Calculating dots per pixel when printing an image

There is a nice article I found explaining dots, pixels, ppi, dpi etc. Here it is. Very good overall, but I got confused at one point where it says:

For example, if you are printing a 150ppi image at 600dpi, each “pixel” will consist of 16 dots (600 dots/150 “pixels” = 4 rows of 4 dots per “pixel”).

Is this true? From what I gather it should have been 4 dots / pixel. Why "4 rows of 4 dots per pixel". Where did those rows came from? Is there something I'm missing? At any rate, I believe that it should be 4 dots / pixel. What is right here?

• Statement makes no sense whatsoever. That's not how it actually works you know. Nov 16 '16 at 17:38
• I know, this is what i'm saying. It makes no sense. Nov 16 '16 at 17:40
• Yes but they cease to be pixels so there no point is saying there is x dots per pixel. The pixels samples get turned to continuous function of some kind for the halftone rasterizer. However it is true that were the halftoner to work the way author envisions there would be 16 dots. Its just that saying there are dots per pixel makes no sense there is 16 halftone samples in something that has been mathematically manipulated to be something other than pixels.. Nov 16 '16 at 18:05
• Yeah, don't worry about the dots per pixel thing. I wanted to know this for an intermediate computation that i have now resolved. Thanks anyway. The thing is that the article's statement is incorrect. Nov 16 '16 at 18:07
• Well as a massive over-simplification it makes sense. 600 / 150 = 4 so the numbers work, but printed dots don't align to an image's pixels so it doesn't work like that in practice.
– Cai
Nov 16 '16 at 18:13

From the article:

For example, if you are printing a 150ppi image at 600dpi, each “pixel” will consist of 16 dots (600 dots/150 “pixels” = 4 rows of 4 dots per “pixel”).

600 divided by 150 is 4, so the numbers make perfect sense.

From what I gather it should have been 4 dots / pixel. Why "4 rows of 4 dots per pixel".

What you have to remember is that the numbers work in both dimensions. So there is 4 dots per pixel, but in each dimension, so you actually have (4 × 4) 16 dots. To get 4 dots per pixel the image would need to be half the resolution.

To illustrate the point, take the following simple image, increased (and resampled) from 150 PPI to 600 PPI. You can clearly see each "pixel" is made up of 16 (4 × 4) pixels: The article is massively over simplifying things though as that's generally not how printing works. A printed dot does not align with the pixels in an image. But as an over-simplification for illustrative purposes, the statement makes sense.