Re: [Fractint] infinity
. "it can be thought in an abstract way as though the closer the scene gets to the singularity, that time is slowing down to the observer of the scene"" . that is exactly what happens when you fall into a black hole (if I understand correctly). the "fallee" will never get to the singularity - he will grow old and die of natural causes or something. but someone outside the event horizon will see him get sucked in real fast. more to the point, the mandelbrot is mathematically connected everywhere (that is theoretically proven now) - even the tiniest minibrot is connected by a very thin fillament ultimately to the main body. so the 2 main bulbs must ultimately be connected at real=-0.75, imag=0. but you need to get to infinity to see it. if you zoom in and see a "bridge" and then up the iterations it again disappears. ad infinitum. maybe the oft hyped (soon to arrive?) quantum computer will be able to do it........... .
Have you ever noticed that when Jim Muth makes a foray into the fourth dimension that he usually seems to do it in a big way? He usually leaps 90 degrees or more into, what he calls the 'rectangular' or 'elliptical' dimension and then looks around. This is really great, but I often wonder how things would slowly change as you just barely peek into the next spatial dimension... JoTz, Have you ever considered a zoom that gradually slips into the fourth dimension from Fractint's usual real / imaginary plane (rather than exploring at a 'distance' from it as Jim does?) (I guess it wouldn't be a zoom, but rather a pan, moving slice or slow roll.) I know there is a whole different world out there in the fourth spatial dimension. I took a look into it a while ago and saw some very strange beasts. I used the older fractal program Quat that generates 3d fractal objects from 4d fractal objects in the quaternions. Its downloadable at: http://www.physcip.uni-stuttgart.de/phy11733/quat_e.html or http://tinyurl.com/5zy9a3 and the home page for Quat is here: http://www.physcip.uni-stuttgart.de/phy11733/index_e.html or http://tinyurl.com/lkroyt I made a movie using Quat where each frame is a slightly different 3d slice into a fractal that lives in four spatial dimensions: http://home.earthlink.net/~hallane/hals_fractals_n_photos/id2.html or http://tinyurl.com/mmjzoh I'd be interested to see zooms in Fractint that incrementally step through the fourth dimension, perhaps using some of Jim Muth's Formulas like SliceJulibrotMin4 or Multirot-XZ-YW-new. Anyone have any interest in fractals that exist in four spatial dimensions? Our computers are getting fast enough to investigate these animals. The Quat animation at my home.earthlink.net link (above) was done several years ago on a Pentium III at 400 MHz... - Hal Lane ######################### # hallane@earthlink.net # #########################
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