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.

Part of Chaos Theory

34 moments in this segment.

1. 1904 — The Koch snowflake. A curve of infinite length enclosing a finite area — an early fractal that defied ordinary geometry.
2. 1915 — The Sierpiński triangle. A self-similar fractal made of ever-smaller copies of itself.
3. 1918 — 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.
4. 1980 — The Mandelbrot set. The most famous fractal — infinitely detailed, self-similar, and generated by one tiny equation iterated over the complex plane.
5. 1995-01-01 — Arthur Clarke - Fractals - The Colors Of Infinity 1 of 6. do5e
6. 2008-10-28 — Benoit Mandelbrot Hunting the Hidden Dimension Nova 2008. Equations of the matrix
7. 2010-12-06 — 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.
8. 2011-01-07 — Benoit Mandelbrot - (full) The Nature of Roughness in Mathematics, Science and Art.. fractal
9. 2011-09-30 — Koch snowflake fractal | Perimeter, area, and volume | Geometry | Khan Academy. Khan Academy
10. 2012-01-06 — What Is The Coastline Paradox?. Veritasium
11. 2014-03-27 — Measuring Coastline - Numberphile. Numberphile
12. 2014-09-23 — Fractals The Hidden Dimension HD 1080p Nova. Universe TV
13. 2014-09-30 — Filled Julia Set. Numberphile2
14. 2015-06-11 — What Is A Fractal (and what are they good for)?. MITK12Videos
15. 2016-08-26 — The Mandelbrot Set: How it Works, and Why it's Amazing!. Jimi Sol
16. 2017-01-27 — Fractals are typically not self-similar. 3Blue1Brown
17. 2017-04-03 — The Julia Sets: How it Works, and Why it's Amazing!. Jimi Sol
18. 2017-04-26 — The Coastline Paradox & Fractals. This video explains what the Coastline Paradox and Fractlas are.
19. 2018-04-11 — Fractals Documentary - The Colours Of Infinity (1995) -. Quixotic Psychotic
20. 2018-12-26 — High Detail Slow Mandelbrot Zoom (2160p/4k). Lazy Ape
21. 2019-04-18 — What's so special about the Mandelbrot Set? - Numberphile. Numberphile
22. 2020-04-01 — Julia Sets, and how they relate to The Mandelbrot Set. The Mathemagicians' Guild
23. 2020-06-24 — Koch Snowflake Fractal: Area and Perimeter Calculation. Tom Rocks Maths
24. 2021-04-03 — Highlight - Mandelbrot Fractal Zoom. Maths Town
25. 2021-10-16 — Beyond the Mandelbrot set, an intro to holomorphic dynamics. 3Blue1Brown
26. 2021-10-25 — The Colours Of Infinity (2010 version). William Rood
27. 2021-12-12 — 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).
28. 2024-01-26 — Decoding Math’s Famed Fractal: The Mandelbrot Set. Quanta Magazine
29. 2024-07-28 — Unlocking The Mystery Of The Coastline Paradox Through Fractals. Seven Liu
30. 2024-09-13 — Fractals Animation | Koch Snowflake - Manim CE, Python. Ptolémé
31. 2026-02-05 — The Beautiful Mathematics of Chaos: Mandelbrot Sets & Fractal Geometry. The Sleepy Computer Scientist
32. 2026-06-09 — The man who changed the way mathematics is perceived forever (Full Documentary) | Benoit Mandelbrot. wocomoDOCS
33. 2026-06-18 — Benoît Mandelbrot: He Saw The Structure Of The World — They Called Him Crazy. Fools!. Rabbi Solomon
34. 2026-07-10 — The Mandelbrot Set Explained | Infinite Zoom Into the Most Famous Fractal in Math. Ratan Chavan