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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I must once again apologize for the lateness of the FOTD. My excuse is that the weather was very hot on Tuesday and I felt lazy. It's really no excuse, but it is the truth. The image that I found when I finally mustered the energy to search is a scene in a valley of the Z^sqrt(2)+C Mandeloid as it appears a meager 1/2 level up the complex logarithmic hyper-spiral. This formula is one of my favorites. It is not as rich as its square, the classic Mandelbrot set, but there is only one fractal that can be generated by the formula Z2+C, while the formula Z^sqrt(2)+C creates nearly an infinity of fractals, all different yet all strangely the same. I'll not try to describe the parent fractal, since it is so easily generated, but the image I found within it rather reminds me of a gala event, which inspired the name "A Jolly Scene". The rating of an average 5 says very little about the image. I did not put enough work into it to rate it any higher, and this type of image has been posted as the FOTD so many times that it has become hackneyed. The parameter file takes 9-1/2 minutes to run on the fast computer. On the slow machine it would take 45 minutes to finish. For convenience the parameter file has been calculated and posted on the FOTD web site at: With a temperature of 97F 36C and oppressive humidity here at Fractal Central, Tuesday was a day to be ignored. And indeed the fractal cats did ignore it. They concerned themselves with the chipmunks (I think there are two of them) that have been running around in the back yard grass. I concerned myself with work first and fractals second. The result speaks for itself in the parameter file. As always, the next in the series of FOTD fractals will appear in 24 hours. Until then, take care, and wait with bated but not abated breath. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
A_Jolly_Scene { ; time=0:09:29.97-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC2 passes=1 float=y inside=0
center-mag=-0.11710695179565920/+1.315337975141092\
00/6925.211/1/45/9.0035527644527491e-011 logmap=549
params=1.4142/0/0.5/0 maxiter=8000 periodicity=10
colors=000S8CQ9DOAELBFJCGGCHEDICEJ9FK7GL5GM7JO8MP9\
PRASSBVUDYVE`XFbYGe_Hh`TkbYnccrecufewhbxi_ujXqjXnj\
WjjVfjXcjY_j_Wk`TkaPkcLkdIkfEkgAkj8oh7kf6gd6cb5_`4\
W_4SY3OW2KU2GS1CR19Q1AP1AP1AO1AN1BN1BM1BL1BL1BK1CJ\
1CJ1CI1CI1CH1DG1DG1DF1DE1EE1ED1EC1EC1EB1FA1FA1F91F\
91FB3GD5HE6IG8JH9KJBLKCMMENNFOPHPQIQSKRTLSVNTWOUYQ\
VZRW`TX_EIaUXcijexxgtthqqjnmkkjliilghlfgldglcflael\
`dlZdlYclWblValTalS`mQ_mPZmNZmMYmKXmJWmHWmGVmEUmDT\
mBTmASm8Rq2Pm7RiBTeGVaKXYOZUT`RXbNadJefFihBnj7rl4v\
n6to8soAroCpoEopGnpIlpKkpMjqOhqQgqSfqUdrWcrYbr_`ra\
_scZteXwggzi`zkTwmStnRtlQskQsjQsiQshQsgQsfQseQsdQs\
cPsbPsaPs`PsZPsYPsXPsWPsVPsUOsTOsSOsROtQOuPOvOOwNO\
xOPyMQzLRzJRzISzHTzFUzEVzDWzBXzAYz9ZzA_zC`zEazGbzI\
czKdzMezOfzQgzShzUizWjzYkz_lzamzcmzemzgmzimzkmzmmz\
mmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmm\
zmmzmmzmmzmmzmmzmmzmmzmmz }
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.
