It is Mother's Day and Dr. J has finally come out of his Deep Thought. And if I can get the latest FractoFax (TM) downloaded without any errors, we might see what he has been up to. Please stand by while I tune in the sound track.
Fax technology, as you know, uses compression techniques to reduce the time for transmission of your pages of information. Since a page of text has many repeating pixels (the white background), use of run length encoding compresses the message to a small file. The FractoFax(TM) is designed to compress images from FractoSpace. It is the state of the art fractal compression. It is theorized that, in FractoSpace, fractals exist in complete accuracy and infinite resolution. That may be true, but then why are the fractals always iterating? And why was Dr. J in so much danger when he nearly stopped iterating?
Anyway, back to tonight's FractoFax. You can see the raw compression codes I received at the end of this page. The decoding process requires a model 19.6 or later FractoViewer such as Fractint. The amount of detail depends on your FractoFax decoder hardware and how much patience you have. Of course, if there is some portion of the message you wish clarified in greater detail, provision has been made for limited zooming and panning of the pictures.
Oh, here comes the sound. It is Dr. J talking...
"Wow, the Mother of All Fractals! And to think I finally saw it all! E? E? Oh there you are. Look, let me show you." His circular component beams the image as he recalls it. (Figure 1.) "Ooops, it seems to be fading. FAP! [an expletive from the '50s] I found the only way to see it all is to solve the complete set of equations analytically. Series solutions are the best way. See?"
Dr. J is very excited about his latest discovery. But Dr. E is not so convinced. "And just how are we going to accomplish this every time we want to see the whole picture? We just can't be zapping ourselves with semi-infinite voltages and dropping into Deep Thought every day, like you just did!"
Dr. E was impressed with the Mother's Day fractal. But perhaps a simple flower fractal would do next time. "I see you show the filaments. The one running straight to the left along the real line is easy, but how do you get the others?" Dr. E plays along with Dr. J for the moment.
"Don't need to calculate filaments explicitly." Dr. J was taking the bait. "There is no part of the set that is not arbitrarily close to one of the midgets. Just calculate all the midgets and you are done."
"Well, get you filaments together and let's go home!" Dr. E didn't want to spend Mother's Day at the hospital tracing filaments.
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Figure 1. Mother of All Fractals.
What's this? It looks like the FractoFax has ended with no attachments! I thought we would get that detailed report titled "A Complete Survey of the Mandelbrot Set" showing the most awesome fractals ever seen. Knowing Dr. J, this is what I should have expected. Oh, I all most forgot, this FractoFax was sent automatically by the hospital security camera. That explains it. Well, maybe next time.
Feel free to zoom into the fractal with your own FractintoScope 19.6. And Happy Mother's Day as you explore the Mother of All Fractals, the Mandelbrot Set.
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.
FractoFax:
Mothers_day { ; (c) Jay Hill, 1998
reset=1960 type=formula formulafile=onepiece.par
formulaname=one_piece_m center-mag=-0.5/-1.33227e-015/1/1/-90
float=y maxiter=253 outside=summ symmetry=xaxis periodicity=0
colors=000KAmcKA<11>cjscmwcmw<77>L1VK0U\
K0UK0U<77>mKAmKAlKA<73>212112001000000
savename=Mothrday
}
frm:One_Piece_M { ; (c) Jay Hill, 1998
; use outside=summ periodicity=0 float=y
done = 1, z = 0, zc = 0, c = pixel
t1=4*(c+1)
if(|t1|<1)
c=2*t1*flip(-1)-.5 ; set up MSet
else
t2=4*(c+1)
t0=(1-sqrt(1-4*c))
B=sqrt(-4*c-7),
t3=|8+4*c*(1-B)|,
z=z + 2*(|t0|<=1) + 2*(|t2|<=1) + 2*(t3<=1)
if(z == 0)
L1=2, L2=2,
if((4*c+3) !=0)
Y=pi*sqrt(-1)/1.5, X = 2*sqrt((4*c+3)/3),
X3 = asinh(-16/X^3)/3, Zz = 2*(c+1)*c + 2
F=X*sinh(X3 + Y), L1= 64*|(c*(F+1)*F + Zz)|,
F=X*sinh(X3 - Y), L2= 64*|(c*(F+1)*F + Zz)|,
z=z + 2*(L1<=1) + 2*(L2<=1)
endif
endif
done=-1 ; color is set for c in a component, skip iterations
endif
: ; initialization.
zc=sqr(zc) + c ; standard MSet iteration
if (|zc| >= 8) ; Bailout at 4
done=-1 ; Set flag to force an exit.
endif
done >= 0 ; Continue if the flag >=0.
}
