Here's a visual to iDad's explanation. I just had to see if there was a mathematical constant here. Ha ha ha, I wouldn't know one if I saw one! There actually is a pattern to the image you posted, but it is not perfectly repeating once you get to the smaller circles. It may be a helpful guide for reproducing to make and use guidelines based on your image. I would set some but for this I might just eyeball it since I'm pretty good at spacing. That said, I made on myself. The starting brush circle was too large so it doesn't work as you want it, but all you have to do is make them the right size. I also made too many compared to your eight. It might take more than one try for you to get them right. But it's easy and fast.
I made center guidelines. Used the circular shape tool set to path, "circle, from center." Stroked the path as a guideline, then made another layer for the brushstrokes. As iDad said, you could make a layer for each on so you can rearrange them, or do as I did and put them all on one layer.
I made one brush stroke then used the bracket key to make it the next bracket smaller and so on. I set them all along the inside of the circular path.
Once I had my red circles, I copied the layer, used transform, rotate 180 degrees and moved it into position. Then I held the ctl/cmd key, clicked on the thumbnail to activate the selction and changed the color.
Then I ctl/cmd selected both and copy-merged them; ctl/cmd + alt/opt + e.
Using the transform and holding down the shift and the alt/opt key, move the handles and make it the size you want. Copy this layer and repeat the process.
There is probably another way, but offhand I can't think of an easier way. You can always make a brush with the pattern and size strokes you want if you think you'll need it again. Otherwise, like I said, iDad's method is easy and fast.
