; Date: Sat, 21 Feb 2004 10:24:34 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 21-02-04 (That's the Way It Is [5]) ; Id: <1.5.4.16.20040221102712.0d773ed0@pop.mindspring.com> ; --------- ; ; FOTD -- February 21, 2004 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; Today's image is a simple view of the Julia set of Seahorse ; Valley. If this is doubted, start the included parameter file, ; then bring up the X screen, drop the maxiter to 100 and restart ; the image. After a few seconds, the screen will show a near- ; perfect Julia set with the inside colored a brilliant orange. ; Why then did I choose this very-familiar Julia set to be the ; FOTD for today? ; ; The answer is obvious when the maxiter is raised to 1000000. ; The Julia set turns out to be not a Julia set after all, but ; rather a slice of the Julibrot that has been double-rotated 1/10 ; of 1 degree from the Julia orientation. (Double rotation is a ; new motion, not possible in 3-D space.) This slight rotation ; has made a great change in the resulting almost-Julia fractal, ; which is now magically filled with curious detail. ; ; The detail filling the Julia set is actually a greatly magnified ; image of the Oblate aspect of Seahorse Valley. It has been ; magnified 573, or tan(89.9), times in fact. (The Oblate aspect ; is what appears on the screen when the real(z) and imag(c) axes ; of the Julibrot are pictured.) To see the unmagnified oblate ; aspect of Seahorse Valley, change the real(p1) and real(p2) ; parameters to zero. This can be done in equal increments to ; make things more interesting. ; ; Now, to prove that it is actually Seahorse Valley we are ; investigating, drop the maxiter to 1000 and change the imag(p1) ; and imag(p2) parameters to zero, while leaving the real(p1 and ; p2) parameters at zero. If this is done in equal increments, ; you will see the Mandelbrot set gradually take shape and rotate ; into its proper position, with Seahorse Valley at the center of ; the screen. It has been Seahorse Valley we have been investiga- ; ting all along. ; ; This magnification of the Mandelbrot aspect as the Julia ; orientation is approached is one of the most puzzling things in ; the Julibrot. I am reasonably certain of what is happening ; here, but a visualization is totally beyond me. In fact, I ; cannot even come close. All I can do is sit back and say ; "That's the Way It Is", which is the name I gave the image. The ; rating of a 5, when adjusted for a slow render time of almost an ; hour, gives an overall value of 8.5. ; ; The hour wait for the parameter file to run may be cut drastic- ; ally by visiting Paul's FOTD web site at: ; ; ; ; and downloading the completed image from there. ; ; A very pleasant Friday here at Fractal Central made for very ; happy cats. The temperature reached only 52F 11C, but the wind ; was light and the sun, which is just now clearing the holly ; trees in the afternoons, was warm, making the cats' time in the ; yard very pleasant. At the end of the day no treat was needed. ; ; For me, the work is heavier than usual for a Saturday. But it ; is nothing that cannot be finished in time to find a fractal. ; Until next FOTD, take care, and do fractals exist on the planet ; Pluto? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ ThatsThe_Way_It_Is { ; time=0:58:58.38--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=-4.44089e-016/3.33067e-016/0.8503401 params=89.9/90/89.9/90/-0.75/0/0/0 float=y maxiter=1000000 inside=255 logmap=yes periodicity=0 colors=000A0EB0GC0ID0KE4MD7OCAQCDSBGUBIWALY9O_9Ra8\ Uc8We7Zg6ai6dk5gm5in7km9lmAmmComDpmFqmGrm8oj9lhAii\ AfdBc_C`VCYRFVQISPLPPOMORJNYINRJgZKmhIjiHgjFdkEalD\ ZmBWnATo8Qp7Nq6Kp7Lp8Mp8Mp9NpANpAOpBOpCPpCQpDQpERp\ ERpFSpFSgIW_L_SOcKRgCUjEWiGXhIZgK_fM`eNbePcdRdcTfb\ VgaWhaYj`_k_amZcnYeoXfqXhrWjsVluUnvTowTmsSkpSjmRhj\ RggQedQcaQbZP`VP_SOYPOWMOVJNTGNSDMQAMP7MNHOLZQJcRH\ hTGiUIgWKeXLcYNaZO_`QYaRWbTUcVSdWQfYOgZMh`KiaKkcKl\ eKmfKnhKoiKqkJrlOsnRtoUuoXvo_vpbwpewphwqkxqnxqqyrt\ yrwzryzrwznuzjrzgozcmz`kzXizUgzQeyNcyJaxG_xHYwIWuI\ UsJSqJQoKOmKMkLKiLIgMHeMIcNKaNL_ONYOOWPQUPRSQQQRPO\ SOMTOKUNLVMLWLMXLMYKMZJN_IN`INaHObGOcFOcFOTEFIE7KH\ 8LJ9MMANOBORCPTDQVERYFS_GTbGUdHVgIWiJXkKYnLZpM_sN`\ uOawOdpRfiUhcXkX_mRboKerEht7kv1mt3nr4np5nn6nl8nj9o\ hAofBodDobEo`FoZGpXHpVJpTKpRLpPMqNOqLPqJQqHRqGSqIV\ kKXeM__NaUPdORfITiCUk6zl7 } 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================================== ;