The secret π in the Mandelbrot Set
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- Опубліковано 5 сер 2022
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The mandelbrot set is probably the single most iconic picture in all of math. Yet, somehow, someway, there's always something about this fractal that I find myself scratching my head about. Today, let's look at one of those things :)
The source code for the animations can be found here:
github.com/vivek3141/videos, which utilize manim: github.com/3b1b/manim
Huge thanks to @alfcnz, @Bean_Piano for reviewing and helping me with the video!
You can find my sources here (including the code used to generate the zoom in section, which I did not do myself, and the math behind how the colors are generated): docs.google.com/document/d/1v...
A portion of this video was sponsored by Wren.
Music (In order)
Knowmadic - Faces chll.to/892bc12e
Philanthrope, mommy - embrace chll.to/7e941f72
Philanthrope, Idealism - Still chll.to/a110849c
Jujutsu Kaisen (but its okay if its lofi?)
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The unexpected pi hidden in the Mandelbrot Set
Some tags: vcubingx, v cubingx, vcubing x, v cubing x, mandelbrot set, pi, fractal,
Haven't been in a great headspace lately, sorry this took so long! If you enjoyed it, let me know and please consider subscribing :D
lets be honest its not even unexpected at this point, i could find my social security and credit card numbers in the mandelbrot set and it would just be like "huh"
beautiful video vivek! the connection to pi was indeed mind-blowing :)
I really appreciate that you put the source code of the animations.
The y=x becoming a tangent/secant line and limiting the process at the touch/intersection point was a nice geometrical reveal to me. So, I guess, for the full complex plane, we should consider a w=z hyperplane in a 4-dimentional complex space C² (with coordinates w and z analogous to y and x in R²), which limits the process when it becomes a tangent/secant to the hyperparabola w = z²+c, and boundaries of the Mandelbrot set are just values of the "offset" parameter "c" when it shifts the parabola so that w=z plane becomes exactly a tangential plane, right?
Definitely reminds me of 3blue1brown’s videos on block collisions counting digits of pi. This seems a little different cause the digits aren’t exact, and while tan(x) appears, the answer isn’t based on tan x being approximately x for small x like the block collision solution is.
GOOD WORK! love to see the video learned a lot!!!
Lovely explanation! Thank you.
I just wanted to say that the quality of your videos has greatly improved since I last saw your channel. This is a great step up.
Fantastic, love to see your videos. I request you to please make one video also on fixed point techniques.
This was fantastic :)
Cool. Thanks for sharing
It's nice to find inspirations that go a bit deeper than the math thought in school. I liked the way the ode appeared out of the blue.
that's insanely cool
I couldn’t of guessed it had to do with the poles of tan that’s so cool
π is everywhere.
Route 113 music was an exquisite choice sir
I don't know about opengl, but I've been playing around with opencl and I seem to be able to get a 1440p frame of an image orbit trap to render fast enough for around 24fps real time on a 6700xt gpu. I only have a basic pyqt script that renders that onto a qt label right now, but its nice to be able to play with image trap boundaries and see an image get warped around the mandelbrot set :) I wanted to also use gl (but not by itself) but it seems cl gl interop requires them to be compiled together :(
Exactly this is what makes math beautiful
Hello! Just asking a doubt based on the installation of Manim : Can we also do it with the Anaconda Distribution of Python? Thanks!