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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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=========================================