The grid shown below is what i have right now but it just overlays. I want the white dots to be using the image texture color. I have this method i have seen with simon tommes. Where he uses a image texture and 'projects' it over the material set up by some math nodes. The image texture does clip to the knittr (in simon tommes shader) i put a picture here. I have this setup, also with math nodes. made a grid of dots This is my set up of nodes
You need to pixelate your UV coordinates which you can do as so:
x - (x modulo pixelSize)
You can then use the same modulo nodes by normalizing their outputs to get the coordinates for your discs:
(x modulo pixelSize) / pixelSize
Create your discs the same way you have already done and use them to mix between your image texture output and a background color.
I hope this helps.
There is another method though [EDIT: the method below is more efficient].
Create a plane and subdivide it a lot.
Create a disc or sphere, parent it to the plane. (in the screenshot it was a cube).
Parent the sphere to the plane.
Go to object properties and where it says instancing, check faces.
Give the sphere a material, add a texture coordinates node, check from instancer and connect the UV out to vector of your logo texture. It's probably easiest to put the logo on a white background.