Visualizing Complex-Valued Functions

This video goes over a few means of visualizing complex-valued functions/transformations, including domain coloring, modular surfaces and Riemann surfaces. The information provided isn't completely comprehensive and not at all rigorous, but hopefully will give you at least a little bit of insight and interest in the math for which these visuals are involved.

Chapters:
0:00 Intro
0:25 Fundamentals
3:55 2D graphs
8:05 Domain coloring
11:42 3D & 4D plots
20:02 Making your own plots

[whoisgliese]

Complex functions are one of the most beautiful things I've ever seen

[Rinvids]

That transition to Part 2: Domain Coloring was smoother than Snoop Dog spreading butter on a hot slice of toast

[annevanderbijl]

Bro, you seriously did an amazing job at explaining. Well done!

[TheJara]

oh man I am speechless, among all the videos on Youtube on complex functions, yours is clear and mesmerising...please make more videos...and often...you are so good at it...

[nipunviraj]

Recommended video for people who want to make an interest on mathematics. Great video.

[_zweh]

I'm blown away by the amazing quality of this video, superb job

[ismersenne]

This is a beautifully made video. It has helped me understand a little more those mysterious (for me) complex numbers.

[davidwright]

Very many thanks for a beautiful and instructive video! I got a great deal out of it, and will get the software you discussed. In half an hour careful watching I learned more about visualizing complex functions than I ever knew - even with some grad work in applied math! You also show how visually impoverished 2D, black-and-white or grayscale, graphs are. Like looking at a vast landscape thru a fixed pinhole.

[Benjax_]

Amazing job! Definitely one of the best videos I've watched in a while. The great graphs + the perfect music choice + your smooth and great explanations are simply all the perfect ingredients for this great work. Been trying to find an intuitive and good explanation of these weird looking graphs for a while, thank you so much!

[ep]

Great work here! I'll definitely be sharing this with others.

[wu.gi.tai.]

Great materials, thank you so much for providing these. They are really helpful.

[BoZhaoengineering]

I should've seen your video on complex function for the visualization. Thank you for making this very clear!

[supu]

Every thing about this video was great

[maxaudibert]

Brillant thank you!! To mappe these complex functions, how did you add the dimension of time to make a video?

[vector]

Your composite functions were truly dazzling. I mean, domain coloring of tan(z^z)^ln(z) is really quite original and appealing, in my book at least. Inspiring work. The artistic qualities of complex functions really pop in you videos. First rate.

[hmdz]

Amazing! Thanks so much for this beautiful video

[Number_Cruncher]

Thank you for the blender add on. This is very useful.

[paulostipanov]

Will you release any of the songs in this video, they're a delight to listen to.

[frankaz]

Marveleos presentation! . Best explanation and video to me about it. Thanks a lot!

[batoulmhawesh]

Dude !! Your video is so underrated !!