If we look how the Moiré pattern is created we can see that it is the result of rotating linear patterns:
This is mostly unwanted on fast method scaling of images that have a regular pattern, or on displaying such images on a display made up of regular patterns too (like our screens).
To intentionally produce this effect we need a source image dithered with a regular pattern such as the halftone dithering of the example given.
Below are steps to transform an image with adding Moiré:
Dither source image using a regular pattern:
Copy the image and paste it as a layer on top of the dithered source
Apply a rotation to the pasted layer (the angle will control the effect size)
Moiré overlay with transparency
Moiré overlay with 50% opacity
Moiré overlay with a line-dithered source
From examples above we can see that the primary dithering technique will deptermine the shape of our Moiré (diamonds produce diamonds and lines will produce lines).