; Date: Wed, 4 Jun 2003 10:03:12 EDT ; From: JimMuth@aol.com ; Subject: [Fractint] FOTD 04-06-03 (All Cracked-up [7]) ; Id: <16b.1f73cf60.2c0f5620@aol.com> ; --------- ; ; FOTD -- June 04, 2003 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; I have named today's unusually somber excursion into the land of ; fractal discontinuity "All Cracked-up", though it really gives ; no impression of being unusually discontinuous. The outstanding ; feature is the preponderance of deep blues, with only a few ; spots of brilliant relief from the overall depressed mood. ; (Maybe it's mimicking the fractal cats.) ; ; In keeping with the unintentional theme of the month, today's ; image is once again part of one of the infinity of fractals ; created by the simple formula Z^(1.5)+C. This time it is the ; fractal found 12 turns up the complex logarithmic spiral, which ; itself is a total abstraction. ; ; In low-order fractals such as today's, as the exponent of Z ; drops ever farther below the value of 2, the midgets become ever ; more difficult to find. When the exponent is 1.5, the midgets ; are rather difficult to track down, though it is still reason- ; ably simple to do. In fact, the task of finding midgets is ; doable down to an exponent of 1.2. Below that value, finding ; them is a matter of luck. ; ; The lowest-order midget I have yet found is one with an exponent ; of something like 1.04. In this range, midgets are nothing more ; than irregular, circular holes, with no bays and no organized ; patterns surrounding them, though the parent fractals are filled ; with large fields of interesting and discontinuous chaos. ; ; Today's image has been rated by me at a 7. Actually, the rating ; of 7 is true only in a dimly-lit room. In bright light it rates ; only a 5 or 6. ; ; The render-time from the attached parameter file is a reasonable ; 6 minutes. By downloading the completed GIF image from one of ; the FOTD web sites, the time can be made even more reasonable. ; The FOTD web sites can be found at: ; ; ; ; and at: ; ; ; ; The rains set in on schedule Tuesday afternoon here at Fractal ; Central. The temperature reached 63F 17C. The cats' moods ; deteriorated as expected, and the customary treat of tuna only ; partially restored their good spirits. The rain, which is still ; falling this morning, will likely continue intermittently into ; tonight. I feel sorry for the sulky duo. ; ; I've got my own problems to sulk about. Customers who want more ; material on a single page than can possibly fit there are a real ; nuisance. But I'll work it out. Until next cracked FOTD, take ; care, and where do fractals end? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ All_Cracked-up { ; time=0:06:44.25--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.69857471108285760/-0.230797030040254\ 00/1.203615e+009/1/42.5/-6.40805482036294061e-006 params=1.5/0/12/0 float=y maxiter=1600 inside=0 logmap=120 periodicity=10 colors=00049F48Q47L47G03C34G65J96NC6QE7TH8PK8_N9cC\ AfJAaOJaLKbIKcFKdCKe8Kf4Hg0Ig3Lh6Nj9OmCQpESsHUvKWy\ NYzQ`zSczZCidEZpGPkOMzWJmcGzrDbXTSJhH6wG4pF3jF2dE1\ ZE0TF3RF6QG8PGBOHENHGMIKLIPJJUIJZHKcGKhFLmELmDLmCE\ mH7hM0cQ5ZW9U`EPfIQkMWqR`vVfzZkz`jzajzbjzcizdizeiy\ fixghvhhuihtjhsifoiekicgibci``i_XiYTiXPiWMmYNpZNt_\ Ow`OuYRtWUsTXqR_pPboMemKhlHkkFnjDqeFjaHdYIYTKSPMLL\ NFHYPDhY9sfgGZeI`dJabKbaMc`NdZOeYPfWRgVShUTiSUjRWk\ PXlOYmNZnMXkLVhKTeJRbJQ_KUYLXXM`WNcVOgUPjSQnRRqQSu\ PSxOAanDYkGViJSgMPePLbSI`VFZYCXZGZ_J``MaaPcbTdcWfd\ ZgeaifejghlhkminoiqpkoqmlsnitpfvrdwsayuZzvXzwUwwRs\ wPowMkwKhwHdxF`xCXxAUx7Qx5Mx2Ix0Fw2Gx4Gy6Gz7Gz9GzB\ GzCHzEHzGHzHHzJHzLHzMHzMIzMIzMJzMJzMKzMKzMLzMLzMLz\ MMzMMzMNzMNzMOzMOzMOzLNzLMzKMzKLzJKzJKzIJzIIzHIzHH\ zHHzGFzFEzEDzDCzCBzBAzA9zBDzCHzDLzEPzESzFWzWaz_azb\ azRpzFzzExzDszCnzBizBdzA_ } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|