What is the Mandelbrot set?

Here are two videos which I found interesting, explaining what the mandelbrot set is. Both of these videos are from the NumberPhile YouTube channel which is full of interesting math related videos.

This first video is by Ben Sparks:

This next video is by Dr. Holly Krieger:

Complex numbers

Mandelbrot and Julia set images are displayed on the complex number plane. Many people may be unfamiliar with complex numbers. Complex numbers are composed of two parts, their real and imaginary components. Naming the second component imaginary may confuse people into thinking that somehow complex numbers aren’t real.

Complex numbers are an essential part of our number systems, they aren’t imaginary at all. Did you know that multiplying two complex numbers is equivalent to vector rotation and scale? There is a very real geometric meaning to complex number algebra.

This video series presents complex numbers in an accessible and entertaining manner. Everybody is encouraged to watch!

Cool properties of the Mandelbrot set.

This video just blew my mind. Once you watch this video, exploring the Mandelbrot set will never be the same again.

This second video is also fun. How on earth are these discoveries made!?

Mandelbrot. Some history.

This video covers some of the history of the sets.

A video by Craig.

This video discusses some absolutely fascinating stuff (well, in my humble opinion…) It builds on the video above by Holly Krieger, introducing Fibonacci and the Mandelbrot set. There are some amazing symmetries present in the Mandelbrot set, Mandelbrot orbit and Julia sets.

Many more.

Once you have started to explore the Mandelbrot and Julia sets, you will start coming across many other types of iterations, fractals and chaos. YouTube is full of videos on these topics and your web search engine will find bazillions of pages discussing these topics. Enjoy!