; Date: Sun, 24 Oct 2010 22:24:17 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 25-10-10 (Seahorse Abomination [6]) ; Id: <1.5.4.16.20101024222415.102f4890@pop.mindspring.com> ; --------- ; ; FOTD -- October 25, 2010 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; Today's image is a "Seahorse Abomination", which is what I named ; it. ; ; Seahorse Valley never deserved to have such things done to it. ; The valley is a nice little place, a four-dimensional complex, ; so what have we done to the innocent valley to cause the gross ; disruption apparent in today's image? ; ; To begin, the image is not a Julia set of the familiar Seahorse ; Valley of the Mandelbrot set. It is a Julia set of Seahorse ; Valley of the Quaternion Mandelbrot set, which is actually an ; eight-dimensional Julibrot complex, with a 4-D Mandelbrot aspect ; and a 4-D Julia aspect. ; ; I'll not go into details about the wonders of the eighth ; dimension; I'm still working on understanding the fourth. But ; one thing certain is that in 8-D space, 28 two-dimensional ; planes pass through every point, with every plane perpendicular ; to all the others. ; ; (There is something puzzling about the two quaternion formulas. ; Today's image was created by the type=quatjul formula, which ; plots Julia sets. This formula has six variable parameters, all ; of which are necessary if we are to move off from the screen in ; the six perpendicular directions. Yet the type=quat formula, ; which plots Mandelbrot sets, has only two changeable parameters ; [plus two unused parameters] both of which have the same effect, ; giving the impression that the quaternion Mandelbrot set is a ; simple three-dimensional thing that would result from rotating ; the classic M-set around the X-axis.) ; ; Be that as it may, today's image, with its minor mathematical ; interest and only slightly better artistic worth, rates a 6. ; ; The fireball-fast calculation time of under 3 seconds will leave ; little time to wonder about higher dimensions before the image ; bursts onto the screen in a blaze of mediocrity. ; ; Those who prefer to remain burst-free may see the finished image ; on the FOTD web site at: ; ; ; ; Sunday here at Fractal Central featured a mixture of sun and ; clouds, and a very pleasant temperature of 70F 21C. The fractal ; cats complained that there was not enough sun then went to sleep ; on the living room carpet. ; ; After my trip back to the nostalgia-infested land of Old Fractal ; Central on Saturday, Sunday seemed relaxing. (Though I still ; wish the Phillies had won the NL pennant.) FL occupied herself ; wondering why I end my FOTD discussions with so many 'silly and ; unanswerable' comments. ; ; The next FOTD will be posted in the generally accepted 24 hours. ; Until then, take care, and if the belief in God and an afterlife ; is a defense mechanism evolved to enable us to cope with the ; awareness of our ultimate mortality, how would society react if ; it were ever demonstrated beyond all doubt that these things do ; not exist? ; ; ; Jim Muth ; jamth@mindspring.com ; ; ; START PARAMETER FILE======================================= SeahorseAbomnation { ; time=0:00:02.70-SF5 on P4-2000 reset=2004 type=quatjul center-mag=-0.0300864/0.01\ 38653/1.05286/1/32.5/0 params=-0.75/-0.055/-0.113/\ -0.013/-0.048/-0.134 float=y inside=0 periodicity=0 colors=000KIcLJcMKcNLcOMcPNcQOcTQcWScYUc`WcbYceZch\ `cjbcmebohcrjetffu_dvTawLZwCXs6Uo0Ti1Td3T`5TY6RV6P\ S6NR6JP4EM38H3BB4C56C58E3BG4EI5HK5KM6NO6PR6SU6VX6X\ _6_b6be6ch8ae9ZcBWbCTaDQ_FN_GK_HH_IF`IE`JD`JC`KB`K\ AaL9aL8aM7aM6aJ2eH0hC0c70Z30V51W62W83X94XB5YC6YD7Z\ F9ZGA_IB_JC`LD`MEaNFa7MeANdDNdFNcIOcKObNObPPaSPaUP\ aM0oN1mO5kP8iQCgRFeSJcTMaUQ_x3pr9llEhfJe`OaR0iS3gT\ 7eTCdUGbULaVP_0J46LABNFGOKLQPQSUCpifQdcRb`SaYT_rp0\ nm2ji9feFb`MZXT7efAceCbdEacG`cI_bLYaNX`PW`RV_TUZ_C\ gZEfZFeYGeYHdYJcXKcXLbXMaWNaWP`WQ_VR_VSZ2gm7djBbhF\ `fJZdNXbRV`faRc_TaYVZWWXUYjY0hX0fW4dW9bVDaVI_UMYUR\ WTVUGTVIUVJVVLVVMWVOXVPXVRYVSZDQNFRPHRQIRRKSSMSTNS\ UPSVRTWSTXUTYk03i17g5Be8EcCIaFL_JPYMSWQWJphKpgLofM\ mfMleNjdOhdPgcPecQcbRbaS`aSZ`TY_UW_VUZbfWadX`cX_aX\ Z`YZ_YYYYXXZWVZVUZ8p9OmYPkZQiZQgZRfZRdZSbZT`ZT_ZUY\ ZUWZVUZ_LiZNfYPdXQbWS`f0V } ; END PARAMETER FILE========================================= ; ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;