|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: As I mentioned in the FOTD of January 13, I have long been searching for a great midget in a Mandeloid fractal with an exponent of Z between 1 and 2. The midget illustrated in today's image might not be great, but it is at least above average. The rating of a 7 might be a bit generous, but regardless, it is still one of the best midgets I have yet found in such a low-order Mandeloid. The overall value comes in at a 61. The exact exponent of Z in today's image is 1.5, which has been calculated 1.5 levels down the logarithmic hyper-spiral. The parent fractal appears as a reasonably normal Mandeloid rotated 180 degrees. On the north shore of the large western bay lies a tiny rudimentary bud, with a curious half-developed valley on its inside top shore. The shoreline of this valley is lined with areas of near total chaos, cut-off bits of which extend some distance inland. Today's scene lies in one of these cut-off inland islands of chaos. As is typical of all fractals with fractional exponents of Z, today's image is filled with discontinuities. The discontinuities are in fact the substance that composes the image. These breaks are a nuisance, but they also show the way to midgets. When one is searching for quadratic midgets, the signposts are areas where the features are arranged roughly symmetrically around a point. When the object of the search is a midget of a lower order, the breaks in continuity serve as the signposts. The breaks usually converge on midgets which otherwise would be nearly impossible to find. I named the image "Fractal Fossil". The name came to me when I started wondering how long this particular scene existed before I discovered it. It certainly existed billions of years, but did it exist before the 'big bang'? As far as that goes, did the 'big bang' actually happen, or is it just a creation myth without an outside creator, carefully designed to fit into our scientific world-view? While pondering the imponderable, I will end today's discussion with the reminder that the 11-minute wait for today's parameter file to run can be avoided by downloading the finished GIF image from Paul's web site at: The snow held off until after dark on Wednesday here at Fractal Central, but with a temperature of 23F -5C and brisk winds, the outdoor conditions were too harsh for the dynamic duo to venture forth. They spent the day indoors, sleeping and eating. Today is starting with a fresh inch of snow and falling temperatures. The cats will likely have another indoor day. With about 4 hours work to finish, I will likely have an indoor day also. And in 24 hours, I shall return with the next FOTD fractal. Until then, take care, and remain fractally oriented. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Fractal_Fossil { ; time=0:11:27.07--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=+0.04526308974509857/+0.771631709693025\
60/698846.7 params=1.5/0/-1.5/0 float=y
maxiter=12000 bailout=9 inside=0 periodicity=10
colors=000DIMEDHF9CG479vwBghDTVFEGgTubOkZJbUEUQ9KL\
4BdkYciWbgVaeU`cT_bSZ`QYZPXXOXWNWUMVSKUQJTOIXL_`QX\
cUTgUQjUNnUKqUHsUErUIqULpUOoUSoUVnUYnU`mUcmUfmUimU\
gkUjjWgiXdhXbgW_fUYfRVfNTfJQeFOeCLe8Je4Ge1Ed3Hc4Kb\
5Ma7P`8R_9UZBXYCZXDaVFcVGfUHhVLiWPiWSjXWjX_jYbkYfk\
ZjkZml_ql_tm_um_um_vm_vm_wn_xp_yr_zv_zzQkcGZc6Nc5P\
`5QZ5RW5SU5TR5UP5VN4XK4YI4ZF4_D4`A4a84b67Z79V8BS8D\
O9GK9IHAKDAM9BO6BUBGZFKcJPhOTmSYrWaiS_`PYTLXKIVBET\
3BS4FR5JQ6NP6RO7UN8YM8cM9gLPkKUnJZqIcsHcvHcqFFkEGe\
CH_BJU9KO8LI6MK5NK4LK3JK2`naXiUTcNPWGLU9JYPIUMIRKI\
OIILGIIEHFCHCAH98H66H34y0Zw0Xu0Ws0Vq0Tp0Sn0Rl0Pj0O\
h0Ng0Le0Kc0Ja0H_0GZ0FX0DV0CT0BR09Q08O07M05K04I03eZ\
8XN6PB4gGLIqMHnLHkKHiJHfIHdHHaGbLcbMbbNacOacP`cQcc\
RfcSjdTndUrdVvdWzdWWcUVbTUaST`RS`QR_PQZOPYNOXMNXM3\
XLMWKLVJKUIJTHITGHSEGRDFQCEZBDPACO9BN8AM79L68L57K4\
6J35I24H137dl9_fAVaBRXCMS }
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(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 20.0 PAR-FORMULA FILE==================================
|
times.
