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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: On Tuesday evening I wondered what would happen if the almost-Mandelbrot set were rotated 180 degrees, so that the main stem fell on the positive half of the real axis instead of the negative half. With the exponent of Z so close to the integer 2, I needed to go 3,141,585 levels up the hyperspiral before the fractal rotated a full 180 degrees. (I assume the proximity to the number PI is coincidental.) What I found at this cosmic level is little more than a mirror image of the ground-level figure. The main stem once again is infinitely divided, with the 'explosion in a rail yard' effect prominent. Instead of investigating the east valley of the largest midget, I checked the east valley of a sub-midget on the main stem of the large midget, and found a nest of sub-midgets arranged as though they were strung out like beads on a string. I named the image "Stringing Along", and rated it a 5, which is average. It might be worth a 6 or so, but I am starting to grow bored with the 'infinitely divided main stem' theme, and could give the image no higher a rating. The render time of 9-1/2 minutes on my 10-year-old machine is on the slow side, especially in a world moving at a hectic pace. But quick relief for latent impatience is on hand at the FOTD web site, which can be found at the URL: A cold, dreary, rainy day on Tuesday here at Fractal Central left the cats' moods on the surly side. Extra tuna made them feel somewhat better in the evening, but it could not make up for an entire day of forced confinement. Today is starting cloudy and cold, with rain scattered around the area. It could be as bad a day as yesterday. For me it's work first. The fractals come later. Until 24 hours have passed, take care, and where do prime numbers come from, if from anywhere? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Stringing_Along { ; time=0:09:38.86--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC2 passes=1
center-mag=+1.78357259738345500/+0.000006023651137\
31/1.04065e+008 params=2.000001/0/3141585/0 float=y
maxiter=5000 inside=0 logmap=228 periodicity=10
colors=0000000000000000000000000100200300400500500\
600600800801801901902A02A02A03B04B04C05C05E06E06F0\
9F0CE3GC8KBCPAHSAKUAMUAOUAQUASUAUUAWUAYUA_UAaUAcUA\
eUAgUAiUAkUAmUAmUAmUAmVAmWAmYAm_AmaAmcAmeAmgAmiAmk\
8nm6ro9rqArsCruErwGrxHryKrzMrzPrzQrzTrzVrzYrzZrzar\
zcrzfrzhrzlrznrzqrzrrzvrzxrzzrzzrzveyoTxhJta9vZ2rY\
1qW1oW0nV0lT0hT0fS0eQ0cQ0aP0ZN0YN0WM0VK0TK0QJ0PH0N\
H0MG0JE0KG0MJ0MM0NP0NS3PV5PY8Q`AQaCSeGThJTlMVoPVrT\
WvWWyZYzaZzfYzeWzeVzeTzeSzcQzcPzcNzcMzaKzaJzaHzaGz\
`Fz`Ez`Cz`BzZzzZzzZzzZzzYzzY4zY2zW3zY3zY3yZ3vZ3t`3\
r`3q`4na4la4jc4fc4ee4ce4ae5Zf5Yf5Wh5Th5Sj5Qj5Pj6Ql\
6Sl6Un6Wn6Yo6_o2`z6aoBbeGcWMcMScEYc6cd0je0qf0og0oh\
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wW`wZZwaZweYxhYyjWzeWzaWzZVzWVzTVzPTzMTzJTzGSzESzA\
Sz8Qz5Qz3Qz1Qz0SzASzNTzaTzqSzrQzrPzrNzrNzrMzrKzrJz\
rJzrHzrGzrFzrFzrEzrCzrBzr }
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.
