; Date: Fri, 06 Dec 2002 10:17:03 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 06-12-02 (Passion Flower [5]) ; Id: <1.5.4.16.20021206101916.29bff446@pop.mindspring.com> ; --------- ; FOTD -- December 06, 2002 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; Today's image catches one of those Mandelbrot midgets at an ; angle where it is most distorted. The actual midget can be seen ; by checking the M-set at the coordinates of (p4) of today's ; image. At the angle of today's slice, little is left of the ; hole, which once was the midget and now lies invisibly at the ; center of the image, or even of the basin itself, for that ; matter. ; ; At this angle, the basin appears to have split into two ; branches, though actually it is the angle of the slice that ; creates the split, cutting the single curved basin in two ; places. The surrounding areas of chaos, which somewhat resemble ; comets, are far better defined in the M-set. ; ; I named the picture "Passion Flower". At one time I thought I ; saw a flower blossom somewhere in the scene, though the bloom is ; now far less apparent. I rated the image at an average 5, which ; is all I could do for it. (The corresponding midget, which ; appears in the M-set, would rate a 6 or 7.) ; ; With a 3-1/2 minute render time, the parameter file is one way ; of viewing the scene. A more efficient way is to download the ; completed GIF image from Paul's web site at: ; ; ; ; or from Scott's site at: ; ; ; ; Today's image is a slice of the four-dimensional Julibrot. The ; Julibrot cannot be accurately considered an object, because ; objects are things that exist objectively in the objective ; world, and to our specialized senses at least, the objective ; world is three dimensional. ; ; I have spent many years trying to visualize a four-dimensional ; hyper-object, knowing all the while that my effort was futile. ; The greatest problem is that the surface boundary of a 4-D ; figure must be three-dimensional, and my imagination invariably ; produces flat two-dimensional bounding surfaces for all my ; mental figures. ; ; A 4-D hyper-object must have on its bounding outer surface as ; many dimensions as there are altogether in our space. On the ; 3-D surface of a 4-D planet, there would be six cardinal ; directions. Three parameters would be needed to fix a location, ; and two parameters would be necessary to define a direction. ; The horizon would not be a circle, but a sphere that totally ; surrounds and encloses a visitor from the third dimension, as ; the heavens surround the planet Earth. ; ; On such a world, the sunrise would first appear as a brightening ; concentrated in a particular area. Then a brilliant star-like ; dot would suddenly pop into existence at the brightest point, ; grow to the familiar blinding disk, then shrink again to a dot ; and vanish. At sunset the same thing would occur at another ; point of the field of view. ; ; At night, assuming perfect clarity of the atmosphere, the stars ; would appear as twinkling fireflies as they rose above and sank ; beneath the horizon, passing through the 3-D visitor's field of ; view. The view on a 4-D world would be interesting indeed -- ; provided, that is, that the visitor could find a way to shield ; his retinas from light from the side, and also a way to avoid ; crumpling into a wrinkled heap as a 2-D sheet of plastic wrap ; does in our 3-D world. ; ; It snowed at a moderate rate all day Thursday here at F.C., ; piling up 8in 20cm by the time it ended at 11pm. Combined with ; a temperature of 27F -3C, the conditions proved far too harsh ; for the intrepid duo, who passed the day alternating between ; the window and the radiator. All things considered, their moods ; were surprisingly cheery. ; ; Unable to get out yesterday, I passed the day getting ahead in ; the work. As a result, after clearing the sidewalk, I will have ; extra time this afternoon to devote to fractal hunting. Hope- ; fully, I'll find something worthwhile. Check back tomorrow to ; see whether I actually find it. Until then, take care, and ; fractals can and do make life interesting. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ Passion_Flower { ; time=0:03:35.04--SF5 on a P200 reset=2002 type=formula formulafile=julibrot.frm formulaname=SliceJB-new passes=1 center-mag=0/0/2.\ 632523e+010/0.006156/-8.21933390591836854/89.48120\ 55080059565 params=0.22/0.51/0.505/0.326/2/0/-0.15\ 40762385267798/1.030994820300086/-0.15407623852677\ 98/1.030994820300086 float=y maxiter=2500 inside=0 colors=000WIFXJGYKHZLHZMI_NJ`OJ`PKaQKbRLbSMcTMdUNd\ VOeWOfXPd`XeZTfXPgVLhUHiSDjQ9mR3jP6hN9eLBcKE`IGZGJ\ XEMUDOSBRP9TN7WJ2_L6YNAWPDURHSTKQVOOXRMZVL`ZJbaHde\ FfhDhlBjo9ls7ms6kqDimKgiRkkVmmWfeXbYW_YXYYYWYYUYZR\ Y_PY_NY`Laa9ceEcgJYaNRWSLQXEKd4Gb6F`8FZAFXCEVEETGE\ SIDQKDOMDMOCKQCISCHUBFWBDYBB_A9aA7cA3dD6gA9j7Cl4Fm\ 2Mk8SiEZfKecMeaOd`PcZQbYRaXS`VT_UUZTVYRWXQXWPYWN_V\ M`ULaTJbSIcRHdQFePEfODgNBhMAiM9jPIlSQmVToYWp_Zrbas\ ecuhevjguiiuhkshlrglpfmofmmenlenjdnicogcoebpdbpbaq\ a`q_`rZ_rX_rWaoXbmYckYdiZfgZgd_hb_i``kZ`lXamUbnSbp\ QcqOcrMdtJdvHewFixDly8lxBiwEfvHcuJ_sJWqJQoJPmJOkJN\ iJMgJLeJKcJJaJJ_JIYJHWJGUJFSJEQJDOJCMJBMBDLFCKJBKN\ AJR9IV8IZ7Ha6He5Gi4Fm3Fq2Eu1Cz0Ex1Fw2Gu3Ht4Ir5Jq6K\ o7Ln8Ml9NkAOiBPhCQgDReESdFTbGUaHV_IWZJXXKYWLZUM_TN\ _RL`SNaTPbUQcVSdWTeXVfYWgYYhZZi_`j`akaclbemcfndhod\ ipekqflrgnshotiqujrvktzmw } frm:SliceJB-new {; by John R. H. Goering, July 1999 pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1), b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), 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)+(p4), z=r+flip(s)+(p5): z=z^(p3)+c |z|<=9 } ; END PARAMETER FILE================================== ; ;