FOTD -- August 30, 2005 (Rating 5) Fractal visionaries and enthusiasts: The following paragraph is off-topic. Those who disdain OT stuff should skip to the next paragraph. Today started out great. When I opened my e-mailbox, I found that I have won not one but three lotteries that I have never entered. And there's a man in Nigeria who wants to give me 14-million dollars to invest for him in the U.S. I also discovered that my ebay account (I have no ebay account) has been suspended due to fradulent activity and that the Mindspring team (which no longer exists) needs me to confirm my billing information. ;-) A whole new industry is developing out there. It's called phishing, and there's still time to get in on the ground floor. ;-) Yes, I realize that we all get this kind of stuff, but now and then I like to have a little fun with it. Yesterday's 'Aching Tooth' image, which was created with the ParabolicMix3 formula, was not overwhelming, but the image was merely a side event. The main purpose of the ParabolicMix3 formula is to find critical points of the expressions entered into it. The formula did its job well, and determined that 0.6447424469 is one of the critical points of the expression 0.5*Z^(1.5)+0.5*Z^(-1.5)+0.5*Z^(2)+Z. I entered this expression as the parameters and the determined value as the starting point of Z in the MandelbrotMix3 formula to produce today's curious Mandelbrot set. Today's image is the entire fractal -- the parent fractal itself. The image was rendered with the outside set to the usual 'iter', producing equal-iteration bands. These bands are the same coloring method that was used in the fractal program that I used to create my first fractal nearly 20 years ago. The 'surface of a boiling liquid' effect is totally due to the generating expression. The Mandeloid is distorted by too small a period-2 bud and by having the other buds drawn toward the main bud. (This always happens when the main bud is smaller.) But the inner details are the same as in the classic Z^2+C M-set, with the bubbling iteration bands persisting all the way down. (At least it's not turtles. :-) ) I named today's fractal "Aching Mandeloid" because it is a part of the same Julibrot that held yesterday's 'Aching Tooth' image. The image is a slight improvement over yesterday's, which earns it a rating of an average 5 -- hardly earth-shattering but worth a peek. And the very fast render time of 13 seconds makes taking that peek an easy task. As always, those with handicapped or over-qualified machines may download the finished GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a high temperature of 86F, 30C, Monday was a bit too warm and humid for absolute perfection, but the fractal cats are stubborn, and despite the less-than-ideal conditions, they spent several hours in the yard. At one point I heard Tippy shout at something, but no disturbance was in sight. He was probably just quarreling with Thomas, as they sometimes do. The evening went smoothly, and they settled down without incident. My day was uneventful. Today is starting cloudy and damp, and with showers forecast, things do not look great for the duo. For me however, it looks like just another normal day coming up. The next FOTD will be coming up in 24 hours. The next burst of eye-opening and hard- hitting philosophy will also be coming up before long. Until 24 hours from now, take care, and as you become aware of the many fractals around you, stop to wonder where they come from. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Aching_Mandeloid { ; time=0:00:13.62--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident logmap=3 center-mag=-1.49125/0/4.191485 symmetry=xaxis params=0.5/1.5/0.5/-1.5/0.5/2/1/1/0.6447424469/0 float=y maxiter=260 inside=0 periodicity=10 colors=000onvifpcZkYReTJ`OBVJ3Qd7WjBXoEYcC_ZAaT8cO\ 6eJ4gE2c51ZU5ZUAaUFdUKgUNiUQlUToUWqUZkVafTd`RgWPjK\ Om8VpK`rWgtgmvsfxBsywhzvYzvNzvCzv2zvCzgMzTVzEHzH3z\ K8zNDzPIzRNzUSzWXzYaz_ZzbXzeVzhTzkRznQzmQzmQzmQzmQ\ zmQzmQzmVze_zZdzRizKmzDnzMozVpzcqzlrztszvKzXJz_Izb\ HzeHzhVzmhzquzuuz9mz1gz0bz0Xz0Sz0Mz0Hz0Cz0FzAHzJJz\ SMzaOzjQzsPzqOzpNzoSziXzcazZfzTkzNpzIuzCzz7VzV0zqA\ zpJzoTznazmkzltzk`z`IzRRzE_z1Zz4Zz7ZzAZzDZzGZzIVzF\ RzCMz9Iz6Ez3Az0DzBGzLIzVLzeOzoQzySzqUzjWzcYzXTzVOz\ UJzTEzS9zR4zQ0zP5zW9zaEzhIznMztxz4ozGgzS_zcSzoKzzM\ zoNzePzWQzMMzSJzYGzcCzi9zo6ztEzrMzpUznazlizjqzhyzf\ tzkpzpkzugzylzkpzYuzKyz7mzCazHQzMFzRvzlsznpzonzpqz\ mtzkwzhzzfqzihzl`znSzqKzsMznOzjQzeSzaUzYZzVczShzQb\ zcXzqRzkMzeGz`BzV6zQFzWOzaWzgdzmmzsuzxCzDIzFOzGUzI\ _zJezKkzMqzNwzOtzUqzZnzdkzihznfzhdzbczXazR_zLYzFXz\ 9UzDOzJIzKCzL6zM0zMSzfszz } 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 PARAMETER FILE=========================================