I built a 4D Engine in Desmos

Join the free discord to chat:

Join this channel to get access to perks:

Shout out to the editor:

Chapters:
0:00 Intro
0:13 Explanation
1:59 Tutorial

[Epic_Ducks]

When should we tell him 3D Desmos already exists and it could be slightly easier?

[AlienXtream]

as others have mentioned, this is a 3D (perspective) projection of a 4D object. a slice would be just a cube (at least in the case of an axis aligned cube. it gets a but trippy when rotations are introduced)

[marcberm]

The cheery "don't forget to piss right off" really got me this time. 😀

[nerdboy]

The dark mode desmos was from the Reverse Contrast setting in case anyone is wondering

[AlexandHuman]

I understand this, but I'm still sitting here like "Any sufficiently advanced science is indistinguishable from magic"

[YourFriendlyNeighbour-br]

I would consider myself decent at math, but this just feels so odd to wrap my head around. I find that quite interesting since I have a "fine" time understanding both the logic and abstract math of things like DEs both PDEs and ODEs, or even complex analysis :)

[qondonyon]

very nice!!

there's slightly wrong imformation though,
that's actually the shadow of the tesseract and not the cross sectiono!!

[PuffyNutty]

0:44 this is not the cross section of a hypercube. That would look just like a regular solid cube to us.

If I asked you to quickly draw a 3d cube on a piece of paper, you would simply outline the cube by drawing its 1d edges. Now imagine your perspective changed so you are directly facing the front of the cube. No other faces would be visible, and it would look like this:

| |
| |


All you see is a square (the cube’s front face) as none of the other faces are visible from your perspective. The edges comprising those other faces are behind this front face. If you were to make the front face completely transparent, you would see the edges behind it, and it would look like this:

| \ _ / |
| |_| |
| /___\ |

You can now see another smaller square inside a larger square, connected to the larger square’s corners. This is the cube shown in the video, just in 2 dimensions. It is the shadow of a 3d cube’s edges being directly projected onto a 2d plane.

If it were the shadow of a 4d cube’s edges being directly projected onto a 3d plane, you get the shape seen in the video.

[AlexandHuman]

I am not too familiar with the mathematics of this, but is there a generalized method of turning polygons into their 4th dimensional counterpart? What about any continuous shape?

[Bard_Gaming]

I always despise these kinds of videos. Not because I find them uninteresting or stupid, but because I hate the idea of never being able to fully visualize a 4D object. Every time I'm reminded of that, I feel frustrated...

[centarian]

Sir, I think you're confusing cross sections with projections. What you were calling cross sections of 4D or 3D objects were actually 3D or 2D projections of 4D and 3D objects. A cross section would be if I cut out a 2D slice out of a 3D cube. Projections are flattening a 3D cube until it fits into a 2D space. They are not the same thing.
Example: An image of a cube is a 2D projection of the 3D object. A slice of that cube is a 2D cross section of a 3D object.

[YahyaKhashaba]

This seems like the projection of the 4d onto 3d then onto 2d, not a slice of 4d in 3d then projected onto 2d.

[TheLucaz]

If you can display 3d on a 2d screen, cant you display 4d on a 3d world?

[AlexMurakami-vgnc]

What if you didn’t set wc to 0 would see a more complete visual of the 4d shape?❤

[marble]

Ok you beat me on this race
Prob Speedrun this if I have the time to memorize

[Vengemann]

Was looking for 3d in 2d desmos and got 4d😭
you have any old videos on tutorials on how to make 3d movements in 2d desmos and stuff?😓😅😅

[trevorallen]

Just use calculus mentally piece by piece by parts in previous dimension or this case your current dimension in 3D then you can visualize higher dimensions better.

[sndrrz]

Have you watched hypercubist math's 2 videos on visualizing the 4th dimension? They're great and I'm eagerly awaiting the third video.

[KingJAB_]

You called it a cross section, but you showed a projection. 2 very different things

[NguyenMinhPhu]

This is not a crosssection! It's a projection, a crosssection is a 0 unit thin slice out of a shape!