FOTD -- March 03, 2005 (Rating 5) Fractal visionaries and enthusiasts: The next paragraph has nothing to do with fractals. The really interesting stuff starts in the third paragraph. My day started with a bang when I checked my e-mailbox and found that I had won three lotteries which I had never entered, and that there were four floating bank accounts totalling over 50- million dollars that people wanted to transfer into my pathetic account. There was also a letter from a large well-known national bank, with which I have no account, informing me that their computer had crashed and they needed me to re-enter my account information. (Don't they keep a data backup?) I also saw that ebay has scrambled my account information, and Earth- link has lost my credit-card information etc. etc. etc. With so many 'phishing' scams out there, it is hard to believe that anyone would fall for such obvious deception. But I suppose public stupidity knows no bounds. In my wonder years, when I was just discovering the world and was hugely fascinated with science, I never missed the daily 'Believe It Or Not' cartoon. (For a while, I took the odd facts that appeared in the cartoon as absolute truth, but I gradually came to realize that the claims were intended more as entertain- ment than as proven facts, and some claims were quite a bit exaggerated.) I named today's image "Believe It Or Not" because it is difficult to believe that the delicate, wispy arches and solid horizontal beams are a part of the very familiar Seahorse Valley, yet it is a fact, and in today's case, most definitely a true unexaggerated one. What happened to the valley is that I have sliced it in an unfam- iliar direction -- the Oblate direction. In the image we are seeing the valley as it appears when the three-dimensional (real(c),imag(c),real(z)) slice of the four-dimensional Julibrot is rotated 90 degrees around the Y-axis, with the eastern edge of Seahorse Valley acting as the axis of rotation, and the resulting image is stretched 400,000 times in the vertical direction. The horizontal breaks in the purplish background are actually the Mandelbrot buds on the eastern shoreline of Seahorse Valley, which have been stretched horizontally to infinity. The greenish foreground elements are lower iteration features whose points have escaped before they had a chance to settle into the familiar Mandelbrot shapes. The Mandelbrot view of the scene can be viewed by going to the 'z' screen and changing the imag(p1) parameter to zero, and then going directly to the 'F6' screen and changing the X-magnifica- tion factor to 1. The symmetry must then be reset to 'none'. Since the resulting image will be very slow, it is best to render it in a thumbnail size. The Julia view of the scene can be viewed by going to the 'z' screen and changing the real(p1) parameter to 90 and the imag(p4) parameter to 0.01360067933, then, on the 'F6' screen, changing the X-magnification factor to 1 and the magnitude to 0.85. The symmetry should be set to 'origin' and the logmap should be reset to zero for fastest and best results. The Julia set is actually quite striking. I was undecided on the proper (IMO) rating for today's image, and finally settled on a rating of 5, which is average in every respect of the word. The bad part of all this is that, even with Y-axis symmetry, the image takes 3-1/2 hours to render. But salvation is at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The image has been sent ahead and should already be posted. Cold winds, snow-covered ground, and a freezing temperature kept the dynamic duo indoors on Wednesday. They took their confinement bravely however, and I rewarded them with an extra big serving of tuna. Today is starting cold and windy again, only slightly less harsh than yesterday. Can the duo be brave two days in a row? For me, the commercial work is minimal, which means lots of time for fractals, and maybe some philosophy. Regardless of what happens, the next FOTD will appear in 24 hours. Until then, take care, and what will we do when we eventually run out of fractals? Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Believe_It_Or_Not { ; time=3:29:45.98--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=0/+0.01360067933683444/551139.\ 1/4.153e-005 params=0/90/2/0/0/0/-0.7499/0 float=y maxiter=500000 inside=0 logmap=1489 periodicity=10 colors=000cuAPZ8PY7PW6PU5OS5OQ4OO3NK0ON3OP5PR7PTAP\ VCQXEQZGQaJRcLReNRgQSiSSkUUlUTmVSmWRnWRnXQnXPoYOoZ\ OoZNp_Mp_Mq`LqaKqaJrbJrbIrcHsdHsdGteFteEtfEugDugCu\ hCvhBviAwj9wj9wk8xk7xl7xl9wmAvmBunCtnDtnEsoGroHqpI\ qpJppKoqLnqMnqOmrPlrQksRjsSjsTitVhtWguXguYfuZev_dv\ acx`dv`du`et`er`fq`fp`go`gm`hl`hkbhieihcwVcwAbjdbk\ cakbbla`l_`lZ_mY_mW_nV_nU_oT_oR_pQ_pP_qO_qM`qL`rKa\ rIasHbsGbtFctDcuCduBduAct9ct9bt9bs9bs8as8ar8ar8`r8\ `r7`q7_q7_q7_p7Zp6Zp6Yp6Yo6Yo6Xo5Xn5Xn5Wn5Wn5Xm4Ym\ 4_m4_l4`l3al3bk3ck3ck3ck2cj2cj2cj2ci2ci1ci1ci1ch1c\ h1ch0cg0cg0cg0cg0be3bd5ac8abA`aC__FYZHWYJUXMSWOQUQ\ OTTMSVKRXJU_JWbJYeJ_jJanIcsJcsKctLcsMcsNcsOcrPcrQc\ pRcpScoTcnTcmUcmVckWZkXUiYPhZOg_Pe`PdaPbbQbcQbcQad\ QaeRafR`gR`hS_iS_jS_kSZlTZmTYnTYnTYoUXpUXqUXrVWsVW\ tVVuVVvWzwWzxWzybzxZzxWzwTzwQzvNzvKzuGzuDztAzt7zs4\ zu0zt1zs1zr1zq1zp1zo1zo2z symmetry=yaxis } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================