; Date: Sat, 07 Oct 2006 07:53:22 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 07-10-06 (Triternion Travels [No Rating]) ; Id: <1.5.4.16.20061007075441.29bf6c50@pop.mindspring.com> ; --------- ; ; FOTD -- October 07, 2006 (Not Rated) ; ; Fractal visionaries and enthusiasts: ; ; The earlier version of today's FOTD will not run because I ; left out the 'frm:' brfore the formula name. This version ; works all right. ; ; Today's image makes use of a formula revised by Gilles Nadeau ; and posted to the Fractint list on Friday. (I have changed the ; space between Neo and T-set in the formula name to an under- ; score. A space band in a formula name is not permitted.) The ; formula is designed to draw the three-dimensional triternion ; Mandelbrot set. It does this very well. But I notice that the ; images it draws are the same as those drawn by the type=quat ; formula in Fractint, which claims to draw slices of a four- ; dimensional quaternion M-set, but which I have always suspected ; actually draws slices of a circular three-dimensional object. ; ; It is apparent that the three-dimensional object being sliced by ; both formulas is the figure that is traced out when the M-set is ; rotated around its X-axis. The value I gave (p1) in today's ; image is +0.64952, which is the Y-value of the prominent valley ; of the large north bud of the M-set. And not surprisingly, the ; valley appears in distorted form in today's image. The large ; open areas at the top and bottom of the frame are oblique slices ; of the northern bud itself, or rather of the donut-shaped ring ; this bud traces out as it rotates around the X-axis. The chaos ; across the middle of the frame is the fringe of the detail on ; the main-bay side of the valley, grossly stretched as would be ; expected when slicing through the edge of a donut. ; ; What I would like to see is a way of rotating the slice 90 ; degrees, so that the circles of revolution are drawn, and also ; the fascinating ovals that must lie in between. I have no idea ; of how to do this however. ; ; The image is titled "Triternion Travels", which is a fair enough ; opinion of the scene. Since the image has mathematical value ; but little artistic worth, I gave it no rating. The render time ; of 7-1/2 minutes on my 10-year-old machine may be avoided by ; visiting the FOTD web site at: ; ; ; ; and viewing the image as it is posted there. ; ; A cloudy cool day here at Fractal Central on Friday went un- ; noticed by the dynamic duo of fractal cats, who still were more ; interested in playing with each other and waiting for another ; mouse to come out. They exhausted themselves playing, and ; showed little disappointment when no mouse appeared. The usual ; evening treat was fully enjoyed. ; ; My day was totally average. Tomorrow will probably be the same. ; Until then, when the next FOTD will shine forth, take care, and ; would the true number of dimensions that make up sub-atomic ; reality please stand up. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Triternion_Travels { ; time=0:07:26.44--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=Neo_T-set center-mag=-0.124889193/0/42.27946/3.2951 params=0.64952/0 float=y maxiter=5000 inside=0 logmap=186 symmetry=xaxis periodicity=10 colors=000kdff_g`ViWQjTJmSKlRLkRMkQNjQNjPOiOPhOQhN\ RgNRgMSfLTeLUeKVdBjCGbRKVdJKuMMsONrQOqSPpUQoXRnZSm\ `TlbVjdWigXhiYgkZfm_eo`dtddqaco_cmYckWciUcgSceQccO\ caMc_KcYIcWGcUEcSCcN5fQAcSFaVK_XPYZTWaYUcbSfgQhlOj\ pMhqPfrSdrVbsX`s_ZtbXueWugUvjSvmQwpOxrMxuKyxJyzHwy\ FuxDsxBqwAow8mv6kv4iu3hu7isBjrFkpJloNmmRnlVokZpibq\ hfrfjsentcrubvx`uuatsasqasoarmaqkapiaqfbpgapgaph`p\ h`pi_oi_ojZojZokYokYnlXnlXnmWnmWnnVqoUnnVknVhnWenW\ cnW`nXYnXVnXSnYQnYNnYKnZHnZ4bsCsWFnZIj`LfbOaeRYgUU\ iXPl_LnbHpeCsh8uk4wn0yh9lcI_ZRNRX4TY8UZBVZEW_IY`LZ\ `O_aS`aVbbYccadcdedghghfdjdbkc_laYm_WnZToXRqWOrUMs\ SKtRHuPFvODwUEjZFZcGNMAELEGKHIKKJJNLJQMITOHWPHZRGa\ SGdUFgVEjXEmYDp_AxfCucDs`EqZGnWHlUIjRJhPPeUVcZ_abe\ _gkYlpWprVsAao8Wg7Q`6KU5EN7LK9RIBYGDcEFjCGpAAsU5ul\ `FLRMJHTI8ZHQaVgdhyfuvXotOirFcp6YmHWkRVh`TfjSdtR`m\ SXfST_TPTTLMUIFUFP`CZfAgm } frm:Neo_T-set { X=real(pixel), Y=imag(pixel), V=real(p1) x1 = y1 = v1 = 0: x2 = x1^2-y1^2-v1^2 + X y2 = 2*x1*y1 + Y v2 = 2*x1*v1 + V x1=x2, y1=y2, v1=v2 z = x1^2+y1^2+v1^2 z < 8 } ; END PARAMETER FILE========================================= ; ;