Jim, I've been exploring your fascinating fractal for today. If you change the real value of parameter 1 from 1.08 to 1.078, draw the midget corresponding to the one you posted today and then look at the south east side of the hook, you will find an area with an infinite number of midgets or holes. Here is a picture of that area: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06a.png and here is a detail of one of the midgets or holes: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06b.png Brian Prentice