FOTD -- October 07, 2002 (Rating 5) Fractal visionaries and enthusiasts: To produce today's fractal, I took Z^(-1.25) and subtracted Z^(-2.75) from it before adding 1/C. With the bailout radius set to 210, this formula draws a parent fractal with a spade- shaped bay whose point faces east. Though the bay is filled with various forms of fractal debris, little of interest lies in this debris. Today's scene is located just north of the eastern point of the parent fractal, where two lacy arms converge. When I saw the image, I was reminded of a monarch butterfly that I had noticed fluttering in the garden earlier in the day. I immediately named the picture "Monarch Butterfractal", and then rated the image an average 5. Like fractals, those butterflies have long been a puzzle to me. They appear every year in late summer and autumn, fluttering around the flowers, storing energy for their migration to the recently-discovered remote mountain valley in Mexico, where they spend the winter in a state of torpor. But how does a single butterfly survive a journey of nearly 5,000 kilometers? Not even considering the hazards along the way, the time needed to complete such a journey would far exceed the life span of a single butterfly. Perhaps the butterflies make the trip in the same manner humanity is supposed to explore interstellar space. The individuals who arrive at the destination are the remote descendants of those who set out on the journey. Or maybe the whole monarch migration story is as much a myth as the idea that humanity one day actually will reach the distant stars. Forgetting butterflies and space exploration, perhaps the best feature of today's image is its lightning speed. It renders in less than one minute on my tired old machine, even in single- pass mode. And as always, the completed image is available on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> And despite recent speculation on another list, Paul is quite alive and active. The fractal weather Sunday here at Fractal Central was crisp and fall-like, with deep blue skies and a temperature of 72F 22C. The cats enjoyed the day lazing all afternoon in the sun on the porch. Unfortunately, with the sun's angle growing lower every day, the holly trees are beginning to cast their shade onto the porch, and soon the cats will have no sun to bask in during the afternoons. Right now, I've got to get busy on a convention program which is a big rush. But then convention programs are usually rush jobs. Well, the best way I know to eliminate the rush is to get busy. Until next time in 24 hours, take care, and before a problem can be solved, it must be understood. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ MonarchButtrfractl { ; time=0:00:48.61--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=2.70058/0.0691111/58.96007/1/-120/-5.05\ 012698326368081e-014 params=1/-1.25/-1/-2.75/0/110 float=y maxiter=270 inside=0 logmap=11 periodicity=9 colors=000RIVNETJARF6PB2NPEWaQcn`kjV_fPOcKDkXAwi8z\ v6wo5rh4mb3hW2cP1ZJ1WE7e9Co4Hx0MNxrLupJrnHolFlkDii\ Bfg9ce7`d7_j7_o7Zu7Zz8Ts8Om8Jg9Da98W93QG4TM4VS4XY4\ _c4ai4ceNeaegZxi`vcauYbtSdrNeqHfpBgo6ilDkiJmfQncWh\ WabOgXGmS8rOGkKNeHUZDaTAhM6oG3vA7lLAbVDTdGJnJAxN9y\ R8yV7yY6yUEqRLjOScLZXIeQFlJCsCKt8St4_w00zs1zr2zq3z\ p3zo4zn5zm5zmBzeGzZMzRRzKIzM9zO1zQEzXRzbbzh4zU7zaA\ ziDzqGzxJzsLznNziPzdSzgUzjWzljzrxzwnzsdzoVzkLzgQza\ UzXYzSbzNfzIjzDnz8izJdzU`zccz`fzZizXkzVnzTqzRtzPvz\ NozcizslzhozYrzNuzCxz2pz3iz3bz4Wz4Pz4Iz5Bz54z5Az6F\ z6Kz6Pz6Uz6Zz6cz6hz6iz9jzCjzFkzIlzLlzOmzRmzTizSfzS\ czS`zSYzRVzRSzRPzRQzYQzdRzkRzrRzxTznUzdVzWHzg4zr6z\ i8z`AzSCzJEzAGz1Fz2Ez2Dz2Dz2mzqfzr_zsTzsMztFzu8zuG\ ztOzsWzsczrkzqszqvzsyztJzALzEMzINzMOzQQzURzYSzaTze\ dzQozBgzI`zPTzVMzaEzh7znMz``zNoz9jzBezCazDXzFTzGOz\ HKzIhzVizWjzXkzYkzYfz`VzX } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================