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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image exists in the fractal that results when the formula Z^(2.003)+C is iterated 300 levels up the logarithmic ladder. The parent fractal at first looks like a classic Mandelbrot set rotated 50 degrees, but closer examination reveals small but interesting changes along the negative X-axis, which cuts through the area of the period-5 radical on the southwest shoreline of the main bay of the M-set. BTW, this formula is the one that holds the curious Julia rectangle that I return to every so often. If real(p2) is set to PI, which is the true ground level of the logarithmic ladder, the rectangle will appear in its proper place. While yesterday's image showed an unusually smooth scene, the image for today shows an unusually busy scene. The picture is so busy in fact that I gave it neither a name nor a rating. The calculation time of just over 11 minutes could be shorter, but those who take the time to run the included parameter file will not be disappointed with the result. Those who are as busy as I am may save the time by going to the FOTD web site at: Monday dawned clear but quite cold here at Fractal Central, with a temperature of 14F -10C. Strong morning sun raised the temperature to 41F 5C by noon, when clouds moved in and halted the rise. Light snow set in at 3pm, but changed to rain by 5pm. The fractal cats were concerned with none of this. They were more interested in chasing each other up and down the hallway. My day was once again quite busy. This busy-ness is getting to be the standard situation, which leads me to wonder if it's time to start thinking of slowing down. If I do slow down, it will not be in the world of fractals. I cannot slow down with the fractals. My time is limited but fractals are infinite. And no matter how many fractals I find, I will still have seen zero percent of all that are possible. The next fractal will appear in 24 hours. Until then, take care, and if eternity is outside of time, will it be possible to see every possible fractal? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
FOTD_for_Mar_20_07 { ; time=0:11:13.67--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC2 passes=1
center-mag=-0.76196900466103390/-0.000129467755220\
64/1.914783e+011/1/82.5/-0.016408177 params=2.003/\
0/300/0 float=y maxiter=2500 inside=255 logmap=302
periodicity=10 mathtolerance=0.05/1
colors=000F6VE4UE3UD1VE2UF3TF4SG5RH6RH7QI8PI9OJAOK\
BNKCMLDLMELMFKNGJNHIOIIPJHPKGQLFRKGQLFQLFQLFPLFPMF\
PMFOMFOMFONFONFNNFNNFNNFMOFMOFMOFMOFLPFLPFLPFKPFKQ\
FKQFKQFJQEJQEJREIREIREIREHSEHSEHSEHSEGTEGTEGTEFTEF\
TEFUEFUEEUEEUEEVEDVEDVEDVEDVEDVEMQGWLIdGJeILeJMeLN\
fMOfOPfPQgRRgSTgUUgVVhXWhYXh_Yi`Zib_icajebjfcjhdji\
ekkhklmknrlovlqzvwzwzzzzzzzzzzzltqkqqkmrjjrigricsh\
`sgYsgUtfRtgNvfOtfOsfPrfPqfQpfQofRnfRmfSlfSkfTjfTh\
fTgfUffUefVdfVcfWbfWafX`fX_fYZfYYfYWfZVfZUf_Tf_Sf`\
Rf`QfaPfaOfbNfbMfbKfcJfcIfdHfdGfeFfeEffDffCfgBfgAf\
g9bgCegFggIljKqhLvgLofMheMacNVbNO_NNYOMWOLTPKSPJRP\
IQQHPQHNRIMRKMSMMSOMNQMJSNETNFUNFVNFXLGZKI_JM`IO`H\
QaIVaJV`KV_LU_MUZMUZMTZMTZLTZLTZLSZLSZLSZLRZLRYMRX\
NRWORVPPUQOTPOSOOSNNSMNSLNSKMSKMRKMQKLPKLOKLNKKMKK\
LKIKKGIKEGICEGACE8AC68A468246024002000000000000000\
0000000000000000000000zzz }
frm:MandelbrotBC2 { ; by several Fractint users
e=p1, a=imag(p2)+100, p=real(p2)+PI
q=2*PI*floor(p/(2*PI)), r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END PARAMETER FILE=========================================
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times.
