In this video we examine how to build a Julia Set by making repeated remapping of a circle on the complex plane. The technique is quite interesting because it allow us to visually understand why Julia Sets have some of their properties, such as rotational symmetry. This video only glosses over the mathematics, and don't worry if you don't exactly understand what is going on. The important part is to look at Julia Set being formed visually. I'm certainly not the first to use this technique, but there isn't much YouTube content, so I've included quite a few visuals, and everything is rendered at a super high 8k resolution. Consider playing the final visuals at slower speeds if you wish to study them. Please subscribe! If you loved this video then why not buy me a coffee: https://ko-fi.com/mathstown In this series: 1 - https://www.youtube.com/watch?v=7MotVcGvFMg The Mandelbrot Set Explained 2 - https://www.youtube.com/watch?v=dctJ7ISkU-4 Julia Sets, and how they relate to The Mandelbrot Set 3 - https://www.youtube.com/watch?v=5T0cC6KRezo How to Build a Julia Set 4 - https://www.youtube.com/watch?v=oNxPSP2tQEk Number Sequences in the Mandelbrot Set Extra Visuals (No commentary): https://www.youtube.com/watch?v=JYlAPaPsoSY - All orbits of the Mandelbrot https://www.youtube.com/watch?v=-ObPTFNVByk - Period 1 orbits of the Mandelbrot https://www.youtube.com/watch?v=4y8OCqceJjo - Period 2 orbits of the Mandelbrot https://www.youtube.com/watch?v=Gmjk5G2TrSo - Building a Mandelbrot step-by-step https://www.youtube.com/watch?v=0E9fT8hOkVQ - Period 2 orbits of a Julia Set https://www.youtube.com/watch?v=CYdKlN38VHE - Period 3 orbits of a Julia Set https://www.youtube.com/watch?v=XWboHruR6N8 - Period 4 orbits of a Julia Set https://www.youtube.com/watch?v=mt6PYJnnUHg - Period 5 orbits of a Julia Set https://www.youtube.com/watch?v=wxkuQdXcp70 - Period 6 orbits of a Julia Set This page offered some inspiration for this video: https://www.karlsims.com/julia.html