On Sat, Oct 22, 2011 at 3:44 PM, Tim Wegner <twegner@swbell.net> wrote:
Mike wrote:
I zoomed into a "two way symmetry" until I found the two armed oval this added to the fractal. That wasn't quite deep enough to test the new capability so I kept zooming until I got to this 4 armed oval at a magnification of 4e355.
Just curious, how do you know this image is not similar to another at a much shallower zoom? From extensive, albeit not recent, explorations I did years ago, I recall that it is devilishly difficult to find deep zoomed images that are "new". I don't mean that they are rare, but casual zooming without letting images fully develop, which is almost a requirement because of slowness of aribrary precision, can easily fall into vortices of self similarity.
Since a lot of time has passed since I tried this, it's possible that images are formed much faster than before, and it's easiere to find new (e.g. not self similar to shallower) images.
Tim
Hi Tim. I did read the comments you posted many years ago about the self similarity of the original "233" fractal and you are undoubtedly correct. However, I don't think a zoom into a two way symmetry point in a self similar image yields exactly the same fractal that can be found at a shallower depth. The reason I say that is that the distance you zoom into a spiral affects the spacing between the rings much deeper near the minibrot. At least that is what I have noticed other times when I have repeatedly zoomed into a spiral before picking some symmetry point to stop the spiral. Anyway, if I am wrong it was still a good test fractal. The reason I picked it, was that it started at a magnification of 1e233 and that saved me a lot of time zooming. I was also curious to see what was in there. Thanks so much for writing FractInt. It inspired a lot of people, me included. I am currently adding some new things to Fracton. I wanted to have Fracton be able to draw the deepest FractInt images so I fixed the magnification limitation. I am also currently working on adding arbitrary precision arithmetic to all formulas. I wrote arbitrary precision versions of all the trig functions and I have a lot of it working. The deep images are really interesting and I think there are going to be some good images there. It is very slow though. The speeds of the formulas I have tested range from 30 to 1000 times slower than the regular double precision math. -- Mike Frazier www.fracton.org