I love the rendering! It looks to me like the work of a master glassblower with mad skills in a much higher plane of existence. My "they always want more" thought, though, was wishing we would fly through one of the sin and cosine arches. Or better yet, a slalom route around all the zeros! ...And a swoop into the valley, too! Ok, fire up the compute farm and get ready to spend $160 in electricity! Thanks as always for the beautiful work!
Surface(cos(u/2)cos(v/2),cos(u/2)sin(v/2),sin(u)/2),u,0,2pi,v,0,4pi Notice that 4 pi are needed to complete the surface. This is a single sided closed surface. The radially symmetric Klein bottle.
![[Visual] The Riemann Zeta Function Visualised](http://i.ytimg.com/vi/GcbML8bGSu8/mqdefault.jpg)
This animation is second to none in expressing how supremely smooth functions are where they're analytic. Brilliant work!
I'm so glad I discovered these.
Eu sou matemático, professor na Universidade de Coimbra!
Parabens pelo trabalho!
I love the rendering! It looks to me like the work of a master glassblower with mad skills in a much higher plane of existence. My "they always want more" thought, though, was wishing we would fly through one of the sin and cosine arches. Or better yet, a slalom route around all the zeros! ...And a swoop into the valley, too!
Ok, fire up the compute farm and get ready to spend $160 in electricity!
Thanks as always for the beautiful work!
Thanks!! Expect a cos fly-through in the next video of the main series. (It won't be glass though, something a little new). I love the slalom idea!
The sine and cosine complex surfaces seem to be an epic challenge for stunt skaters.
Thank you for your labor. I definitely have already applied this to my theory crafting and storytelling. You have done a remarkable service 🐕🦺
Your videos and effort go tragically unappreciated. Not sure what to make of this information but this is far out✌️
Surface(cos(u/2)cos(v/2),cos(u/2)sin(v/2),sin(u)/2),u,0,2pi,v,0,4pi
Notice that 4 pi are needed to complete the surface. This is a single sided closed surface. The radially symmetric Klein bottle.
Those are some beatiful shots. Also i finally know what this stuff is my PC is rendering on SheepIt all the time :D
Can we integrate them like a function z=f(x,y)? How must we do that?
If f(t) = u(t)+iv(t) where u(t) gives the real part and v(t) gives the imaginary part
then ∫ f(t) dt = ∫ (u(t) + i v(t)) dt = ∫ u(t) dt + i ∫ v(t) dt.
Assuming t = x+iy in your example
Now i'm wondering if this actually helps, I need to take some time on this :D
@Nimbo Stratus The key should be to derive it.
Gorgeous
Must've taken ages to render!
Yes it did!!! 4-5 mins per frame on a 64-core CPU. There are around 10,000 frames. Mostly, it was done on a render farm, I did around 2000 myself.
@@TheMathemagiciansGuild Can you show us a way to get this?
Am i a true math lover now? Jokes aside that render is impressive
Yes you are!
Now try the mandorbolt 😅😅😅 and watch it predict were you wanna go
I will do the Mandelbrot at some stage. :-)
Bhai galgotia m aaja ek din k lie sab maths le lenge
That’s weird