FOTD -- May 02, 2004 (Rating 3) Fractal visionaries and enthusiasts: Today's image is a second thought. When I first stumbled upon it, I noticed its flatness. Flat images such as today's often do quite well with the alternate rendering options, so I tried some of them. The 'decomp' feature worked very well with the image, so I used it for the rendering. I named the result "Fractal Cheating", and decided that it would be the FOTD for today. I chose this name because the picture said more about the features of the program than it said about the scene I had discovered. Then I decided that the full worth of the 'decomp' feature would not be apparent unless the 'decomp' version could be compared to the drabness of the original 'outside=iter' version. Today's image is this 'iter' version. It rates only a 3, but the incred- ibly short render time of 40 seconds results in an unexpected and unjustified overall value of 449. The 'decomp' version of today's scene, which will rate notably higher, will appear as tomorrow's FOTD. Actually, all the 'outside' options do better than the standard 'iter' rendering of today's image, which is basically flat and featureless, but the scene renders so fast that the viewers can try these for themselves. I named the version of the scene that appears as today's image "Fractal Patches". That's all it is -- a few flat patches of color. The flatness is why the scene renders so fast. There is no fine detail to calculate. The route I took to today's image is rather interesting. Using the MandelbrotMix3a formula, I entered 1 and 2 as the p1 parameters, which drew the classic Mandelbrot set. Then I added 0.075 part of Z^3. This moved the M-set a bit to the left but had no other effect on the screen image. Next I entered -8.888... as the real(p5) parameter, which determines the initial point of Z, and just happens to be a critical point of the formula. The result was a blank screen. Never put off by blank screens, I did an outzoom and discovered that the action had moved far to the left. I zoomed in on the area of interest and found a new M-set. Except for the oddly- shaped iteration bands, this set looked normal, but on the X-axis some distance to the right of the new set, I spotted a tiny dot. This dot proved to be a tiny disconnected M-set with even smaller M-sets surrounding it like satellites around a planet. And I found that these satellites are in turn surroun- ded by satellites of their own. Today's image is that of a satellite of a satellite. Its surroundings are so flat because of its extreme isolation. The image may be seen by running the included parameter file or by downloading it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A pleasant spring afternoon here at Fractal Central on Saturday brought out the best in the dynamic fractal cats. Lots of sun and a temperature of 79F 26C were just what they needed for a comfortable three-hour lounge in the yard. But today things look ominous. It is starting cloudy with heavy rain forecast. Heavy rain does not stop the fractals however, so the next one will appear in 24 hours, give or take an hour or two. Until then, take care, and search for answers to the mysteries of life. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Patches { ; time=0:00:39.99--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident center-mag=-22.97767772633961000/+0.06349061612053\ 014/3.426261e+008/1/-152/0.00023170776981063651 params=1/2/0.075/3/0/0/0/0/-8.88888888889/0 float=y maxiter=300 inside=0 logmap=34 periodicity=10 colors=000bEKWILPNMIRNCVNQ_ZbdiohtPW2RU5TT8VSAWRDY\ QF_PI`OKWVSSa_OhgKooGuwO0MT2OX4Q`6Se8UiAWmCYqEZ0BJ\ LDKeFLzHMwFLuELrDLpCLmAKk9Kh8Kf7Kg7KcmzzzVzzWzzWzy\ WzxXzwXzvXzuXztWysWxsVwrVvqVuqUtpUspUroTqnTpnTomSn\ mSmlSlkRkkRjjQijQhiQghPfhPegPdgOdfOceObeNbdNadNacM\ `dM`eL_eL_fLZfKZgKYgKYhJXhJWiJWiIVjIVjIUkHUkHTlHTl\ GSmGSmFRnFRnFQoEPoEPpEOpDOqDNqDNrCMrCMsCLsBLtBKtAK\ uAJuAIv9Iv9Hw9Hw8Gx8Gx8Fy7Fy7Ez7Ez6Dz6Dz6Cz7Cz7Cz7\ Cz8Cz8Cz8Cz8Cz9Cz9Cz9Bz9BzABzABzABzBBzBBzBBzBBzCBz\ CAzCAzCAzDAzDAzDAzDAzEAzEAzEAzF9zF9zF9zF9zG9zG9zG9\ zG9zH9zH9zH8zG9zH9zH9zHAzHAzHAzHAzHBzHBzHBzHCzHCzI\ CzICzIDzIDzIDzIDzIEzIEzIEzIFzIFzIFzJFzJGzJGzJGzJGz\ JHzJHzJHzJIzJIzJIzKIzKJzKJzKJzKKzKKzKKzKKzKLzKLzKL\ zKLzLMzLMzLMzLNzLNzLNzLNzLOzLOzLOzLNzMOzLOzLOzLPzL\ PzLPzLPzLQzLQzLQzLRzLRzLRzLRzLSzLSzLSzLTzLTzLTzLTz\ LUzLUzLUzLVzLVzLwzHpzIizJ } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================