; Date: Mon, 31 Jan 2005 11:37:23 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 31-01-05 (The Beast Itself [6]) ; Id: <1.5.4.16.20050131113947.29cfc93a@pop.mindspring.com> ; --------- ; ; FOTD -- January 31, 2005 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; Today's FOTD is an image of a beast -- a fractal beast no less. ; The beast is a midget located in a spiral on the southern shore ; of the period-4 bud on the northeast shore of the main bay of ; the Mandelbrot set. It is a rather handsome midget, with well- ; defined spiral arms that are twisted to just the right degree, ; and many sub-spirals to add fractal excitement. ; ; The spirals resemble both elephant trunks and seahorse tails -- ; kind of a blending of the two. One would never imagine that an ; elephant and a seahorse would make a couple that could produce ; hybrid offspring, but in today's image they apparently have. ; ; I consider the midget a beast because it is an impostor. It is ; not the animal it first appears to be. Look carefully at the ; parameters and you will see that the value of Z has been initial- ; ized to the same value as C, and not to zero, as would be the ; case when calculating the true M-set. Also notice that the ; orientation of the slice has been double-rotated half way from ; the Mandelbrot direction toward the Julia direction. We are ; looking at a scene in what I call the shadow set -- a second ; Mandelbrot set with dimensions sqrt(2) times those of the true ; set. ; ; Since today's midget is actually a beastly impostor, there can ; be nothing wrong with distorting it. And why not? After all, ; the image is a slice of the Julibrot, which is a 4-dimensional ; thing that can be sliced in more directions than can be imag- ; ined, and some of these slices do quite unexpected things to the ; beastly midget. ; ; But we will leave the distortions and variations to the next few ; FOTD's. Today's image shows the beast as its undistorted self. ; I have therefore named the image "The Beast Itself". ; ; I took some extra time with the coloring, but such scenes have ; been pictured so many times that they have become hackneyed. As ; a result, I could rate the image no higher than a 6, which is ; still a little above average. How high, or low, the coming ; variations of today's scene will rate has yet to be determined. ; ; The render time of under three minutes is true on my fractal- ; dedicated machine, which is almost ten years old. The image ; will likely finish in under one minute on most present-day ; units. But some present-day units don't know what they are ; missing, and will choke on the VESA video modes used by Frac- ; tint. For the convenience of those with such handicapped units, ; the finished GIF image has been posted to the FOTD web site, ; from where it may be downloaded in a video mode all computers ; can display. The web site may be accessed at: ; ; ; ; Light snow continued into the early afternoon here at Fractal ; Central on Sunday, keeping the fractal cats confined to the ; porch. But fractal cats are known for their stoicism, and the ; duo took their confinement without complaint. Today is starting ; sunny and chilly, with a warming trend forecast for this after- ; noon. The cats should be happy. ; ; I have a moderate amount of work before me, which will bring ; happiness my way when it is behind me. Until next FOTD, when ; the true or false, take your choice, philosophy will resume, ; take care, and be wholly fractal. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= The_Beast_Itself { ; time=0:02:49.71--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 center-mag=0/0/719412.8\ /1/90/-1.23373533611470521e-014 params=45/0/45/0/\ 0.288136932805/0.482645405409/0.288136932805/0.482\ 645405409 float=y maxiter=5000 inside=0 logmap=288 periodicity=10 colors=000SYsSXrSWqSVpSUoSTnSSmSQlTOkUMjVKiWIhXGgY\ Ef_CeaAdcAceAbgAaiA`kC_mEZoGYqIXrKWsMTrOSqQRpSQpUP\ oWOnXNnYMmZLl_KlaJkcIjeHjgHkhGkgFlfEldDmbCm`BnZAnX\ 9kV8hT8eR8bP7_N7XL7UJ6RH6OF6LD5IB5FC5CC49D46D43D45\ E57F59G6AH6CI6EJ7FK7HL8JM8KN8MO9OP9QQARRATSAVTBWUB\ YVC_WC`XCaYEbZGbZHc_Jd`Kd`MeaNebPfbQgcSgdThdVheWif\ YjgZjh`kiakjclkdmlfmlgmmimminmjomjpmjqnjrojtpjuqjv\ rjwsjxtlxujwtivshurgtqftpdsocrmbqlapk`oj_oiYnhXmgW\ lfVkdUjcTjbRiaQh`Pg_OfZNfYMgXKgVJgUHhTGhREhQDiPBiN\ AiM8jK7jJ5jI4kG2kF1kE0gH1dJ1aM2ZO2WR3TT3QY4Na4Kf5U\ o5cs2mz5mz8mzBhtEcrHZqKUoNPnQLmTMkWNjZOiaPidQhgRhj\ SgmTgpShsTgrTfrTfqTeqUepUbpU_pUZoUUoVTnVTnVSnVSmVR\ mWRnWQoWQpWPqWPsXOuXOwXNxXNzXMzYMzYLzYLzYKzYKzVOzS\ SzQWzN_zLczPgzUkzZozcszhvzmuzmwzmvzmvzmuzmuzmtzmtz\ mszmszmrzmrzmrzmqzmqzmpzmpzmozmozmnzmnzmmzmmzmmzml\ zmlzmkzmkzmjzmjzmizmizmiz } 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========================================= ; ;