Create a network of nodes using Geometry nodes?

Question

I have this 2D image of a network I created:

I'd like to convert this to 3D using geo nodes, such that the circles are spheres, and the lines are thin cylinders. I want to do this such that I have one parameter that I can turn up to increase the number of triangles like so:

Knob at 1:

Knob at 2:

Knob at 3:

And so on.

What I've tried so far has failed. First I made a triangle object by deleting one of the vertices of a square and selecting all then F (to fill in a face).

Then, I added point instances of spheres to that:

When I tried subdividing however, I did not get the exact same shape I drew:

Answer 1

easiest way I can think of is using the Grid Node, it's perfect for this...

the blend

Answer 2

I know that there's already a checked answer for this question but in case you want to try out another method to create the network, here's a hardcore way of achieving the network :)

You can, ideally, have two points at the starting (or 1st position of your network) that you can use to instance the first two curve lines of your network. Since these lines are instances, you can take their indexes and use the Modulo math function to a mask so that you can tell Blender to rotate the lines in 2 opposite directions. It'd look something like this.

Now, we need to repeat this step for every iteration (or knob) for the network to keep expanding. For this to work, you'd need to be able to select only the last points of every iteration (or knob). Since you're using curve lines from the beginning, you can take advantage of the Endpoint Selection node with Capture Attribute to achieve this.

These "last points" can be re-used for instancing the UV spheres later on. Our node setup at this point would look something like this.

Once you're done with the 1st iteration (or knob) of your network, you can group all the nodes together and start passing out the needed outputs to keep repeat the process over and over again.

With 8 iterations:

You can keep doing this until you're satisfied with the result. Here the full node setup:

For this method, there are a couple of things that are worth to be noted:

Advantage points:

Lines length: You can adjust the lines (thus increasing the overall size of the network) and still be able to keep all the lines and spheres correctly connected.

Angle: The spreading angles can be freely adjusted.

Disadvantage points:

Peformance-wise: the more iterations you have, the more time it'd take to process things.

Time-consuming: Passing each output through node groups one by one takes quite some time.

Here's the blend file in case you want to take a look later. Extra reminder, it's recommendable you're using Blender 3.2+ since there are some nodes that aren't available in the 3.2 or below version.