FOTD -- January 28, 2004 (Rating 8) Fractal visionaries and enthusiasts: Unless I am mistaken, today's FOTD is the third consecutive one that rates an 8. Combined with the render time of 19 minutes, its overall value is 41. This unexpected spate of excellence might have been equalled sometime in the past, but at the moment, I cannot recall when. But how did this excellence come about? Surely the extra time available for fractal exploration, due to the bad weather and resulting lack of work, is largely responsible. When I saw the golden ratio mentioned on the list, having nothing else to do, I was inspired to venture into the fractals that this mysterious number can produce. Turning to the MandelbrotMix4 formula, I checked the fractal that results when 0.8 parts of Z^(1.618) are subtracted from 0.8 parts of Z^(-1.618) and (1/C) is added. This fractal is an oversized thing consisting of three main Mandeloids, the largest of which barely appears in the southwest corner of the default screen. In today's scene I ignored this giant Mandeloid, which is mostly off the screen, and turned instead to the larger of the two Mandeloids that fit entirely onto the screen. This Mandeloid appears to be in what I call a condition of stress, as though it were ready to be cut off by a too-small escape radius. But stressed as it might be, the midget still has some interesting areas to check. The area I chose is the interior of the west branch of the valley leading to the large southern bud of this midget. Hidden there, deep in a cut-off area of interest, I found the midget that appears in today's image. And what a splendid midget it is. It is so splendid in fact that I named it "The Quintessential Midget", a title that is too long to fit into the allotted space in the parameter file. Actually, the midget looks as though it could use a few more iterations. This could easily be done, but if I raised the maxiter, it would mess up the color palette, which is what really makes the image. The render time of 19 minutes is a small price to pay for such a fine example of a midget. And there is even better news -- the completed GIF image is available for download on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Freezing drizzle prevailed all day Tuesday here at Fractal Central, making the area roads an ice-skating rink. The drizzle did not stop until it was replaced by heavy snow around sunset. With a temperature of 25F -4C, the day was a true winter wonder- land. Unfortunately, the fractal cats do not enjoy wonderlands, and passed the day indoors by the heat. I have lost track of the snow depth this morning. It appears to be around 1 foot in the U.S. measuring system, or 30cm in the rest of the world. Whatever the exact amount of snow, the dynamic duo will have another indoor day. For me, the work appears to have come to a halt, probably because everyone is snowed in. This means a good opportunity to find more great fractals. Any success I might have in Fractal Land will appear as tomorrow's FOTD. Until then, take care, and keep those fractals iterating. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ QuintesentialMidgt { ; time=0:00:00.00--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.39979361592270500/-0.608017365655577\ 00/4795150/1/-75/-1.8414457056414868e-008 params=-0.8/1.618034/0.8/-1.618034/0/0 float=y maxiter=2400 inside=0 logmap=305 periodicity=10 colors=000HEZJEVLERMENRCTVBY_9bc8gh6ll5qj6sh7tf8ud\ 8vTIoHRi5_c4`a4a_4bY4bX3cV3dT3eR3eQFdZQdg`dodephep\ keqoeqreqUmaSgdQbgPYjNTmLOpKJsIEvH9xLBwPDwTFwXHw`I\ wkBmv4duB_tHWtNSsTNrZJrdFnaLk_RgYXdWb`UhYSnUQtROzT\ LxUJvVGtWErYCpZ9n_7l`5kD7y9Bq6Fi3Ia4Oe5Th6Yl7bo6Xi\ 5Rc4LY3FS29MfspiodllToiIq`FrSCsJ9tA6u23t45s67s79r9\ BrADqCFqDHpQJzzzzzmzwMxgGsUHn9Ii8Jd8J_7KV7LQ6ML6MK\ INKTOKdPKoPK_WKKbK5hzPkrabjmUcyMWvSOtXGrb8pg0nlAqq\ KtvUwzUwzUwzUwzUwzUwzDP6W9IG49icjYUZNKNBABDqoftncb\ RaM3TK4LJ5CH64G7HQJUZVfgepTgzEhjFlWGpHHt2HxQnkYsPd\ w2J7DRc1DK0gXnC5a9gLxmGcXAKG5H`yBOd5CKdBrF5LfzMWeG\ LSBAE5cu7Uf5KT3N4VH5ZB5a56e06h0IW0UJ6QGBNEGKBMH9RE\ 6WB4YH7_M9aRCcWEe`HfeJidPkcUmb_oadr`it_ovZtxYyuZwr\ ZvoZum_tj_sg_re_qZ`iTaaNaUTeVYhVckVhnVkqUnsWqvYtx_\ wzaxzcyzezzgzzizzkzzmzzozzqzzszzuzzvzzwzzxzzyzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================