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Date: Thu, 14 Oct 1993 13:33:56 -0900
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From: KENELM W PHILIP <FNKWP@ALASKA.BITNET>
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Re: Have we seen it all?
 
        I should be more specific about what I was referring to yesterday,
since I was thinking of one particular type of higher-order structure in
the M-set. If you look at Map 45 on page 86 of The Beauty of Fractals, you
will see a common structure in the M-set, which I refer to as a 'double
spiral'. What my brother found some time ago was that higher-order forms
of this double spiral structure exist, which we named double-double spirals.
Using extreme magnifications enabled us to get to fourth-order versions
(DDDDS), and it became clear that there is an infinite number of higher-
order versions. DDSs may be found by zooming in on the arms of double
spirals.  I give the coords of a typical example:
 
        Re = 0.294 475 813 427 845 8
        Im = 0.016 316 351 337 855 1
        mag = 6.6e13
        max dwell = 4000
 
and another:
 
        Re = -0.748 583 238 358
        Im =  0.063 076 937 582
        mag = 4.2e9
        max dwell = 2000
 
Higher-order versions (beyond four or five) are so complex that one really
needs a large-screen image to have the resolution needed to appreciate the
fine detail.
 
                                                Ken Philip
                                                Fairbanks, AK