; Date: Wed, 21 Dec 2005 01:03:41 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 21-12-05 (Julibrot_Jubilee [5]) ; Id: <1.5.4.16.20051221010547.364fbbca@pop.mindspring.com> ; --------- ; ; FOTD -- December 21, 2005 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; It's the day of the Winter Solstice not only here at Fractal ; Central, but everywhere in the Northern Hemisphere. It's also ; the solstice in the Southern Hemisphere, but down there it's the ; Summer Solstice. The solstice is the shortest (or longest) day ; of the year, but it is not the day of the earliest sunset. Due ; to the earth's elliptic orbit, the earliest sunset came two ; weeks ago here at latitude 39N, and the latest sunrise will not ; come for two more weeks. It's all so confusing, but this is ; what those figure-eight things printed on the Pacific Ocean ; areas of world map globes are supposed to make clear. ; ; Today's image tells us that a small departure from the Julia ; orientation can make a huge change in the appearance of the ; resulting fractal. The image shows one of the Julia spirals ; connected with the period-4 bud on the northeast shoreline of ; the Mandelbrot set. The spiral is evident on the left side of ; the image. But it is no longer a spiral. ; ; The direction of the slice has been rotated in the fourth ; dimension a couple degrees from the Julia direction. This ; slight rotation has totally changed the scene from a nice neat ; spiral to a crazy "Julibrot Jubilee" of twisted arms and rioting ; colors. The horizontal blue bar across the lower part of the ; image is actually one of the valleys of the period-4 Mandelbrot ; bud, stretched out to near infinity. ; ; The rating of a 5 was held down by the coloring, which could ; have used much more work. Unfortunately for the rating, I was ; not in the mood to tweak colors. I would rather write philoso- ; phy, so I gave the palette a cursory fine tuning and started ; iterating. ; ; The render time of 2-3/4 minutes is acceptable to all but the ; most impatient or those with balky computers. For these fractal- ; ists the completed GIF image has been posted on the FOTD web ; site at: ; ; ; ; from where it may quickly be downloaded. ; ; Yesterday I suspected that the philosophy bug might strike in ; the near future, causing another outburst of condensed wisdom. ; And indeed, as the following four paragraphs show, it did strike. ; ; I am occasionally asked if I hold a grudge against science and ; why I sometimes criticise it. The answer to the first part of ; the question is that I hold no grudge against science. How ; could I hold a grudge against so effective a discipline, which ; has given us the life we now enjoy? But sometimes I do get ; frustrated with those who continue to search for answers to deep ; questions using the same old methods that have failed for many ; decades. The physicist's search for a 'theory of everything' ; and the cognitive scientist's search for the 'origin of con- ; sciousness' are two immediate examples that come to mind. ; ; Ever more complex math and ever better imaging of neural acti- ; vity are keeping the excitement going by breeding ever more ; fantastic ideas. I have lost count of the number of 'new break- ; throughs' in both fields that have burst upon the scene with a ; flash of anticipation, then died a slow whimpering death, leav- ; ing the basic questions no closer to being answered. I no ; longer feel anticipation when I read of yet another new scienti- ; fic breakthrough that has occurred in these fields. I assume ; that the new breakthrough will soon prove to be just another ; dead end. So far I have not been wrong. ; ; I have been following these two searches with particular ; interest for many years, and after so many let-downs, I have ; come to suspect that they are two different aspects of the same ; search. I am also beginning to suspect that the traditional ; methods of science, which were developed to investigate the ; intuitive material world of our five senses, will never lead to ; the answers to questions about things so far beyond the range of ; the senses. At least, the physicists now realize that their ; answers will lie far beyond our intuitive material world view. ; Cognitive scientists are still searching the material brain for ; the non-material self. I guess we can't blame them. The physi- ; cists have given them nothing else to search. ; ; No, I am not suggesting that we surrender and say 'God did it', ; or visit the local fortune-teller for a psychic explanation, but ; I feel we will need a totally different approach to these and ; other difficult questions if we are to have any chance at all of ; finding answers. I am cannot imagine what course we might take. ; We would probably need a new means of verification. Entities ; such as probability waves and self-awareness are rather diffi- ; cult to spread on a table for dissection. At the same time, ; without empirical evidence, there is no science. The problem is ; deep, and at the present time I see no way out. Oh well, what ; the heck, this kind of stuff is what makes life interesting. ; ; Cold blustery weather kept the fractal cats snug indoors all day ; Tuesday here at Fractal Central. An extra treat of tuna in mid- ; afternoon kept them happy. The duo seems to have accepted that ; the next few months will be spent mostly inside. For me, the ; work was light and finished early. The next FOTD will probably ; appear on schedule in 24 hours. Until that wonderful time at ; last arrives, take care, and where are those answers hiding? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Julibrot_Jubilee { ; time=0:02:41.26--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=t periodicity=10 center-mag=0/0.131074/3.138989/1/-90/3.8857806e-016 params=90/90.07/92.48/89.01/0.2438/0.5139/-0.0081/\ 0.5024 float=y maxiter=2500 inside=0 logmap=yes colors=0000A_pAZ0AYnAX0AWlAV0AUjAT09Sh8R07QfFP06Od\ KN05MbPL05L`RL04LXSL04LTQL04LPOL0TGNXLIVYNSURMWVBS\ Z0PWAVTJ`QTfNalLaqYafZac_aa_a_`UY2XnZVf_Sb_P_`MW`J\ TaGPmBNgCMaDMy6Rq8PjAObCNWEa9JhDIoHHuLGrPFlSGTaBLf\ 3Gi9FmEFmKFmPFqMHqPGlUFfWEQZIU_GY_Fa`De`CejDffCgcB\ h`BhYAiV9jS9kP8kM8hPCeRFcTI`VLYYOW_RT`ZTaYSbXRcXIc\ NQcKNcNKcPHcRFcTCcV9cX6cZ4c`8cZ9duAezBfkCgYDhKEilE\ jYAkK6l6GnHQiSRYpWai_dbAKRKSTU_VDu3cgW_`ZWUaTNcPGf\ L9iYPqQEnnKtYBoI3kOEWadLZZJXUIUPHSKGyH7gGBND3QFFSG\ RVIbXJnTPxZKydGyiCyo8yr5yt4yr6sq7mp8gnAamBWn3Jm6Lm\ 8NlAPlCQlESkGUkIWiHbkKXmMRoOLqQFsR7rS9qTBpUCoVEnWF\ mXHlYKkZJj_Ji`JhaIgbIfcEebGdaHc`Ib_KaZM`YO_XQZWSYV\ UXUWWVYVW_UXaTYcSZeRZgQZiPZkOZlNZmMZnLZoKZpKYqKYrK\ YsKYtKYuKYvKYwKXxKYyKYzKYzKYzKZzK_zK`zKazKbzKczKcz\ KczKczKczKczKczKczKezKgzKizKkzKlzKmzKnzKozKpzKqzKr\ zKszKtzKuzKvzKwzKxzKzzKzz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } ; END PARAMETER FILE========================================= ; ;