I was just playing with the (very awkward) computer graphics program "Grapher" on my Mac, reproducing one of the first computer programs I ever wrote -- around 35 years ago -- that draws iterated cycloids produced by rolling circles on circles on circles on circles. By playing with the 8 parameters of 4 radii and 4 frequencies -- especially the latter -- one can of course drastically change the look of the picture. I was very suprised that one combination of frequencies resulted in a picture of a bagel with a square hole, the inner envelope of the iterated cycloid. (The outer envelope has 4-fold symmetry but is far curvier than a square.) This was particularly unexpected since the frequencies were 23, 70, 162, and 162 [sic]. So I wonder, how could one predict, from these parameters, striking features of the resulting shape like this square inner envelope. --Dan Sometimes the brain has a mind of its own.