FOTD -- January 26, 2004 (Rating 8) Fractal visionaries and enthusiasts: In the discussion of the "Whirling Devilish" fractal of two days ago I remarked about the straight edge cutting through the upper right portion of the image. I commented that some very unusual chaos lies in this area but that the exploration there is too slow to be practical. Well, for today's image I have turned impractical and wandered into the chaos along the straight-edge. Today's FOTD is what I found there. I have rarely seen an image with such contrasting parts, the dull reddish rocky lower part contrasting as starkly as it does with the ethereal blue celestial spiral filling the upper part. The lower part of the picture reminds me of one of those mesas found in the southwest desert area of the U.S. The upper part reminds me of nothing other than a fractal spiral. Combining the two impressions, I named the image "Spiral Mesa". I feel that the rating of an 8 is justified, though the extreme slow- ness holds the overall value to a lowly 4. Perhaps the most incredible thing about the image is that it is produced by Z^1.003. The graph of this expression is basically a straight line, and linear expressions do not make fractals. It is only at very large values of Z that the slight curve in the graph becomes noticeable, which is why a maxiter of 20000 is necessary to reveal the chaos. An unfortunate effect of the high maxiter is the 3-hour render time. The wait can be eliminated however by downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I sent the image file to Paul several hours ago, so the image should be posted shortly after he receives this discussion. As a matter of interest, I made a 0.65-degree change in the rotation of the image since I sent it. This was done so that the border between sky and mesa would be level. To see a perfectly straight horizon, run the parameter file; to see the image without a wait of several hours, download it. The only difference is in the orientation, which is barely noticeable. Thickening clouds and cold temperatures prevailed all day here at Fractal Central on Sunday. The high temperature of 18F -8C and lack of sun kept all thoughts of outdoors from the minds of the fractal cats. They were quite content to lie by the heat source and occasionally ask for food. This morning we have 6in 15cm of fresh snow on the ground and a temperature of 17F -8C, which makes the outdoor conditions worse. The forecast is for freezing rain, sleet and more snow. I feel sorry for the duo. There is no reason to feel sorry for myself however. The work is caught up, leaving me little to do but sweep the powdery snow and explore the world of fractals. Until next time, take care, and don't forget to remember. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Spiral_Mesa { ; time=3:08:09.19--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.84105158773950410/-0.082216007167982\ 33/10307.65/1/-176.85/6.14521628028441569e-012 params=1.003/0/1040/1500 float=y maxiter=20000 inside=255 logmap=4824 periodicity=10 colors=000_00ODNQCMPBLT9JU8IV7HX5GY4FX2FZ3EZ4D_4D_\ 5C`6BW6BY7AZ8A_89a98bA8dA7eB7bC6hC5eD5kE4hF3lE4gR5\ lE6gT7kE8aD9kDAfDBkDCjQDjDEeOFjCG_CHiCIiRJiCKdULhU\ McBNhBOcBPhBQbCPgDPgPPgPOgQOgUObUOgUNbUNgUNgYNgUMg\ NMgNMYOMgPLgQLgRLYSLgTKgTKgUKgVKgWJhXJiYJg0EkYJa1N\ qYSdJWvY`wUexYddIcxdbyAayk`yo_yrZrnUkkQdhMYeIRbEK_\ ALZCMYEMYFNXHNWIOWKOVLPVNPUPQTQQTSRSTRSVSRWTQYTQ_U\ P`UPbVOcVNeWNfWMhXMjXLkYKmYKnZJpZJq`KpaLpbMpdNoeOo\ fPohQoiRnjRnlSnmTmnUmpVmqWmrXltYluZlvZltYmrYmqXmoX\ mmXmlWmjWmhWmgVmeVmdUmbUm`Um_TmYTmWTnVSnTSnRSnQRnO\ RnNQnLQnJQnIPnGPnEPnDOnBOnAOnEQpIRqJQtLSuMTvNVwOWx\ PXyRZzS_zTazUbzVczXezYgzZiz_kz`mzbozcpzdqzerzfszht\ ziuzjvzkwzlwzkwzjvziuzhtzgszfrzeqzdpzcozbnzamz`lz`\ kz_jzZizYgzXezWczVazU_zTYzSWzRUzQUzPUzQUzRUzSUzTUz\ UUzVUzWUzTUzQUzNVzLWzI_zFdzDhzAlz7pz5tzCuzIvzOwzVw\ z`xzfyznzzlyzjxzhwzfvzemz } 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==================================