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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image starts off the new month by returning us to the scene of yesterday's image. The only difference is that today's image is sliced in an entirely different direction -- 1/3 of the way from the Parabolic toward the Elliptic orientation. The result is a much distorted and stretched version of the elements that appeared in yesterday's image. The other rotations in hyperspace stretch and twist the image elements in various other ways, but after unstretching and skewing, the underlying effect remains pretty much the same as today's. Therefore, today's FOTD will be my only attempt to see what changes in the image the different orientations can make. Since today's image is not really a new one, and with only a few minor changes, I used the same color palette, I could not give it an actual rating. The name "Warped Perception" indicates that it is only our limited view of the transcendental four-dimensional Julibrot that has changed. The basic formula, Z2+C, remains the same. The calculation time of 20.20 seconds has nothing to do with vision. It is the time it takes the parameter file to finish running on the speedy P4-2000mhz computer. On the slow old P200 unit, the parameter file will finish in a still-speedy 2 minutes. Of course, the easiest way to see the image, as always, is to visit the FOTD web site at: With deep blue skies, low humidity and a high temperature of 79F 26C, Friday here at Fractal Central was as close to perfection as it is possible to come on this planet. The fractal cats agreed as they searched for mischief, finally finding it by knocking a picture off the wall. My day was not quite as perfect as the weather. An unsatisfied customer spoiled what might have been a near-perfect day. But the problem was quickly solved, and all ended well. The next FOTD will appear in 24 hours. It will be an all new one this time. Until then, take care, and since time and space are mere subjective creations of the mind, why not change our perception of them like we so often do with fractals? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Warped_Perception { ; time=0:00:20.20-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot2a inside=0 symmetry=none
params=30/90/0/0/-1.999999779397065/0/-1.999999779\
397065/0/2/0 float=y maxiter=1000000 periodicity=10
center-mag=+1.832893479e-014/+1.040270804e-014/3.4\
05775e+013/0.1704/166.246022919272576/23.573377344\
1832462 outside=tdis mathtolerance=0.05/1
colors=000wfapfZifW9x5PoH7phIlbTiYcbxcdmcebbJncVcQ\
kbViZ_gWVPFYVK``PVrUYnT`jTC4SKaXUdVeJ1dRBcZKQ5LJJP\
JJjU_bUSiXWdZ_`acXRPrbWeGG2MR9S`GYaNO3LWNPzr2zhBzU\
KzzQzzRVTS__TNLRzYSWmS_aTcz7arFblMOK1SQ8WWF_aMzcz`\
czzczbczzczWczzczaczzczWczzczpczzczgczzczWczzczdcz\
zczyczzczvczzczoczzczcczzczgczzczgczzczfczzczbmzcm\
zcmzcmzHmzTmzomzkmzgmzemzrmznczjczfczWczZczamzu2ho\
GbiUY3rGMlNLM`6`KoNziXKWk1Yi8_hFagMFRjSZzK1GRFLYTP\
1j8BiELhJVgOStVVpUYmU`iTHBHTRN9fvPfgQGHVPL_YPtQcVB\
HYML`XP86095pHFjPOdXYZOt19KuHY8TbJ_v`qndlk`ghXbBGc\
MLcXPsEuoMmkTfg__4McGT_S_WUmtYjj`haIRCQXIXaOWpfYmb\
_k_ahWwBNpMPiXR`6JaGMbPOcYRL9JSLNYWQhoSflTejTdhTHs\
HNoKTlNZiQVzZYsX`lVhGgeU_2ljFjdShZptolpiimcfiYR0FY\
MMwowplliibqpVllUgiTt3NoDPkNQgXSMUp5XuD4tMHjVUaCw1\
MqBVkKtlWkiUUxcXs`ZoYajVjmJgjNehQhHVeUU9j0Hi8PhFXg\
Mi2EWz7cGzd8ZcQWZNi`Ucb`Y }
frm:SliceJulibrot2a {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z| <= sqr(real(p5)) }
END PARAMETER FILE=========================================
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times.
