I'd like to do something like this in photoshop or illustrator:
I've already tried drawing some circles of different tints and i've used the liquify tool (PS) but the result was too "mixed". How would you make an effect like that?
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You have at least two Photoshop filters which distort things by causing rotation. They are Polar Coordinates and Zwirl. Actually also radial spin blur is possible, but it creates fuzziness. Using filters maybe help if you want to experiment without having a clear enough idea what to paint directly. You can paint anything and with these you get something rotational.
An example of rectangular to polar coordinate conversion:
Have a square image. Use only a few colors. Keep different colors in different layers to prevent mixing them. You can also paint with the eraser and the smudge tool. I have only 2 layers. Keep in mind some things:
Duplicate the layers, merge the duplicates and apply Filter > Distort > Polar Coordinates > Rectangular to Polar. Apply the Cutout filter before Rectangle to Polar conversion if there's some mixed colors or too complex edges. Here's the result before and after applying the coordinate conversion:
Applying some other distorting filters before Rectangular to Polar conversion you probably can get richer shapes.
Filter Cutout and adjustment Posterize reduce the number of colors. Cutout also simplifies edges.
Editing after R to P conversion isn't forbidden. If you are lucky, you find what you actually want and paint it.