; Date: Thu, 03 Mar 2005 12:13:06 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 03-03-05 (Believe It Or Not [5]) ; Id: <1.5.4.16.20050303121339.22678ee0@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; 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========================================= ; ;