Am I correct in thinking that the radial spokes in the FOTD 25-01-11 (A Googol is Deep [No Rating]) (it's actually January 26th's fractal) are structures associated with period doubling? I'm used to seeing (for example) a pattern repeated eight times around a minibrot, surrounding a similar one repeated 16 times, surrounding a pattern repeating 32 times, etc. The largest number of these repeated structures that I've ever been able to see in the past was 256. In your FOTD there appear to be 128 of the largest spokes surrounding a smaller ring of (apparently) twice as many yellow and purple spokes, surrounding a smaller ring of (apparently) four times as many yellow and purple spokes -- still clearly visible. This would make 512 easily-visible period-doubled spokes, and is double my previous record. ;-) For a minute I had thought I had figured out that I was seeing 1024 spokes, but I had gotten it wrong. Perhaps one could see 1024 if the image were calculated at a substantially higher resolution. I'm not going to do that today, because the one I put on your FOTD web page at 1200 x 900 took about 6 1/2 hours on my 2.2 GHz machine. It's fortunate that "symmetry=xaxis" is in your parameter file and halves the calculation time... On a slightly different aspect of this image -- the fact that it uses about 100 digits of arbitrary precision math -- makes me wonder how many sheets of paper it would take if all the numerical values of all the iterations calculated for all the 1,080,000 pixels I calculated were printed out on 8 1/2 x 11 inch paper... Again, am I correct in thinking that the radial spokes in the "A Googol is Deep" image are associated with the usual period doubling seen in many fractals? - Hal Lane ######################### # hallane@earthlink.net # #########################