So the #mandelbrot set is connected, because there is a one-to-one (conformal) mapping f(p) between its complement and the complement of the closed unit disk.

Has anyone made an animation of the Julia set of f(p(t)), where p(t) goes around the unit circle?
(i.e. p(t)= (1+ε) · e^(2πit) for some small positive number ε)

#fractal

For newcomers and beginners...

𝐌𝐚𝐤𝐞 𝐘𝐨𝐮𝐫 𝐎𝐰𝐧 𝐌𝐚𝐧𝐝𝐞𝐥𝐛𝐫𝐨𝐭 𝟐𝐧𝐝 𝐄𝐝𝐢𝐭𝐢𝐨𝐧

(the second edition now introduces the "distance estimation method" for finding sub-pixel detail)

https://www.amazon.com/dp/B0CQS8JYJC

#maths #fractals #mandelbrot #python #generative

Make Julia fractals using your phone and a mirror!

Interactive Video-Loop Julia
https://www.shadertoy.com/view/scsGDH

This tiny shader computes the complex square function. If you have a webcam, point it at your screen to make a video loop. If you point it off center, a translation is introduced, and we get a computation like this:

z -> z² + c

It's Mandelbrot's formula! You can see a Julia fractal!

#glsl #mandelbrot

I just released v1.1.0 of Complexitty, my little #Mandelbrot explorer for the #terminal. This release is all about an optional method of making it faster.

#python #programming #textual #numba

https://blog.davep.org/2026/02/28/complexitty-1-1-0.html

The Mandelbrot Sets Evil Twin by @twoswap with OST music by @6884 🙂♾️

https://youtu.be/Ed1gsyxxwM0

#Fractal #Mandelbrot #VisualArt #Mathematics

🌀 Mandelbrot fractal
🧭 Center: (-0.548696, -0.646329)
🔎 Zoom: 18.48842588950363
🎯 Iterations: 100
🎨 Palette: offset 201°, scale 1.00

🔗 https://fractalus.hippy.cz/?cx=-0.5486957288125679&cy=-0.6463290239736775&z=18.48842588950363&iter=100&offset=201.01503999999835&scale=1

#Fractal #Fractalus #WebGL #MathArt #GenerativeArt #Mandelbrot