[math-fun] Nearly circular curve

cos(x) + cos(y) = 1 + cos(1). The plot of this equation is, I believe, an infinite grid of near-circles. I plotted this on Replot, but I couldn't visually distinguish the curves from circles. I'd be curious to know how different the curve centered at the origin is from a unit circle. I suspect it is circumscribed by the unit circle centered at the origin. What is its circumference and area? I suspect these curves are related to the dots used in halftone printing. Do they have a name?