Watch at: https://youtu.be/ttB-KYZbfIQ
Play at: https://editor.p5js.org/PotatoImaginator/sketches/dGEAgixYA

#youtube #youtuber #youtubechannel #p5js #js #javascript #animation #animated #animation3d #3danimation #art #artist #artistsonmastodon #mengersponge #fractal #fractalart #math #maths #mathematics #programming #programmer #code #coding #creative #creativecoding #scripting #nerd #geek #computer #ComputerScience #3d

   
❛❛ Teen #Mathematicians Tie #Knots Through a #Mind-Blowing Fractal ❜❜

Three high schoolers and their mentor revisited a century-old #theorem to prove that all #knots can be found in a #fractal called the #MengerSponge.
Gregory Barber for #QuantaMagazine

🔗 https://QuantaMagazine.org/teen-mathematicians-tie-knots-through-a-mind-blowing-fractal-20241126/ 2024 Nov 26 ce
🔗 https://Wikipedia.org/wiki/Menger_sponge … #MengerSponge
🔗 https://Wikipedia.org/wiki/Topology … #Topology

#Community #TimeTravel #Research #maths #dimensions #Kronodon

Here's a \(\textit{void-sponge}\) using sphere inversion, unlike for instance the #MengerSponge which is built using only linear transformations.

Unlike the previous inversion sets, this one is built in 4D and then stereographically projected into 3D. That's because the most symmetric structure of spheres is at the vertices of a regular polychoron, and the projection to 3D is conformal, so retains the uniform sphere intersection angles.

To render, the sample point is stereographically projected into 4D, then sphere inversion iteratively applied around the polychoron vertices.
The sphere radii are identical and set such that they meet at angles of \(\pi/j\) for integer j. This value affects how thick the limbs of the sponge are.

"To put things into Perspective: ..."

#mengersponge #mathart #codeart

Iterating the Menger Sponge, Spooky Season Edition!

Full-Size Full-Length Version: https://youtu.be/JqhjaGntljU

#codeart #fractal #mengersponge #mastoArt

Yup got it right. ^^

#mengersponge #fractal #codeart #mastoart