; Date: Mon, 29 Nov 2004 12:10:04 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 29-11-04 (Funny Face [3]) ; Id: <1.5.4.16.20041129121141.29dfb36e@pop.mindspring.com> ; --------- ; ; FOTD -- November 29, 2004 (Rating 3) ; ; Fractal visionaries and enthusiasts: ; ; Today's image takes us to the 'quat' formula, which draws slices ; of the supposedly 4-dimensional Mandelbrot set created by 4-part ; quaternion numbers. I have several problems with this formula. ; To start, the parameter screen of the formula is puzzling. ; While spaces exist to enter four variable parameters, only two ; are used, as though the formula were still being developed. And ; a little bit of investigation will show that only one parameter ; is needed to draw all the images that the formula can create. ; There must be a reason why the two unused parameters exist, or ; more importantly, why there are not six parameters, as there are ; in the Julia version of the same formula, which is far richer ; than this Mandelbrot version. ; ; With two 4-part numbers included in its calculation, the ; quaternion Julibrot figure must be 8-dimensional, so there must ; be six directions perpendicular to any image on the screen, and, ; as is the case in the Julia version, it should be possible to ; move the illustrated slice in any of these six directions. I ; can't escape the feeling that, as it is written, the formula ; short-changes the user. (The hypercomplex Mandelbrot formula ; has the same parameter limitation, though in that case I have ; written my own formula that includes some of the missing ; parameters and draws some very curious and interesting images.) ; ; Actually, I wonder whether the quaternion Mandelbrot set is ; 4-dimensional at all. It appears to me that we are examining a ; figure with only three dimensions, which is the 3-dimensional ; figure that would be traced out if the 2-dimensional Mandelbrot ; set were to be rotated around its x-axis. All in all, I find ; the quat formula one of the more disappointing in the program. ; (Though maybe I am missing the formula's main features.) ; ; So what do we do with such a disappointing formula? Why we draw ; funny faces. Today's image resembles a funny face, and that is ; what I named it. Try as I might, I could find nothing in it ; worth a rating higher than a 3. The render time is mercifully ; short, and this results in an inflated overall worth of 121. ; ; The funny face can be found leering from the FOTD web site at: ; ; ; ; The rain cleared out quickly here at Fractal Central on Sunday, ; leading to a sunny and mild afternoon with a temperature of 59F ; 15C. These conditions must have pleased the cats, for they ; spent almost three hours in the holly thicket at the bottom of ; the yard, keeping watch on the neighborhood goings-on. When the ; day ended, no tuna was needed to put them in a good mood. Today ; is starting sunny but chilly. We'll wait to see how it goes ; with the dynamic duo. ; ; With me it will go good enough once I finish the three hours or ; so of work that waits to be done. Then it will be on to Fractal ; Land and the goodies therein. The next glorious fractal will ; appear in 24 hours. Until then, take care, and do you believe ; in the great fractal? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Funny-Face { ; time=0:02:28.19--SF5 on a P200 reset=2004 type=quat center-mag=-0.085743250969516\ 82/0/701.1023/0.03524/-90/7.67164110015983169e-014 params=0/0/0.65/0 float=y maxiter=2500 bailout=9 inside=255 logmap=45 periodicity=0 colors=000OSjPTiQUhRVgSWfTXeUYdVZcW_bX`aYa`Zb__cZ`\ dZaeXafVbgTbgSchQciOdiNdjLdkJekIelGfmEfmDgnBgo9go8\ cjA_fBXbCTZDQVEMRFINHFJIBFJ8BK47L13M47N7AOADPCGQFJ\ QINRKOSNRTQUUSWUTWTTVSTTRURQUQPUOOUMNVKNVIMVHLVFKW\ DJWBIW9HW8HZBJ`EKcHMeKNgNOjQQlTRoWTqZUs`Vmcjgfz_cs\ T`mMYfEV`7SU0QO3SO5TO8VOAWOCXOFZOH_OJ`OMbOOcOReOTf\ OVgOYiO_jOakOYZNUNNRBNSDRTEUUFXVG_WIcXJfYKiZLl_Mo_\ Nn_Nn_Om_Om_Om_Pl_Pl_Pl_Qk_Qk_Qk`Oh`Ne`Lc`K``IZ`HW\ `FT`ER`CO`BM`9J`8G`6E`5B`39`26`14_47Z69Y8BYADXCFWE\ HWGJVJMULOTNQTPSSRURTWRVYQY`P_bOadOcfNehMgjMilMilN\ imNimNinNinNinSheWhYUi_Si`QiaOibMjdKjeIjfGjgEjhCkj\ Akk8kl6km5knKpkYtikxghvfftedrdbqd_kaXf_UaXRXVORSLM\ QIHNGCLIDKJEJKFIMFINGHOHGPHGRIFSJETKDVKDWLCXMBYMBc\ QIiTOoXUt__k`Zc`YCxGApM9hR7aX6Ua4MU3FUAJUHMUKKUKKU\ KKUKKUKKUG19J8HMEOPKVSKbVKiYKpWKjUKeSK`RKWPKRNKLMK\ GKKBIK6HK1GK6GKBGKGGKLGKQ } ; END PARAMETER FILE========================================= ; ;