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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is more a curiosity than a work of art. The name "New Low Record" has nothing to do with the weather. It refers to the exponent of Z in today's fractal, 1.05, which is the new low record. I have never before found a midget in a Mandeloid of such a low order. And what do midgets in this range look like? As today's image shows, they look like little more than lopsided ovals centered in a splash of total but semi-orderly chaos. I chose a color palette with very narrow and sometimes clashing color bands to emphasize the confusion. The question might arise as to how I manage to find the midgets in such unpromising fractals as today's parent fractal. To see the difficulty, zoom out of today's image to a magnitude of 0.5 while keeping the same center coordinates, and see if any visible sign exists that a midget might lie at the center of the frame. Nothing is there but waves of chaos. But Fractint is very versatile, and has built into it a secret method of finding hard-to-find midgets. Take the hopeless outzoom with its waves of chaos, change the 'outside' option from 'iter' to 'fmod', with a proximity factor of 0.1, make sure the 'logmap' is off, and re-calculate the hopeless image. Surprise! The location of the hidden midget is now indicated by a bulls-eye. Simply continue zooming into the center of the bulls-eye until the midget is reached. The location of other hidden midgets lying nearby is also apparent. These 'fmod' bulls-eyes do not always lead to midgets, sometimes they lead to bottomless spirals, but they lead to midgets often enough to make the 'fmod' outside option one of the most useful. I must congratulate the one who thought of putting it into the program. The question arises of why I would want to find such chaotic midgets in such low-order Mandeloids. The reason is just for the fun of seeing how low I can go. My goal is to find a midget in a Mandeloid with an exponent of Z less than 1.01, but that might be impossible. I could rate today's image no higher than an average 5. It has no center of attraction and only a vague overall theme. The elements near the shoreline of the midget sub-divide so rapidly that they soon disintegrate into fractal sand. The render time of 13 minutes is a bit slow. But the image may be viewed in its completed form on the FOTD web site in almost no time. The FOTD web site may be found at: A partly cloudy and warmer day, with a temperature of 66F 19C, here at New Fractal Central on Sunday went un-noticed by the fractal cats, who spent most of the day staring and sniffing at the hole in the floor by the radiator pipe, waiting for the mouse to pop out again. Unfortunately for them, the mouse is now cat-wise, and is unlikely to show itself in such dangerous territory. When the evening treat time came, I wondered if the cat duo might have preferred mouseburgers. My day was as pleasant as things can be expected to be in this far from perfect world. The work is caught up, albeit temporarily, and the fractals are in no danger of running out. The next fractal will appear in 24 hours. Until then, take care, and the human eyes never see all that lies before us. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
New_Low_Record { ; time=0:13:06.91--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC2 center-mag=-0.2055129638\
737225/-5.1312228660223/6.741629e+007/1/-117.5/0
params=1.05/0/-37/10000 float=y periodicity=10
maxiter=10000 inside=0
colors=000Pr1Pp1Oo1Nm1Mk1Mj1Lh1Kg1Je1Jc1Ib1H`1GZ1G\
Y1FW1EV1DT0CR0CQ0BO0AM09L09J08H07G06E06D05B0490380\
360240130010bwb_r_XmXUiURdRO_OLWLIRIFNFCIC9D969634\
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25612i8Fg7Ef7Ed7Dc7Db6C`6C_6BZ6BX5BW5AKYeJYfIWdHUb\
GT`FRZEQXDOVCNTCLRBKPAIN9HL8FJ7DH6CF6AD59B47936724\
5133100011IR4Ty2Sw1Ru1Qt1 }
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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