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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's parent fractal came about when I combined 0.1 part of Z^(10.5) with 1 part of Z^(1.05) and added straight C. It reminds me of a Mandelbrot set with a clumsily trimmed peacock's tail. The head of the set faces east-northeast, while the peacock tail extends out from the East Valley area toward the west-southwest. Today's scene is located in the peacock tail. I almost gave today's image a name. But at the last minute I decided it had been given too little effort to be worth naming. The coloring is responsible for almost the entire effect of the image. Since I did put a little extra effort into the coloring, I did give the image a rating. I rated it at a 6. The calculation time of 1-1/2 minutes is pleasingly brief. The time required to view the image on the FOTD web site at: In a day or so, I will include an article I am writing, telling how I pick good parameters for the MandelbrotMix4 formula, which automatically initializes Z to a critical value of the expresion being iterated. A critical value of a function is a point where the rate of change of the function is zero. When an expression is iterated with Z initialized to a critical point, the resulting fractal is most likely to contain intact midget Mandelbrot sets. The critical point of the formula of the classic Mandelbrot set, Z2+C, is zero, but this is not true for most formulas that contain more than one exponent of Z, such as those calculated by the MandelbrotMix4 formula. Lots of clouds obscured the sun here at Fractal Central on Monday, but the temperature reached a very mild 59F 15C. The fractal cats ignored the weather. They were too busy chasing each other up and down the hallway. Nicholas, the big clumsy one, got a bit out of control when he leaped onto a table and knocked over a lamp. Luckily the lamp was not harmed and Nico escaped with only a warning. Cassie, the small, delicate and very agile lady, watched all this with amusement. My day was about average. Unless something goes wrong, tomorrow will be the same. The next FOTD will appear in 24 hours. Until then, take care, and surround yourself with the fractal light. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
FOTD_for_Mar_27_07 { ; time=0:01:28.05--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident logmap=45
center-mag=-0.28037047337586200/-0.033742345705927\
44/1.055854e+007/1/-123.5/-9.13899942181495284e-008
params=0.1/10.5/1/1.05/0/0 inside=0 periodicity=10
float=y maxiter=300
colors=000AAUAAKAAUAAKAAUAAKAAUAAKAAUAAKAAUAAKm00h\
09c0BZ00U00zzmzmLzzmzm0zzmzm0_imHU02D0DJ0PP2aW6na9\
zeBaeJDzR0e_0ee0Yl0Rr4LyyzzR9zc4zn0zRBr8OR0a2zy00Y\
00H0040000000zlpyizyizWz0Ou2FiH8_Y0Pn0Fz08zwz0rz0p\
zFlwUiniggyzezzczzcawcFgc0Wc0JP08B000600F00P00Y00c\
2Di9PpHcwPpz0Up09e02c00a20_90_Pzp0Hn00n00n00n00n02\
n09n0Fn0On0Un0Wi0Wg0Yc0Ya0YY0_W2_R2_P4WU6UY8Ra9PcB\
OgDLlFJpHHrJWnLilOyiPzgRzeLzcHzaDzaBzc9ze8ze6zg6zg\
FznPzu_zzizzuzzazuJze2zR4zP6zO8zL9zJBzHDzFFzFOzJUz\
L_zOUzYPzeJznFzy9zz6zz0zz0zz0zz4zrLzcazPUzJLzDDz86\
z20z00z90zO0zc0zr0zz0zzDzzRzweziuz_uzauzeuzguzluzn\
uzpuzuuzwuzyizn_zcPzWFzL8zD0z40z00z00z00z00z00z00z\
00z00z00z00z04z08z0Dz0Hz0Dz4Bz69z88zB4zD2zF0zJ0zL0\
zO0zR0zU0zW0zY0z_0za4zc6ze9zgDziHzlJznOzpRzrWzuYzw\
WzrUzpUzlRziRzePzcOz_OzYLzULzRYzJgzBrz4zz0yz0uz0pz\
0nz0iz0ez0az0_z0Wz0Rz0Oz0 }
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 PARAMETER FILE=========================================
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times.
