def collage(p):
  w=getWidth(p)
  h=getHeight(p)
  p2=makeEmptyPicture(w,h)
#this will paint p2 with four 
#half-sized views of the original
#picture:  the picture itself,
#a grayscale image, a negative
#grayscale image, and a "posterized"
#color version that uses a small
#palette of colors.
  for x in range(1,w/2):
    for y in range(1,h/2):
      px=getPixel(p,2*x,2*y)
      r=getRed(px)
      g=getGreen(px)
      b=getBlue(px)
      c=getColor(px)
#paint upper left original color
      px1=getPixel(p2,x,y)
      setColor(px1,c)
#paint upper right grayscale of original color
      av=(r+g+b)/3
      gs=makeColor(av,av,av)
      px2=getPixel(p2,w/2+x,y)
      setColor(px2,gs)
#paint lower left negative grayscale of original color
      px3=getPixel(p2,x,h/2+y)
      ngs=makeColor(255-av,255-av,255-av)
      setColor(px3,ngs)
#paint lower right posterized color
      g=255*((127+g)/255)
      b=255*((127+b)/255)
      r=255*((127+r)/255)
      px4 = getPixel(p2,w/2+x,h/2+y)
      setColor(px4,makeColor(r,g,b))
  return p2