FOTD -- April 18, 2004 (Rating 7) Fractal visionaries and enthusiasts: Take (1/Z), mix it with 1/2 as much Z^(-2), and add (1/C). What do you get? Why, a fractal of course -- an oversized fractal that is too large to fit on the default screen and needs to be shrunk by an outzoom before it becomes completely visible. This fractal has X-axis symmetry, but only because the exponents of Z are whole numbers. Changing (1/Z) to Z^(-1.1) or Z^(-2) to Z^(-2.1) gives a pair of entirely new fractals with no symmetry. This parent fractal is far richer in detail that the classic Mandelbrot set. The detail might not be any more varied, but it covers a far larger area. The fractal has an interesting area around +7 on the real axis, where two graceful arcs of delicate filaments come together. Today's scene is located in one of these arcs, very near the point where it touches the X-axis. I have colored the image to resemble something like a brilliant star blazing away in empty space, and named it "Fractal Splendor". I seem to remember a somewhat similar FOTD image from several years past, but if today's image is a near-repeat, I will consider it simply a variation on a splendid theme. I rated today's image at a 7, mostly because of the extra effort I put into the coloring. The render time of 11 minutes gives the image an overall value of 59. As always, the image may be seen most conveniently by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday was as close to being a perfect day as we have come in quite a few months here at Fractal Central. Warm sun, light winds and a temperature of 84F 29C gave the fractal cats all they could ask for. If they had been 10 years younger, they would have romped all afternoon. But being 14-year-old cats, they slept in the shade of the holly trees most all afternoon, and romped, (if what they did can be called romping), only a few minutes. Today is starting just like yesterday. I assume the cats will have an equal day. As for me, I'll put off the grass trimming one more day, and take it easy. The work is light and I should have lots of time to get it done on Monday. The next FOTD will appear in 24 hours. Until then, take care, and try to prove that fractals are not real without defining reality. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Splendor { ; time=0:11:55.35--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+7.02311504952539200/+0.000296216423795\ 89/7.833267e+008/1/-142.5/0.00233171123971526173 params=1/-1/0.5/-2/0/0 float=y maxiter=2000 inside=0 logmap=248 periodicity=10 colors=0007LK7LK7LK7LK7LL7LL6LL6KM6KM6KM6KN6KN6KN6\ KN6JO6JO6JO6JP5JP5JP5JP5IQ5IQ5IQ5IR5IR5IR5HS5HS5HS\ 4HS4HT4HT4HT4GU4GU4GU4GU4GV4GV4GV4FW3FW3FW3FX3FX3F\ X3FX3EY3EY3EY3EZ3EZ3EZ3EZ4F_4G_5H`5I`6Ia6Ja7Kb7Lb8\ Lc8Mc9Nd9OdAOeAPeBQeBRfCSfCSgDTgDUhEVhEViFWiFXjGYj\ GYkHZkH_lI`lI`lIamJbmJcnKdnLeoMfoNgpOhpPiqQjqRkrSl\ rTmsUnsVosWptXqtYruZsu_tv`uvauwbvwcvxdwxewyfxygxzh\ yziyzjzzkzzlzzmzznzzmzzlzzkzzjzzizzhzzgyzfxzewzdvz\ cuzbuzatz`tz_szZszYrzXrzWqzVqzUpzTpzSpzRozQozPozOn\ zNnzMnzLmzKmzJmzIlzHlzGlzGkzGkzFjzFjzEjzEizEizDizD\ izChzChzChzBgzBgzBgzAgzAfz9fz9fz9ez8ez8ez7fz8ez8ez\ 8dz9dz9cz9cz9bzAbzAazAazB`zB`zB_zBZzCZzDZzEZzFZzG_\ zH`zIazJbzKczLczMdzNdzOdzPezQezRezSfzTfzUgzVgzWgzX\ hzYhzZhz_iz_iz_izZjzZjzZkzYkzYkzXlzXlzXlzWmzWmzVnz\ VnzVnzUozUozTozTpzTpzSpzSqzRqzRrzRrzQrzQszPszPszPt\ zOtzOuzNuzNuzNvzMvzMvzLwz } 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==================================