; Date: Mon, 04 Sep 2006 23:44:09 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 05-09-06 (Is This Seahorse Valley? [7]) ; Id: <1.5.4.16.20060904234503.2a0f7f02@pop.mindspring.com> ; --------- ; ; FOTD -- September 05, 2006 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; Seahorse Valley never looked like this before. The unexpected ; shape inspired the name "Is This Seahorse valley?" But the ; image most certainly is one of Seahorse valley. The scene is an ; oblique view of the valley, rotated 13 degrees from the Julia ; orientation toward the Rectangular orientation. If anyone ; doubts this, change real(p1) to 90 and watch the Seahorse Valley ; Julia set appear. And while you're at it, change poth parts of ; (p1) to zero and watch Seahorse Valley itself appear at the ; center of the screen, awkwardly rotated 90 degrees. ; ; With all these unfamiliar aspects, what shape then is the entire ; Seahorse Valley area of the Julibrot? It is a tapering four- ; dimensional wedge that terminates in a sharp plane. A sharp ; plane would describe the razor edge that a 4-D man would use to ; shave his chin, just as a 3-D man uses a blade with a sharp line ; as the cutting edge. Yes, I know it's silly to think that a ; plane could be sharp, but the fourth dimension makes many imposs- ; ible things possible. A sharp plane could extend indefinitely ; in all directions, yet a 4-D man could cut himself seriously if ; he carelessly touched it. ; ; Thank goodness we can see our fractals only two dimensions at a ; time. ; ; The included parameter file of today's image runs in a little ; over 1-1/2 minutes. The image is also conveniently available ; for download on the FOTD web site at: ; ; ; ; I'll probably post a few more unexpected aspects of Seahorse ; Valley before moving on to East Valley, which, if anything, is ; even more varied than Seahorse Valley. ; ; The weather turned quite pleasant here at New Fractal Central on ; Monday, with warm sun and a temperature of 73F 23C. The fractal ; cats enjoyed the fine weather as they sat on their scratching ; posts, soaking up the sun. My day was reasonably quiet, but ; that big job is still looming for later this week. The job will ; not arrive tomorrow however, so expect the next FOTD to be ; posted on schedule in 24 hours. Until then, take care, and a ; four dimensional man would probably cut himself in half if he ; stepped on one of our sidewalks. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= IsThisSeahrsValley { ; time=0:01:39.03--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=1 center-mag=0/0/1.127829/1/-90/-1.2337e-014 params=77/90/2/0/0/0/-0.75/0 float=y maxiter=50000 inside=255 logmap=yes periodicity=10 colors=000E2hC2iA2p82o62n40m50l60k70j70i80h90gA0fA\ 0eB0cC0aD0_D0XE0UF0RF5OCAKAEH7HL5KQ2LV0MZ4PZ8SZCUZ\ GXZJ_ZMYZOWZQU_SS_UQ_WO`YM`_K`aIacGaeEagCbiAbk8cm6\ co4bq4aq4`p4_p4Yp4Xp4Wp4Vo4Uo4To4Ro4Qn4Pn4On4Nn4Mn\ 4Km4Jm4Im4Hm4Go2Em4Fl6Fj7Gi9GgAGfCHdDHcFHaGI`IIZJI\ YLJWMJVOJTPKSRKQTKPULNWLMXLKZMJ_MHaMGbNEdNDeNBgOAh\ O8jO7kP5mP2qR4nP5kO7hM8eL9bJB`ICYGDVFFSDGPCINAJNFK\ NKMNPNNUPNUONUOOUPOZROcTOhVOmTOgROaPOWNOQLSJJWDH_7\ Eb0Gc1Ic2Jc2Ld3Md3Od4Pd5Re5Se6Ue6Vf7Xf8Yf8_f9`g9bg\ AcgBehBfhChhCihDkiEliEniFoiFnjEnkEnkEmlDmlDmmDmnDl\ nCloCloCkpBkqBkqBkrBjrAjsAjtAit9iu9ju9kv9kw8mx8oy8\ rz7sz8uz8uz8sz8qz9nz9lz9jy9ix9hwAfvAfuAftAftBftBft\ BesBesBesCerCerCdrCdqDdqDdqDdpDcpDcpEcoEcoEeoEgoFi\ oEkoEmoEooDqoDsoDuoCwoCxoCzoCzoBzoBzoBzoAzoAzoAzo9\ zo9zo9zo9zo8zo8zo8zo7zo7zo7zz7zz8zz9zzAzzBzzCzzDzz\ EzzFzzGzzHzzzzzzzzzzzzzzz } 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========================================= ; ; ;