pro ring_map_multi_watch,  delay,  a

  sigma = 185.7
  Rs =  60.4

  red =  [0, 1, 1, 0, 0]
  green = [0, 1, 0, 0, 1]
  blue = [0, 1, 0, 0, 0]
  device, decomposed = 0
  window, 0, xsize = 600, ysize = 600
  tvlct, 255*red, 255*green, 255*blue

  plot, [0, 0], [0, 0], /nodata, xrange = [-sigma, sigma],  yrange = [-sigma, sigma],  xstyle = 1, ystyle = 1,  color = 0, background = 1,  xtitle = 'r!In!n cos( theta!In!N )',  ytitle = 'r!In!N sin( theta!In!N )',  title = 'Rings, a=' + string(a)
    

;  itterations = 1000
;  skip = 900
  itterations = 100

  n = 100000L
  rmin = Rs
  rmax = sigma
  r0 = findgen(n) * (rmax-rmin) / n + rmin

  rn = r0
  rn_m1 = r0
  
  tn = rn * 0

  plot, rn*cos(tn), rn*sin(tn), xrange = [-sigma, sigma],  yrange = [-sigma, sigma],  xstyle = 1, ystyle = 1,  color = 0, background = 1,  xtitle = 'r!In!n cos( theta!In!N )',  ytitle = 'r!In!N sin( theta!In!N )',  title = 'Rings, a=' + string(a) +',  n ='+string(0), psym = 3

  for i = 0L, itterations do begin
    begtime = systime(1)
    while( (systime(1) - begtime) lt (delay/1000.0) ) do i = i
    
    tn = tn + 2*!PI*((sigma/rn)^1.5)
    rold = rn
    rn = 2.0 * rn - rn_m1 - a*cos(tn)/( (rn - sigma)^2 )
    rn_m1 = rold
    plot, rn*cos(tn), rn*sin(tn), xrange = [-sigma, sigma],  yrange = [-sigma, sigma],  xstyle = 1, ystyle = 1,  color = 0, background = 1,  xtitle = 'r!In!n cos( theta!In!N )',  ytitle = 'r!In!N sin( theta!In!N )',  title = 'Rings, a=' + string(a) +',  n ='+string(i), psym = 3
    
  end

  theta = findgen(201) * !PI / 100
  oplot, Rs*sin(theta), Rs*cos(theta), color = 2
  oplot, sigma*sin(theta), sigma*cos(theta), color = 2

  oplot, sigma*sin(theta)/1.5, sigma*cos(theta)/1.5, color = 3
  xyouts, sigma/1.5, 0, '1.5',  color = 3

  oplot, sigma*sin(theta)/2, sigma*cos(theta)/2, color = 3
  xyouts, sigma/2, 0, '2.0',  color = 3

  oplot, sigma*sin(theta)/2.5, sigma*cos(theta)/2.5, color = 3
  xyouts, sigma/2.5, 0, '2.5',  color = 3

  oplot, sigma*sin(theta)/3, sigma*cos(theta)/3, color = 3
  xyouts, sigma/3, 0, '3.0',  color = 3

end