I need to turn this flat pattern into a series of gradients - how can I do that?

Question

I have this pattern of contentric shapes I created in Illustrator. In either Illustrator or Photoshop, I'm lookin for a method to turn this into a series of conentric gradients, rather than flat black and white. The gradient should roughly work like this: the middle of the black sections should be black, and then transition to medium gray and then to white by the middle of each white section, and then transition back to black, repeating the gradient all the way to the center.

I've tried using Gausian Blur but it doesn't seem to be allowing me any way to convert that blurred result to the gradient pattern I'm requesting, so I hope there's some other way.

Answer 1

Okay, I figured out you can apply a gradient to a stroke. That's pretty much all I needed to accomplish what I'm looking for, thanks!

For anybody else looking to do something like this

Go to Window > Gradient. Select the Linear option and be sure to select the "Apply Gradient Across Stroke" in the Stroke type.