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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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 20.0 PAR-FORMULA 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 20.0 PAR-FORMULA FILE==================================