FOTD -- October 12, 2004 (Rating 6) Fractal visionaries and enthusiasts: To get a fair assessment of the many formulas in Fractint, it would be necessary to spend at least a month with each one, and not the mere hour or so that I am now spending. But even an hour can give a basic idea of what a formula has to offer, and besides, if I were to spend a month with each formula, it would be quite a few years before I finished the Fractint tour. Today's image takes us to the complexnewton formula. This formula works the same as the complexbasin formula that created yesterday's image, but instead of coloring the points according to which root they converge on, today's formula colors the points according to how many iterations it takes for the points to reach the root. Since we are searching for an imaginary root in today's image, we find an infinity of complex solutions waiting for us, arranged in a truly fractal pattern. Regardless of how deep we search, there are always an infinity of similar smaller basins and their roots ahead of us. Since the process is unending and the detail appears to change little, I stopped my search at a relatively shallow depth when I found today's scene. Actually, there is nothing unusual about today's scene. With small variations, the entire parent fractal, which is infinite in size, looks the same as the tiny part visible in today's image. This parent very graphically displays the infinite multi-dimensional spiral that results because of the multi-valued functions used in the calculation. When the time arrived to give my latest creation a name, I studied the image for nearly 10 minutes. Then, for some reason, I started imagining lobsters in the image. I named the picture "Vision of Lobsters". Thanks to its brilliant coloring, the image is rated higher than the recent ones. I decided on a rating of 6, which the render time of 1 minute and 23 seconds raises to an absolute value of a respectable 429. Skipping over the diffusion fractal type, which draws fractal trees, and the dynamic type, which draws diamonds, tomorrow's image will explore the 'escher' fractal, which does strange things with Julia sets. Exactly how strange these things are will have to wait until tomorrow to be determined. Today's image may be seen by running the included parameter file or by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday was slightly breezy and chilly here at Fractal Central. The temperature never rose above 62F 17C, but the duo of fractal cats braved the harsh outdoors for all of 1/2 hour. I braved the harshness by sitting in front of my fractal-dedicated computer and seeing what I could wring out of the complexnewton formula. Today is starting less harsh; I expect more bravery from the cats. The next FOTD will appear in 24 hours. Until then, take care, and when life gets harsh, soothe yourself with a fractal. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Vision_of_Lobsters { ; time=0:01:23.92--SF5 on a P200 reset=2003 type=complexnewton center-mag=+0.794221\ 4425060987/+0.02949640821997954/550.0325/1/-15/1.3\ 616607841e-012 params=0/-10/1/0 float=y maxiter=500 bailout=9 inside=0 logmap=12 periodicity=0 passes=1 colors=000Qp_Om_NjYJgXIdVGaVEZTDWR9TQ8QQ6NO4LN2HL0\ CL08J03I00G00I00G00G40G91GG1GL2GQ2GX4Ea6Eg6El8Es8E\ x9Ez4Dz9EzDGzGGzJIzNJzQJzTLzXNz_NzbOzfQzhQziQzKqzQ\ lzRizVfzXbz__zaXzdTzfQziNzkJznEzpBzs8zt4zx1zz0zz0z\ z0zz0zz0zz0zz0zz4zzGzxRztbzsnzslztkztgzwfzwdzxazx_\ zzYzzXzzTzzRzzQzzNzzLzzJzzIzzEzzDzzBzz8zz6zz4zz2zz\ 0zz0zz0zz0zz0zz0zz1zz4zz8zzBzzEzzIzzJzzNzzQwzTtzXq\ z_nzbkzfhziexkgxnkwqnwtqtxstzwszzszzqzzqzzszxszwtz\ stwqwsnwpkxkixgfzddzapdLzJ4z00z00z40z80zD0zG0zL0zO\ 0zT0zY0za0zf0zi0zn0zl0zq0zw0tz0lz0fz0Yz0Rz0Tz0Tz0T\ z0Vz0Vz0Vz0Vz0Xz0Xz0Xz0Xz0Yz0Yz1Yz2Yz4_z4_z6_z8_z9\ azBazBazDazEbxGbwIbwIdtJdtLdsNdsOfqOfqQfpRfpTgnVgn\ VglXglYik_ikaiiaiibkgdkgfkfgkfgldflbdnabn_apYapY_q\ XYqVXsTXsRVtQTtQRwOQwNQxLOxJNzILzILzGJzEIzDGzBEz9E\ z9Dz8Bz69z49z28z16z14z02z02z01z00z00z00zQ0xt0ts0sq\ 2qp6pp8lnBklEYxdXtdTqbRpa } END PARAMETER FILE=========================================