Gosper Curve L-System : Walking a Plane-Filling Curve @MathVisualProofs

Uploaded January 2025 | Updated September 2026, 2 weeks ago

In this video, we describe two how to draw a plane filling curve called the Gosper 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 6 Gosper curve (to dramatic music).

If you liked this video, consider liking or subscribing. Or you can support me by buying me a coffee at buymeacoffee.com/VisualProofs
Thanks!

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

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/Gosper_curve

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

#turtlegraphics #fractal #math #manim #mathvideo #Lsystem #Gosper #gospercurve #planefillingcurve #visualmath #fractalcurves

___________________________________________
Music in this video:
Rise Again 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

$Gosper Curve L-System : Walking a Plane-Filling Curve In this video, we describe two how to draw a plane filling curve called the Gosper curve using an L-system. While the substitution strings are a bit complicated, the rules for this system are easy to implement and use to draw a level 6 Gosper curve (to dramatic music). If you liked this video, consider liking or subscribing. Or you can support me by buying me a coffee at https://www.buymeacoffee.com/VisualProofs Thanks! If you want to see other constructions of like this, see https://youtu.be/GVhLhAXAWoI https://youtu.be/MEzgGGq2l5E https://youtu.be/8Q_zuRKKh2g If you want to know more about L-systems or turtle graphics or the Gosper curve, check out these wikipedia sites: https://en.wikipedia.org/wiki/L-system https://en.wikipedia.org/wiki/Turtle_graphics https://en.wikipedia.org/wiki/Gosper_curve To learn more about animating with manim, check out: https://manim.community #turtlegraphics #fractal #math #manim #mathvideo #Lsystem #Gosper #gospercurve #planefillingcurve #visualmath #fractalcurves Music in this video: Rise Again by Alex-Productions | https://onsound.eu/ Music promoted by https://www.free-stock-music.com Creative Commons / Attribution 3.0 Unported License (CC BY 3.0) https://creativecommons.org/licenses/by/3.0/deed.en_US$

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