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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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=========================================