FOTD -- June 05, 2003 (Rating 5) Fractal visionaries and enthusiasts: In yesterday's FOTD I wrote that I had once found a midget in the Z^(1.04)+C fractal. The graph of Z^1.04 is nearly a straight line, and since linear functions do not make fractals, it should not be expected to create a fractal. But in today's image, we wander far from the principal image, and at the remote level 100 turns up the logarithmic spiral, Z^(1.04)+C produces an interesting parent fractal -- a sprawling oversized bay with much chaos on the southern shoreline and a smaller amount of chaos on the northern shoreline. Today's image is a scene in the chaos along the northern shore- line of the parent. I have named the image "Low-Low Textures", since the exponent of Z is so small and the image consists of nothing more than a simple texture, with the elements endlessly repeated at smaller scales. Yes, I once did find a real midget that did not vanish when the maxiter was increased in one of the Z^(1.04)+C Mandel fractals. I have no idea where I found it. There could be an infinity of midgets in today's image, in fact there certainly are, but in the range of 1.04 they are so tiny and buried so deeply, with no hint of symmetry around them, that they are virtually impossible to find. I rated today's image at a perfectly average 5. If I had actually found one of those impossible-to-find midgets, I might have rated the image a 6. The render time on my worn-out fractal machine is 1/100 second less than 6 minutes. It will be faster on more vigorous units. The fastest way of all to see the texture in today's image is to download the completed GIF image file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rain continued through the day here at Fractal Central on Wednesday. The temperature hovered at 57F 14C. The two fractal cats had no time at all in the great outdoors, and as a result, were unhappy cats. A treat of tuna in the evening made them less unhappy, but fish is no substitute for a trip to a great place. The feline duo ended the day in a mood of resignation. I finished yesterday's work on time, and hope to do the same today. The next fractal will arrive in 24 hours. Until then, take care, and hidden jewels are sometimes found in the lowly places. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Low-Low_Textures { ; time=0:05:59.99--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-6.563247556907927/+1.425281219594758/2\ 66.6667/1/-5/9.7999386383662568e-013 params=1.04/0\ /100/1000 float=y maxiter=600 inside=255 logmap=116 symmetry=none periodicity=10 colors=000LJWMKXMLYMNYNOZNP_NQ`OSaOTbOUbPVcPXdPYeQ\ ZfQ`gQagRbhRciRejSfkSglShlTjmTknTloUmpUoqUpqVqrVrs\ VttWuuWvvWwvVvuVuuVutVttVstVssVrsUqsUqrUprUprUoqUn\ qUnqTmpTlpTlpTkoTjoTjoTinTinShnSgmSgmSfmSelSelSdkR\ ckRckRbjRbjRajR`iR`iR_iQZhQZhQYhQXgQXgQWgQWfPVfPUf\ PUePTePSePSdPRdOSePRdPRdQRdQQdRQdRQdSPcSPcSPcTOcTO\ cUOcUNbVNbVNbVNbWMbWMbXMbXLaYLaYLaYKaZKaZKa_J`_J``\ J``J``I`aI`aI`bH_bH_cH_cG_cG_dG_dFZeFZeFZfEZfEZfEZ\ gEZgDYhDYhDYiCYiCYiCYjBXjBXkBXkAXlAXlAXj9TlAXmA`oB\ cpBgqCksCntDovCpuDquDruDsuDttDutDvtDwtExsEysEzsEzs\ EzrEzrEzrFzrFzrFzqFzqFzqFzqFzpGzpGzpGzpGzoGzoGzoGz\ oHznHznHznHznHznHzmHzmIzmIzmIzlIzlIzlIzlIzkJzkJzkJ\ zkJzjJzjJzjJzjKzjKziKziKziKziKzhKzhLzhLzhLzgLzgLzg\ LzgLziKzgLzfLzeLzdLzcLzbLzaMz`Mz_MzZMzYMzXMzWNzVNz\ UNzTNzRNzQNzPNzOOzNOzMOzLOzKOzJOzIPzHPzGPzFPzEPzI7\ zJ9zJAzJBzKDzKEzKFzLGzLIz } 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==================================