At 01:44 PM 1/26/2011 -0500, Hal wrote:

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?

Yes, the radial spokes are associated with period doubling. The period continues doubling as a minibrot is approached, until I assume it reaches infinity at the edge of the minibrot. In minibrots of limited magnitude, the high-order elements lie so close to the minibrot that they cannot be resolved, but as the magnitude increases, the basins around the minibrots grow larger, and the farther from the minibrots the higher-order elements lie. The image of Jan 26 is of such a high magnitude that the period-1024 elements lie far enough from the minibrot to be rather easily resolved. The situation becomes complicated with minibrots that lie in the basin of a larger minibrot, as does the minibrot in the Jan 26 image. In this case the doubling sequence reaches infinity well away from the minibrot then resets itself to a lower value and starts doubling all over again. This is quite clear in the image for Jan 25, where we see 128 greenish then 256 amberish stripes around the edge, yet find only 16 amber-blue spokes at the center.

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...

I imagine it would take a googol sheets of paper. ;-) Seriously, as a wild guess, the number would probably be well into the billions. Jim