Uploaded May 2025 | Updated September 2026, 2 weeks ago

In this short, we show what happens when iterating the procedure of choosing a heptagon vertex at random and moving 0.692 of the distance from the current dot to the chosen point.

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If you want to know more about the Chaos game, see the following links:
en.wikipedia.org/wiki/Chaos_game
https://mathworld.wolfram.com/ChaosGa...
https://math.bu.edu/DYSYS/chaos-game/...
youtu.be/kbKtFN71Lfs
youtu.be/IGlGvSXkRGI
youtube.com/shorts/yDHkNDrHfIw

#chaos #chaosgame #heptagon #mathvideo #math #mtbos #manim #animation #theorem #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractal #fractals

To learn more about animating with manim, check out:
https://manim.community

$Chaos in a Heptagon! In this short, we show what happens when iterating the procedure of choosing a heptagon vertex at random and moving 0.692 of the distance from the current dot to the chosen point. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you want to know more about the Chaos game, see the following links: https://en.wikipedia.org/wiki/Chaos_game https://mathworld.wolfram.com/ChaosGa... https://math.bu.edu/DYSYS/chaos-game/... https://youtu.be/kbKtFN71Lfs https://youtu.be/IGlGvSXkRGI https://youtube.com/shorts/yDHkNDrHfIw #chaos #chaosgame #heptagon #mathvideo #math #mtbos #manim #animation #theorem #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractal #fractals To learn more about animating with manim, check out: https://manim.community$

$Mediant Inequality from Slopes This is a short, animated visual proof demonstrating what one might call the mediant inequality. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! For an alternate visual proof of this fact, see: https://youtu.be/RKeBuWL1B4A https://youtube.com/shorts/cI92ZID95g4 https://youtu.be/pODylgdI3p8 For the wide format of this video, see: https://youtu.be/AuxqpiDTCyU?si=kLa0Un4L8ADM6a_q This animation is based on a visual proof by Li Changming from the January 1988 issue of Mathematics Teacher (https://www.jstor.org/stable/27965677 - page 63). #math #inequality #numbertheory #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #fractions #mediant #mathematics #fareyfractions #farey #mathshorts #mathvideo To learn more about animating with manim, check out: https://manim.community$

Visualizing the Digits of e | 1000 Digits of Euler’s Number

Sigmoid Curve as Area Accumulation of Standard Normal Distribution

Da Vinci’s Pythagorean Theorem Proof (Right triangle theorem)

Arithmetico-Geometric Series via Gabriel’s Staircase

Visualizing the Digits of 1/7, 2/7, 3,7, 4/7, 5/7, and 6/7

$Hilbert Curve from an L System In this video, we describe two how to draw a plane filling curve called the Hilbert curve using an L-system. While the substitution strings are a bit complicated, the rules for this system are easy to implement and use to draw a level 8 Hilbert curve (to dramatic music). If you liked this video, consider liking or subscribing. Or you can support me by buying me a coffee at https://www.buymeacoffee.com/VisualProofs Thanks! If you want to see other constructions of like this, see https://youtu.be/GVhLhAXAWoI https://youtu.be/MEzgGGq2l5E https://youtu.be/8Q_zuRKKh2g https://youtu.be/UKNcbNpP w If you want to know more about L-systems or turtle graphics or the Gosper curve, check out these wikipedia sites: https://en.wikipedia.org/wiki/L-system https://en.wikipedia.org/wiki/Turtle_graphics https://en.wikipedia.org/wiki/Hilbert_curve To learn more about animating with manim, check out: https://manim.community #turtlegraphics #fractal #math #manim #mathvideo #Lsystem #hilbert #hilbertcurve #planefillingcurve #visualmath #fractalcurves Music in this video: Voyager by Alex-Productions | https://onsound.eu/ Music promoted by https://www.free-stock-music.com Creative Commons / Attribution 3.0 Unported License (CC BY 3.0) https://creativecommons.org/licenses/by/3.0/deed.en_US$

Mathematical Visual Proofs |