In this video, we show how to generate the Lévy Dragon using an L-system given by the following rules:
Start with F and iteratively perform the following replacements:
F replaced by +F−−F+
replaced by +
replaced by -
Once you stop, you walk on the plane using the following rules:
For F: Take one step forward
For +: Rotate 45 degrees clockwise
For - : Rotate 45 degrees counterclockwise
In this video, we compute the sequence where 65535 steps are taken and show the creation of the curve in this case.
The amazing music in this video is from James Whetzel : www.jameswhetz...
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoff.... Thanks!
Here are some other L-system visualizations:
• Sierpinski Arrowhead C...
• Walking the Dragon and...
Also, check out these videos for related constructions:
• Mandelbrot Quintet Fra...
• Chaos Game in a Hexagon
• Levy Curve from the Ch...
This animation was inspired by an article written by Larry Riddle that appeared in the the November 2016 issue of Math Horizons:
doi.org/10.416...
See more here (larryriddle.ag...) and on his website: larryriddle.ag...
#Lsystem #levy #levydragon #mathvideo #math #mtbos #manim #animation #theorem #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractals #cthulhu
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14 окт 2024
