How to do a "Turing Pattern" dither/halftone effect?

Question

I've been searching for a way to do a halftone like this:

As you can see this is not a simple halftone effect, with circles or anything. It uses the Turing Pattern as the filler element, but it also fades away as gradient loses intensity. I've been trying to achieve this result using Photoshop's custom dither pattern when you turn an image into bitmap. I'd say results are 50% there, but not quite there yet. I used as the pattern tile something similar to this on a simple gradiente from black to white:

https://upload.wikimedia.org/wikipedia/commons/thumb/a/a1/TuringPattern.PNG/320px-TuringPattern.PNG

But I can't get the fading correct like you have both on the nike swoosh and on the 'air' wording behind it.

Any thoughts? (It can be in illustrator as well, ps or ai)

Answer 1

Proper guidance is given in the 1st comment, but it maybe doesn't get much attention. This is an attempt to fix it.

Scientist and WW2 hero Alan Turing (Manchester, UK) wondered how fungus, bacteria, pigment cells in animal's skin etc... can make stable, sometimes very complex and fine looking structures. The structure stays, no matter tissue renewal is going on. The wonder there was that the structure of seemingly stable pattern was written nowhere. The growth obeys its local laws only, but the pattern stays like someone had planned it. Turing reasoned a mathematical local growth formula which can create stable structures. The Turing pattern in computer graphics applies his idea in a simple way. An example:

This is the starting point. A solid grey 700 x 700 pixel which gets some graininess. Here the grain is just inserted. It's noise, the strength is 2%. Any grain is ok, but the result varies drastically depending on the spatial and strength distribution of the grain.

In the next image the shown 3 step "Turing" action (recorded in the first pass) is applied once:

The black and white foreground and background colors are needed in tresholding. After running the action another time the image became this:

Running the action a few times more the image stabilized to this:

As said, any graininess can be used. Here's a photo of 2 dogs (not copied from the web) after applying the action few times and clipping along the edges of the original animal shapes:

I'd say: Well worth trying!

About Turing: His work in WW2 was top secret and he himself was an unknown academic obscurity for ordinary people, not a celebrity. In the beginning of 1950's his life became dire. He was caught being a gay. It made him a leper and pariah. In that time homosexual behaviour was a crime and the tendency itself was a mental disease. Turing was driven to a blind alley. He solved the situation by committing a suicide. Quite a big loss - we might have learned something.

Answer 2

I am new here as well!

Maybe the solution is found within computational design tools, like for instance Drawbot, or Processing? I took the liberty, and searched for "pattern", which is superficially related to your question in the drawbot forum here. Also, I want to link to Processing examples provided here, as well, to provide a few visual samples of what can easily be achieved outside of the Ps workflow, while being easily integrated into said workflow. I am myself looking into computational design a lot recently, so maybe I'm in a situation where I assume that everything is a nail, because all I have is a hammer, but I still hope that I am pointing you in the right direction.