I visualized 4D shapes #SoME2

#some2

In this video I am trying to construct a visualization of 4D shapes

[CodeParade]

Nice! I also played with the same 4D models in my new game. Great to see a quality video about the less talked about ones like the duocylinder and tiger. Another interesting fact about the tiger is that it can be used to link a chain in 4D, which can't be done with a regular spheritorus like you might expect.

[angeldude]

The ability to create shapes by multiplying other shapes really is a cool way to do things. I'm curious how you're handling the simulation and rendering. Can't wait to see the 5D version!

[carykh]

oh wow, awesome video! It's fascinating how many types of 4D cylinders and toruses there are.

[schoo]

So good to see something that isn't just Flatland repackaged (though of course its impossible not to reference) but actually explains things in a different way. I understand a little more now, and have a million more questions haha

[toasteduranium]

Last year, I was looking for a lot of videos on 4D shapes, and I couldn’t find any good ones. This is probably one of the best ones I’ve seen..

[ArtemYashin]

5:59 Should be “extrusion” instead of “revolution”

[macronencer]

I think this might be the best video about 4D shapes that I've ever seen. Bravo! And thank you.

[Fulgur]

After all these years, I still consider the tiger to be one of my finest ideas. Though it's just the name for the toratope, not for the product of two cylinders (Wendy Krieger called that "duocylinder margin").

The tiger was found through visualization of mid-cuts of various 4D toruses. (4D ball has to be counted among them -- it's sort of a "zero" element among 4D toruses.) Mid-cut of a 4D ball is a ball. Mid-cut of a spheritorus is either two offset balls or a torus. Mid-cut of a torisphere is either a torus or two concentric spheres. Mid-cut of a ditorus is always two toruses, but they can be concentric (same inner diameter, different outer diameters), co-circular (same outer diameter, different inner diameter, leading to one torus inside of the other), or offset. Tiger fills in the remaining "elementary" mid-cut: two toruses with vertical offset. In fact, all of its coordinate midcuts look like that.

Later, I and few others developed the toratopic notation which allows to determine the mid-cuts easily and has some other fun applications.

I'd suggest to try duocylinder where the radii of the two generating circles are not the same. The same for tiger. The symmetry is lower, but there would be visibly distinct mid-cuts.

[BlackAhorn]

This video finally made 4D click! For the first time i feel like i truly understand the concept. Thank you very much!

[lexinwonderland]

This was absolutely fantastic and answered questions I didn't even know I had -- I can't wait for the next one!!

[sparecreeper]

This video has more quality than some channels with over a million subscribers, you’ve definitely earned a sub from me

[NoLongerBreathedIn]

The duocylinder can be made by spinning a cylinder in the plane containing its axis.

[DragonSageKaimus]

Hi
I believe you are competent at this topic.
Please do not be discouraged from visualizing 5D shapes

[fetterkeks]

This is such a well made video/explanation/visualization, amazing job!

[louiesumrall]

This is some amazing quality content. I feel like I found a hidden gem. Keep making videos on cool geometry ideas and working with your awesome presentation style! You are definitely going places :D

[jackfrederiksen]

This is an incredible video! This is the most fascinating and helpful visualization of 4D geometry that I have ever seen, good job.

[velkykoblyh]

Awesome video, there is so much energy coming from you via the commentary or the editing, I am very interested in seeing more from you

[DeclanMBrennan]

That was a spectacular 4D safari and the closest I've ever been to groking these exotic shapes. Thanks for the trip.

[jimday]

Cool! We are waiting for the next video!

[Fireheart]

This is B Y F A R the best video on 4d objects I've ever seen! You actually showed how more complex shapes change instead of just showing expanding spheres and cubes and stuff!