The shouting and cries for help were heard across most of Fractal Space and almost to the Real World. Dr. J just had to look one more time for even more roots. What he found is yet more Jello. This time he tapped into the main feed from the nearby Jello factory. He should have studied his FractoScope more closely. As he floundered in even more Fractal Jello he lost his footing and went down into the slippery mess. In Figure 1, we see the picture that made the FractoPapers last month. I was as deep in my work that month as Dr. J is his Jello, so I didn't see the picture until tonight. And, I'm sure you can understand, Dr. J didn't push the image my way. This is because, according to the reports, Dr. J was rescued by the volunteer FractoFire Dept. How pathetic Dr. J looks, covered with 16 flavors of Jello!!
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Figure 1. Rescue from Fractal Jello.
This fractal is another two in one, combining the standard Mandelbrot set with the Jello fractal. The pixels are up like a checker board with the light squares using one formula and the dark squares the other. In the Mandelbrot set fractal, I use special tests to color Dr. J's period 1, 2 and 3 components. The Jello methods are an extension of earlier FotN issues. Please consult earlier discussions background analysis.
Stay dry,
Jay
The parameter and formula files for Fractint are included below. Copy them
into a quickie.par file for quick loading into Fractint. For longer term
use, copy the frm: block into a FotN.frm file. But this time leave off the
'frm:' part. Then copy the rest (the par parts) into your FotN.par
file.
frm:J-in-Jello { ; Jay Hill, 1998
; use outside=summ periodicity=0 passes=1 inside=249
; p1=width of root finding
; p2 = shift of first midget
; p3 = scaling factor of first midget
done = 1
if(whitesq)
z = 0, zc = c = (p3*pixel+p2)
s=|c|, t1=(256*s - 96)*s + 32*Real(c),
t2=16*s + 32*Real(c) + 16
; component tests
B=sqrt(-4*c-7), t3=|8+4*c*(1-B)|, t4=|8+4*c*(1+B)|
; set colors
z=z + 249*(t1<=3) + 250*(t2<=1) + 251*(t3<=1) + 252*(t4<=1)
if(z>0) ; for periods 1, 2, 3
done=-1 ; color is set, skip iterations
endif
else ; not whitesq
c = pixel, z = iter = 0
range = 15, w = 7/8
R=(-1)^(2/15), R2=sqr(R)
root1 = 1, root2 = c^(1/15), root3 = root2*R,
root4 = root2*R2, root5 = root4*R, root6 = root4*R2,
root7 = root6*R, root8 = root6*R2, root9 = root8*R,
root10= root8*R2, root11= root10*R, root12= root10*R2
root13= root12*R, root14= root12*R2, root15= root14*R,
root16= root14*R2
endif:
if(whitesq)
zc=sqr(zc) + c ; standard MSet iteration
if (|zc| >= 4) ; Bailout at 4
done=-1 ; Set flag to force an exit.
endif
else ; not whitesq
w14 = w^14
deltaw=(((w - 1)*w14 - c)*w + c)/((16*w - 15)*w14 - c)
w = w - deltaw
;
IF (|deltaw| < p1)
angle=abs(imag(log(deltaw)))
range_num = (|w - root2| < p1)+\
2*(|w - root3| < p1) + 3*(|w - root4| < p1)+\
4*(|w - root5| < p1) + 5*(|w - root6| < p1)+\
6*(|w - root7| < p1) + 7*(|w - root8| < p1)+\
8*(|w - root9| < p1) + 9*(|w -root10| < p1)+\
10*(|w -root10| < p1)+11*(|w -root12| < p1)+\
12*(|w -root12| < p1)+13*(|w -root14| < p1)+\
14*(|w -root14| < p1)+15*(|w -root16| < p1)
done=-1 ; Set flag to force an exit.
z = range*(angle/pi + range_num)-angle/pi + 1
ENDIF
iter = iter + 1
z = z - iter
endif
done >= 0 ; Continue if the flag >=0.
}
J_in_Jello-0 { ; (C) by Jay Hill, 1998
reset=1960 type=formula formulafile=n6jatnm.par
formulaname=j-in-jello passes=1 center-mag=-0.0707051/0/8/1/90
params=0.001/0/-1.02/0/-7.8/0 float=y maxiter=254 inside=249
outside=summ logmode=fly
colors=000<14>w00000<13>0w0000<13>00\
w000<13>ww0000<13>0ww000<13>w0w000<1\
3>wU0000<13>Uw0000<13>0wU000<13>U0w0\
00<13>w0U000<13>0Uw000<13>www000<13>\
UUU000<13>``0000<13>0cc000<6>000m00c\
UUmUAmUAm00000000 cyclerange=1/240
savename=JinJello
}
