How can I achieve this sort of pattern?
I presume from these sample images I found from a poster made by Laurient Durieux, it is made using illustrator. Or am I wrong? Is there a proper way to do it?
This is the texture I'm trying to achieve:
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As Troodi mentions, that particular style is emulating etching. Specifically cross-hatch patterns to create shading. The most common place this is seen is in the portraits on US currency.
There are filters for PhotoShop that can emulate this to an extent. However, my guess is that if that was indeed done in Illustrator, it's emulating it via patterns of lines using the blending tool. Create a thick line, duplicate it, make the copy thin, then blend between the two to create an ever decreasing gap. Repeat this again on the opposite axis and overlay on a dark color.
There are some photoshop actions and filter to get this effect. Maybe you can try this, but not free. LINK
I've remember seeing something like this as a photos-effect filter in Photoshop, but it was a premium one and am unable to find it now.
There is an iPad app called "Etchings" which is close, but may not have the controls you'll need to recreate the textures shown in your example.