Concentric Circles like a grid, centered at origin

Question

I would like to include a sequence of concentric circles as a grid in a plot of points. The goal is to give the viewer an idea of which points in the plot have approximately

Answer 1

How about this with ggplot2 and grid:

require(ggplot2)
require(grid)

x<-(runif(100)-0.5)*4
y<-(runif(100)-0.5)*4

circ_rads<-seq(0.25,2,0.25)

qplot(x,y)+
  lapply(circ_rads,FUN=function(x)annotation_custom(circleGrob(gp=gpar(fill="transparent",color="black")),-x,x,-x,x))+
  geom_text(aes(x=0,y=circ_rads+0.1,label=circ_rads)) + coord_fixed(ratio = 1)