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