Original upload date: Wed, 03 Jun 2020 00:00:00 GMT
Archive date: Sat, 30 Oct 2021 01:19:10 GMT
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, Fibon
...
acci 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.
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://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
Mentioned in video:
https://youtu.be/4LQvjSf6SSw Numberphile video (Mandelbrot & Fibonacci)
https://youtu.be/TOxs1vLgQ_M Mapping a polar grid to the Mandelbrot