So this makes us think about having different topologies.

So we can start to go to higher dimensioned topologies.

So we can start to use 2D topologies, or 3D.

and you can see here, here as we have lets say 16 nodes arranged in a

2-dimensional mesh, versus, here we have a 2D torus.

And the difference between the 2D mesh and the 2D torus is that there's what's

called end around in our, in the torus. And that makes the routing from here to

there much, much faster, and effectively, we'll cut the, average

routing time, or average routing, excuse me,

average, hop count by a half. Because you can go either way now, and go

around the ends. Sometimes, these 2D toruses are called, a

2D mesh with end around. That means it's a torus.

just, I just wanted to throw that nomenclature out there, because sometimes

you'll see, you'll see both. A good example of a simple routing

protocol is if you're at this node here. And you want to communicate some data you

can send the data in all directions. And then everyone else sends it in all

directions. And everyone else sends it in all

directions. And it'll just flood the network, and

it'll get everywhere. And you're guaranteed that it's going to

at least get to the receiver, and you have some guarantee that when it

gets to the receiver, the receiver sees the, the packet and takes it off.

Now that may not be what you want to do. [LAUGH].

That's, that's probably not low power, and it's probably going to cost a lot of

congestion on your network, but you may want to think about a

flooding protocol. Okay, so wherever there is 2D we can

start to go to 3D. So here we have a 3-dimensional cube.

Sort of. It's the best I could draw.

It's, it's hard to draw 3-dimensional things on 2-dimensional space.

And if, if we had 3D space I could have drawn this much cooler.

so this is a hypercube. Hope these are actually hypercubes.

So, all the hypercube is, is it's saying that the number of the mentions you have

[COUGH]. is equal to the number, or the degree or

the outbound links of a, of a, of a node in the, in here.

So, if you look at this node, we have a three dimensional hypercube.

So it can go this direction, that direction, or that direction.

Every node has a out degree of three, or a connectivity of three.

Here, we have a four dimens, a four dimensional cube, but this is, by

definition, a hyper cube. So, because, if you look at any given

point here. So, we're going to define a hyper cube as

the out degree, of the nodes is equal to the dimension of, of the, the links.

And, you can't go build here a, if you were to add one more node to the system,