Welcome to part 4 of our little Mandelbrot Explained series. In this video we explore the bulbs around the main cardioid, and find that they contain number sequences such as the natural numbers, Fibonacci sequence, and the rational numbers. We then investigate them in terms of their Julia Sets to try and understand visually why they are there. Finally, we look at precisely where the bulbs are attached to the cardioid. If you loved this video then why not buy me a coffee: https://ko-fi.com/mathstown In this video: 00:00 Introduction 00:30 Period of the bulbs 01:45 Signposts in the Mandelbrot Set 02:42 Number Sequences 04:24 Rational Numbers 07:06 Julia Sets of the bulbs 11:36 Location of the bulbs 13:15 Why signposts? 14:30 Building a Mandelbrot Set 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 Mentioned in video: https://www.youtube.com/watch?v=4LQvjSf6SSw Numberphile video (Mandelbrot & Fibonacci) https://www.youtube.com/watch?v=TOxs1vLgQ_M Mapping a polar grid to the Mandelbrot