; Date: Tue, 30 Aug 2005 12:01:40 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 30-08-05 (Aching Mandeloid [5]) ; Id: <1.5.4.16.20050830120401.38778450@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; 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========================================= ; ;