Make the dots the color of your logo 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.