How to achieve this half tone effect?

Photoshop offers

Filter > Pixelate > Color Halftone

Filter > Filter Gallery > Sketch > Halftone Pattern

but I prefer using Pattern Layers  set to the Blend Mode Hard Mix.

If one has created a useful Pattern it can be easily scaled in the Pattern Layer dialog and contrast edits can be done with Adjustment Layers between the image Layer/s and the Pattern Layer.

Yea, not quite it.

Maybe not quite the same:

Well I found what I thought might be it, but I'm not sure how it would apply to your image. Here's the link:

Tutorial: Reaction-Diffusion in Photoshop on Vimeo

See this link also: Please someone tell me how to get this texture!

c.pfaffenbichler​ was it you who knew how to create this pattern?

I've seen that effect before and how to do it, but I can't remember. Will have to see. I do recall it was a process that took several steps to achieve that pattern.