This is a grid pattern created in my country in the sixties, taking binary values for lights and shadows. I couldn’t find this anywhere else, or maybe I’m not using the proper words for it. The literal translation would be something like photohatch but couldn’t find anything like this. We did this in design school (this is before computers) as an analogic exercise
Anyways, take a look to the pictures and let me know if there’s a way to do this in an automated way
You say the pattern is binary, but in fact it consists of 4 different “tones”:
Create a pattern for each of the middle tones (with the circles) by making a selection and choosing Edit > Define Pattern. (In this example I’ve made the squares 32×32 px)
Convert the image you want to transform to grayscale and scale it down to a fitting size.
Let’s take this image of a monkey skull by Didier Desouens (CC BY-SA 4.0), scale and crop it down to 36×36 px.
Then upscale the image by 3200% using Nearest Neigbor interpolation.
Now each pixel is the same size as the pattern squares: 32x32px.
Use Image > Adjustments > Posterize to reduce the image to consist of 4 levels.
Use Magic Wand with Anti-alias and Contigous ticked off and click one of the dark gray pixels. Add a Pattern Fill layer and select the dark square with a white circle.
Then click one of the light gray pixels and add a Pattern Fill layer with the white square with the black circle.
You can make another pattern to create a grid and get this final result: