; July 12, 1997: The Stem Gone Nertz ; ; nertz ; ; Fractal visionaries: ; ; Today's fractal is a real quickie -- it draws in under 25 seconds -- but ; don't let its speed deceive you. It's quite an unusual image. ; ; For quite some time now I've been involved with the four-dimensional ; julibrot figure, (or object, or whatever it is), and the more I explore, ; the more bizarre become the objects I find. The midget pictured in ; today's fractal is one of the most bizarre. ; ; The julibrot figure is like a swiss cheese, with midgets sprinkled all ; through it. Many of these midgets do not exist in the plane of the ; classic Mandelbrot set, and today's picture shows one of these obscure ; midgets that live in the remote outskirts of the julibrot. ; ; I have examined this midget from other angles, and so far have been ; unable to find a slice that resembles the expected Mandelbrot midget ; shape. This may mean that it doesn't have such a slice, or simply that ; I have not yet located it. ; ; The attached image shows the midget sliced in the XW plane direction. ; In this direction, the midget resembles neither a Mandelbrot nor a Julia ; plane object. My first impression was of an arrow or chevron. So I ; named it "Arrow". Bits and pieces of Mandelbrot and Julia debris lie ; scattered around the midget, mixed together in a most unexpected ; fashion. ; ; Almost all objects in these odd planes are stretched, sometimes by a ; factor of tens of thousands. When exploring in these planes, one must ; become skilled at unstretching, (or stretching in the opposite ; direction). Luckily, Fractint makes this simple. ; ; Today's image has been posted to a.b.p.f. and a.f.p. for the convenience ; of those who can't spare the 25 seconds it takes to draw it. Tomorrow, ; I'll post a series of six fractals, all of another way-out midget, this ; one sliced in the six perpendicular directions. ; ; Before ending, I'd like to recommend Benno Schmid's Julibrot web site. ; It's still at an early stage of development, but already quite ; interesting. The URL is ; ; ; ; Jim Muth ; jamth@mindspring.com ; ; START 19.6 FILE============================================= TheStem_Gone_Nertz { ; time=0:00:08.29-SF5 on P4-2000 reset=1960 type=formula formulafile=jim.frm formulaname=XWplane passes=1 center-mag=-1.74179/-1.11022e-016/51.50983/0.5395 params=-1.7442/0 float=y maxiter=1500 inside=0 logmap=yes periodicity=10 sound=off colors=000Ieqs0VF0dF0tF0vF0ZF0ZF0ZF0ZF0ZF0ZF0ZF0ZF\ 0ZG3YH3XI3XJ3WK3VL3VM3UT7S_BQgIPkQNobLslczzzwmcthe\ uddvZcvWawT`xQZyNYvKUsIQqFMnCIkAEh7Af56eACdFIdKOcP\ TcUZbZdL4FL9GKEHKJIJOJJTKIYLIbMLZQNUUQQYTM`WIdYDh`\ 9leCjkFgpIekFieCm`AqV7uQ4yR4oT3dU3VW2KX2AJMbLKZOIV\ QFQSDMUDWWEfYEp_Ki`RcbXXdcQfiJgpDiv6ebAaKEXMFSOGMQ\ HHSICUJK_RTf_`lgispqyxrssslnsfit_duU_VGM53878E8CKA\ HQCMXDQbFVhGZnIct2Y64ZE7_M9`UBa`EbhGcpY_6U`KQaXMbj\ `ceXciTcmPcpLctck6`jDYiKVhRTgXQfcNejKdqY4fUDjQMoMV\ sFvtGquHlvIgwx1VmBabLiSVpjn_dldZjiTgnNesEpgR_PP`VO\ a`MafLblJcrSlctXylZyd_xXaxPbwx_xbawhNJaRTVWcO_myRR\ rTXjVacYgW_lPar0799OZLpiLnkKmmKkoJipJgrIftIdvL`PPn\ ReZfUao2u88oQDifQawObwMbwKcwprgiojblnWiqPftdQL_TTW\ W`RZhMapFfZGecHehHdmIcrQt1OqDNmPLj`Jfl4`E6aL8aRAbY\ CbdEcjGcqDkMEiWGgdHenwSwiWwW_wWqvUovSmvQkwOiwMgwKe\ wvqMajdV2uNsJMpQLnXKkcJhj } frm:XWplane {; Jim Muth z=flip(imag(pixel))+real(p1), c=real(pixel)+flip(imag(p1)): z=sqr(z)+c, |z| <= 36 } ; END 19.6 FILE=============================================== ;