Numberphile by Henry Segerman (September 27^th, 2016) ► A complement of the previous video: how to prove than £[2=\sqrt{2}£].
- Hilbert's Curve: Is infinite math useful? by Grant Sanderson (July 21^st, 2017) ► The problem of mapping the 2D space onto the 1D line, and getting a feeling that Hilbert curve is a continuous space-filling curve.
Dragon curve
- Dragon Curve - Numberphile by Rob Eastaway (February 5^th, 2013) ► A presentation of the dragon curve.
- Wrong Turn on the Dragon - Numberphile by Donald Knuth (December 30^th, 2014) ► Donald Knuth has an (erroneous) dragon curve mosaic in his house.
- Unfolding The Dragon | Fractal Curve | by "Think Twice" (October 22^nd, 2017) ► A good animation.
- L'énigme du Dragon - Chasse au trésor mathématique by Mickaël Launay (March 12^th, 2018) ► A simple question about the dragon curve.
- La courbe du dragon - Myriogon #20 by Mickaël Launay (April 22^nd, 2020) ► Some information about the dragon curve and Koch snowflake.
Sandpiles
- The Amazing, Autotuning Sandpile — A simple mathematical model of a sandpile shows remarkably complex behavior. by Jordan Ellenberg (April 2^nd, 2015) ► The Abelian sandpile model produces beautiful fractals and avalanches.
- Sandpiles - Numberphile by Luis David Garcia-Puente (January 13^th, 2017) ► A clear, simple, but educative introduction to sandpiles.
Koch Tessellation
- Le pavage de Koch by Alexander Thomas (April 22^nd, 2022) ► An explanation of a tessellation using Koch snowflakes of two sizes.
- L'étonnant puzzle fractal de von Koch - Micmaths by Mickaël Launay (April 28^th, 2022) ► The same.
- ↪Le flocon de Koch en 3D - Micmaths by Mickaël Launay (May 21^st, 2022) ► A 3D Koch snowflake is a cube.
Newton’s method and Newton’s fractal
- Problèmes de voisinages sur l'ile de Wada by Jérôme Cottanceau (June 27^th, 2017) ► The lakes of Wada and the Newton fractal.
- Newton’s fractal (which Newton knew nothing about) by Grant Sanderson (October 12^th, 2021) ► Newton’s method and the fact that the regions defined by the convergence toward each root are fractal.
- ↪Beyond the Mandelbrot set, an intro to holomorphic dynamics by Grant Sanderson (October 16^th, 2021) ► Holomorphic dynamics (fixed points and cycles), Mandelbrot sets, Fantou Set, and Julia sets.
- Maxime Bouchereau - Méthodes et fractales de Newton by Maxime Bouchereau (February 13^th, 2024) ► A short presentation of Newton’s fractal.