This visual shows a series of balls on the complex plane. The equation z=z²+c is applied to every ball once per iteration. Those balls outside the Mandelbrot will escape, and head towards infinity. Those inside the Mandelbrot Set will remain bounded within the radius two circle. This video is extra footage associated with the explainer video "The Mandelbrot Set Explained". https://www.youtube.com/watch?v=7MotVcGvFMg If you look carefully you can see the period motion associated with the periods 2 and 3 bulbs. For example you will notice that the balls return to the period 3 bulb every third iteration. The colour of the balls is graduated for each ball, so that you can get a rough idea of where it started. This graphic shows the first 400 iterations. I will attempt to upload extra graphics associated with the main sequence of explainer videos, you will find them by exploring the channel playlists. Generally I'll set these videos so that subscribers aren't notified, so that subscribers aren't pestered by these uploads. Join the Maths Town Twitter feed if you would like to be notified about everything I am doing (including the Maths Town channels). https://twitter.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 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