|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: I wrote another quick new formula since yesterday's FOTD, and gave it the impressive name 'multXYZWcompjb-min'. The only difference from yesterday's formula is that today's calculates (-Z) instead of (Z). The difference in the formula is small, but the change in the appearance of the fractals with fractional exponents of Z is great. Today's fractal shows a scene in the four-dimensional Julibrot of the formula (-Z)^1.4142*C^0.03+C. The orientation of the slice is very close to the Julia direction. But being close does not make today's image a Julia set, so I have named it "A Nothing Set". The true Julia set may be seen by changing the value of (p1) from 81,90.2 to 90,90. The Mandelbrot aspect of the scene appears when (p1) is set at 0,0. The point that corresponds to today's image lies in the disconnected triangle in the M-set. The other values of (p1) draw various oblique slices through the Julibrot, some of which are quite interesting, while others have little to offer. The image relies mostly on intense coloring for its effect. As a result I limited its rating to a 7. But the render time is a fast 2-3/4 minutes, which boosts the overall worth to 257. And don't forget the FOTD web site at: The clouds hung tough most all day on Tuesday here at Fractal Central, but the temperature rose to 36F 2C, which was comfortable enough for the fractal cats. Unfortunately, the warmer temperatures started melting the snow, which then wet the paws of the duo, sending them scurrying back to the porch, where they sat for nearly an hour watching the birds fly by. The evening treat of tuna was a bit larger than average. Today is starting warmer with lots of clouds. But with so much snow still on the ground, it looks doubtful that the duo will have a good day. Since the work is still caught up, my day will be good. And when 24 hours have passed, the next FOTD will appear in all its glory and wisdom. Until then, take care, and be awe-struck in the presence of a fractal. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
A_Nothing_Set { ; time=0:02:43.52--SF6 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=multXYZWcompjb-min function=ident/flip
passes=1 center-mag=-0.306729/0/1.253133
params=81/90.2/1.4142/0/1.03/0/0/0/-0.76/0 float=y
maxiter=2000 inside=0 symmetry=xaxis
logmap=yes periodicity=10
colors=0004AA6AA8AAAAACAAEAAGAAIGLKKPMNTPQXST`VWdY\
Zh`alcdqfgtiixikyikzhkzgkzflzelzdlzclzbly`mx_nwZov\
YpuXqtWrsVsrUtqTtpStoRtnQtmTrlVpkXnlZkm`hnbeodbmf`\
khYijVglSelPcjMagJ_dGYaDWZAUW7SS5QP4OM4MO3KQ2ISCGU\
EFVGGWIHXJIYKJZKK_KK`KKaKKbKKcKKdKKdKKdKKdKHdKEdKA\
cK7bK4aK6`K7_K8ZIAYGBXFCWDEVBFUAGT8IS6JR5KP3MN1NK0\
OKh8ervdsodthdzaccXcYScMNcAJcFNcJQcNTcRWcVZcZacbda\
fgZjjWnmTrpQvsOupNtnMskLriKqfJpdIpaHo_GnXFmVElSDkP\
CkMPhKKeKFaK0ZH3WI6TH9VGCXGFZGI`FLbFOdERfETgEUcDV_\
DWWDWSDXODYKDYGDVJKTLRROYPQdTPgWOi_NkbMmeLoiKqlJso\
IujGmfEfaC_YBT`AWb9Ye8_g7ai6cl5en4gq3is2ku1ml4fc7`\
VAVMDPQCRTCTWBVZBWaAYdA_gA`hGXhLUiQQiVNj_JjdGkiCkn\
9elF`jLWhRRfWMdaHbgCalHZjLXhQVfUTdYRbbPafN_jLYoJWs\
HUwFTsHSpISmKSiLSfNScOS`PS_UO_YL_aH_eE_jB_n7_r4_v1\
buBetLgtVjsdmrnorxnmumhrlhpkkmknkmqcotXqwPszIuzBqz\
LSzbUzfXziZzl`zoTznLzmDzm }
frm:multXYZWcompjb-min {; draws 6 planes and rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5:
z=(-z)^(p2)*(c^(p3-1))+c,
|z| < 400 }
END PARAMETER FILE=========================================
|
times.
