Hilbert Curve from an L System @MathVisualProofs

Hilbert Curve from an L System @MathVisualProofs

Uploaded September 2025 | Updated September 2026, 2 weeks ago

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).

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Thanks!

If you want to see other constructions of like this, see
youtu.be/GVhLhAXAWoI
youtu.be/MEzgGGq2l5E
youtu.be/8Q_zuRKKh2g
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:

en.wikipedia.org/wiki/L-system
en.wikipedia.org/wiki/Turtle_graphics
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 free-stock-music.com
Creative Commons / Attribution 3.0 Unported License (CC BY 3.0)
creativecommons.org/licenses/by/3.0/deed.en_US

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

30 Regular Polygons

$Summing Powers of 1/6 via a Square Dissection This is a short, animated visual proof demonstrating the infinite sum of the powers of 1/6 using a square. The result is somewhat surprising given that it doesnt seem obvious how to decompose a square into powers of 1/6 and how the resulting area could easily be seen as 1/5 of a square. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you like this type of video, here is my geometric sum playlist: https://www.youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw This animation is based on a proof by Tom Edgar from the December 2023 issue of Mathematics Magazine pages 563-565. (https://doi.org/10.1080/0025570X.2023.2266415 ). #mathematics #mathvideo #math #calculus #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricseries #series #infinitesums #infiniteseries #selfsimilarity #fractal To learn more about animating with manim, check out: https://manim.community$

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$Self-Similar Geometric Series Sum Self-similar geometric series sum This is a short, animated visual proof demonstrating the infinite sum of the powers of 1/2 using a square. To see a longer version with explanation, check out: https://youtu.be/AiznRQPIwTs If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you like this type of video, here is my geometric sum playlist: https://www.youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw This dissection is loosely based on a proof by Roger B. Nelsen from the February 2006 issue of Mathematics Magazine page 60. (https://doi.org/10.2307/27642904). An animated version of that exact dissection is here: https://youtube.com/shorts/RoovN01q83Y or https://youtu.be/saJJGNlsfn8 #mathematics #mathvideo #math #calculus #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricseries #series #infinitesums #infiniteseries #selfsimilarity #fractal To learn more about animating with manim, check out: https://manim.community$

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$Koch Snowflake: Infinite Perimeter but finite area This is a short, animation showing the Koch snowflake and discussing the fact that it has infinite perimeter but encloses a finite area. #mathshorts #mathvideo #math #fractal #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #limits #mathematics #perimeter #kochsnowflake This is a standard result that can be found in numerous places, such as Wikipedia. To learn more about animating with manim, check out: https://manim.community$

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