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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> 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 20.0 PAR-FORMULA 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|<a } END 20.0 PAR-FORMULA FILE==================================