|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: I'm busy again today, so the discussion will once again have to be brief. Today's trip takes us into the depths of the Mandelbrot set, to a fine spiral and the ghost of a bud. Images such as today's are what sparked my interest in the four-dimensional aspect of fractals. When I began exploring the perturbed M-sets, I found it puzzling that the low-iteration features should change so quickly when the starting point of Z is changed, while the high-iteration features, such as the background buds, remain unchanged. After a bit of thought, I realized that regardless of where the points start, if they do not escape first, they will eventually settle into the same orbits as the points that start at zero. In today's image, the foreground spiral consists of the low-iteration points that have escaped before settling into the conventional M-set orbits, while the background bud consists of the high-iteration points that have endured many iterations and found the time to settle into the M-set orbits. I named today's image "Spectral Bud", which is a recognition of the ghostly nature of the background bud. Pictures such as today's can be given a striking three-dimensional appearance by using the 'ranges' feature of Fractint, though I lacked the time to use this feature on today's image. I could honestly rate today's image no higher than a 4. When the render time of 2-1/2 minutes is considered, the overall value comes in at 152. The image may be seen either by running the included parameter file, or by downloading the completed image from: The weather was pleasant here at Fractal Central on Wednesday, though it was a bit chilly. The temperature of 43F 6C was tempered greatly by a warm sun, which made the cats' two hours in the yard a pleasant experience. When the day ended, they settled for the evening without complaint. Today is starting similarly. For me, things are a bit more settled today, but still relatively busy. If all goes well, I'll finish in time to find a top-rated fractal. If not, I'll find a medium-rated fractal. Until next time, take care, and find only good fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Spectral_Bud { ; time= 0:02:38.35--SF5 on a P200
reset=2003 type=mandel passes=1
center-mag=-0.23028521918996140/+0.644699549704085\
40/1847.458/1/-5/-3.77822773067748585e-014
params=0.3991/-0.6312 float=y maxiter=100000
bailout=9 inside=0 logmap=49 periodicity=10
colors=000LKULKULKULKUKKUKKUKKUKKUKKUJKUJKUJKUJKUI\
KUIKUIKVIKVHKVHKVHKVHKVGKVGKVGKVGKVHKVGKVGKVGKVGKV\
GKVGKWGKWGKWFKWFKWFKWFKWFKWFKWFKWFKWFKWEKWEKWEKWEK\
WEKXEKXEKXEKXEKXDKXDKXDKXDKXDKXDKXDKXDKXCKXCKXCKXD\
KYDKYDKYDKYDKYDKYCKYCKYCKYCKYCKYCKYCKYCKYBKYCKYDKZ\
DKZEKZEKZEKZFKZFKZFKZFKZGKZGKZGKZHKZHKZHKZHKZJKYJJ\
YJJYKJYKJYKIYKIYLIYLHYLHYMHYMHYMGYMGZNG_NG`OF`PFaP\
FbPEcPEdQEeQEeRDfRDgRDhRDiRCiSCjSCkSBlTBmUBmUBmUAm\
VAmVAmVAmW9mW9mW9mW8mX8mX8mX8mY7mY7mY7mX6mY7mZ8mZ9\
m_Am_Bm`Cm`DmaEmbFobGqcGscHudIwdJxeKyeLzfMzgNzgOzh\
PzhPziQziRzjSzkTzkUzlVzlWzmXzmYznYznZznZzkwzkwzlwz\
lwzmwzmwznwzowznwznwznwznwznwznwzmwzmwzmwzmwzmwzmw\
zlwzlwzlwzlwzlwzlwzkwzkwzkwzkwzkwzkwzlwzkwzjwzjwzi\
wzhwzhwzgwzgwzfwzewzewzdwzdwzcwzbwzbwzawz`wz`wz_wz\
_wzZwzYwzYwzXwzXwzWwzVwzVwzUwzUwzTwzSwzSwzRwzQwzQw\
zPwzPwzOwzNwzNwzMwzMwzLwz }
END PARAMETER FILE=========================================
|
times.
