Spots on kitchen wall

We've had some nickel-sized purplish spots on our kitchen wall for sometime now. It started out as two of them about 8 inches apart. Now there is one on each side of the original ones, about 6 inches away. And then another is forming in between on each side but up a couple inches. The spacing is very uniform as is the size of the spots. On the other side of this wall is our laundry room. The breaker box is installed there. Any ideas what this might be? The house was built after Katrina but I don't think it's Chinese drywall as we don't have a sulfur smell or corroded wires.

OK, this got interesting enough to re-read.

Is your dryer vent on the same wall as the spots?

Is your water line on this wall?

Do you show water stains on the base boards or on the back side of the wall?

Is there a pocket door on the wall that is showing stains?