The Mandelbrot Set Explained

We take a deep dive into the Mandelbrot Set, and try to understand what is happening under the hood. In particular we introduce the concept of orbits and their unusual behaviour. I hope by introducing such detail that you will find concepts in future videos easy to understand. This video contains many handcrafted visuals that took days code and animate, plus several hours to render them in 8k. Please subscribe! Welcome to the channel! I'm new at making mathematical explainer videos, but I hope you get something from these videos. Feel free to leave some love or constructive feedback in the comments section. Questions are also most welcome. If you loved this video then why not buy me a coffee: https://ko-fi.com/mathstown In this video: 00:00 Introduction 1:51 Chaos & The Mandelbrot Set 2:40 The Equation 3:31 Looking at z squared 6:48 Mandelbrot, the real part. 15:24 Complex numbers 18:35 Full Mandelbrot Set 23:23 Mini-Mandelbrots In this series: 1 - https://youtu.be/7MotVcGvFMg The Mandelbrot Set Explained 2 - https://youtu.be/dctJ7ISkU-4 Julia Sets, and how they relate to The Mandelbrot Set 3 - https://youtu.be/5T0cC6KRezo How to Build a Julia Set 4 - https://youtu.be/oNxPSP2tQEk Number Sequences in the Mandelbrot Set Extra Visuals (No commentary): https://youtu.be/JYlAPaPsoSY - All orbits of the Mandelbrot https://youtu.be/-ObPTFNVByk - Period 1 orbits of the Mandelbrot https://youtu.be/4y8OCqceJjo - Period 2 orbits of the Mandelbrot https://youtu.be/Gmjk5G2TrSo - Building a Mandelbrot step-by-step https://youtu.be/0E9fT8hOkVQ - Period 2 orbits of a Julia Set https://youtu.be/CYdKlN38VHE - Period 3 orbits of a Julia Set https://youtu.be/XWboHruR6N8 - Period 4 orbits of a Julia Set https://youtu.be/mt6PYJnnUHg - Period 5 orbits of a Julia Set https://youtu.be/wxkuQdXcp70 - Period 6 orbits of a Julia Set Deep Mandelbrot Zoom video (from introduction): https://www.youtube.com/watch?v=u1pwtSBTnPU Panning around the Mandelbrot: https://www.youtube.com/watch?v=BsjHdx83J9A /******************************************************************************** Discord: https://discord.gg/q4xsmSHV Twitter: https://twitter.com/MathsTown Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town ********************************************************************************/