Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal
The original web page describing the development of a 3D equivalent to the Mandelbrot set.

#fractal #Mandelbrot #Mandelbulb

jus' JosKn #Monday #Mathart #Mandelbulb #Mood

"Just remember," she says. "I'm holding you responsible for all of this."

#Monday #Mathart #Mandelbulb #Mood

While sitting in bed, waiting for the medication to do it's work, I'd like to show you a fractal animation, I made with the free software
#Mandelbulb. I hope you love the beauty of math too 🫶 btw, you can do this too 👍
The sound is borrowed from the Amiga
"2010.mod" by VCC+GIGICAR 1989
Composed by blackstar and trixal in 1989
#animation #fractal

https://www.youtube.com/watch?v=zt9y-9VKVWY

#ExperimentalMusic #ModularSynths #Fractals #Mandelbulb

One way to avoid the sharp edges seen on the Mandelbox is to replace the non-smooth fold operations with something more like a wrap operation.
As with the #MandelbrotSet and the #Mandelbulb we square the vector magnitude each iteration and find a way to multi-cover the remaining degrees of freedom.
Unlike the Mandelbulb we can make this multi-cover conformal on the sphere by treating it as a Riemann sphere and using the transformation:
\( \frac{-z}{2\sqrt{2}}\Pi_{j=0}^2 \frac{z-\sqrt{2}e^{2ji\pi/3}}{z-\sqrt{1/2}e^{(2j+1)i\pi/3}}\)

The result is quite odd:
(image by pupukuusikko: https://www.deviantart.com/pupukuusikko)

and deeper inside reveals these elaborate ceilings and ornamentation.
The nice looking arches are because the +c part stretches the spherical curves from the sphere inversions into ellipsoids. The orthogonal linear folds (called a box fold) also contribute to its architectural appearance compared to for example the #Mandelbulb.
info: https://sites.google.com/site/mandelbox/gallery

#thursdayfractal #trippy #mandelbulb #sierpinski

Asteroid Belt #Mandelbulb #Fractal #MathArt #Design ~:::<>:::~

Hi Everyone, new podcast episode with dreamy and light-hearted mood ✨ Beautiful visuals / 3D art by Alessandro Granito . Enjoy! 😊

🎧👉 https://linktr.ee/digigroovesession

#melodichouse #organichousemusic #mix #djset #auja #tracklist #mandelbulb #3D #fractal #glsl #3dart #artcode #trippy

#mandelbulb #animation created with #WolframLanguage

#fractal #mandelbrot #math

A render of Adam Burch’s A-Wing model. Using a fractal render for the background generated in #mandelbulb. Rendered in #Lightwave3D and pixel poked in Photoshop #StarWars #StarWarsArt

@neozhaoliang I believe this is generated using a Mandelbulb library! Escape fractals can be symmetrically-lifted in many ways! There is a great trove of YouTube videos under #mandelbulb

Did you know the #mandelbulb?
And the #juliabulb?
http://www.bugman123.com/Hypercomplex/index.html

Fractal Mindblow 1/2022 (4K) | morn1415

https://www.youtube.com/watch?v=Vpzgb5AYe6U

#morn1415 #3d_fractal #mandelbulb #riemann_sphere #hypercomplex #mandelbrot_set #beautiful_fractals #4K_fractals #infinity #infinite_fractals #fractal_zoom

Oops. That first link I sent was actually part 2. Start reading from here:
https://www.skytopia.com/project/fractal/mandelbulb.html
#mandelbulb #mandelbrot #fractal #3d #math

This article is an epic tale of mathematical research and computer graphics. After I first read it in 2009, the #Mandelbulb immediately became my desktop background. And it still is today:

The #Mandelbulb is a 3D variant of the original Mandelbrot set. This blogpost explained how it was "discovered" by Daniel White.

https://www.skytopia.com/project/fractal/2mandelbulb.html
#fractal #math #3d