;     Date: Thu, 16 Jan 2003 10:19:00 -0500
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 16-01-03 (Negative is Positive [4])
;       Id: <1.5.4.16.20030116102148.2a07d21c@pop.mindspring.com>
; ---------
; FOTD -- January 16, 2003 (Rating 4)
; 
; Fractal visionaries and enthusiasts:
; 
; I am always fascinated by polytopes of higher dimensions, 
; particularly the regular polytopes of the fourth dimension.  In 
; 4-space, six regular polytopes exist.  The 5-cell corresponds to 
; the tetrahedron of 3-space; the 8-cell, to the cube; the 
; 16-cell, to the octahedron; the 120 cell, to the dodecahedron; 
; and the 600-cell, to the icosahedron.  But in 4-space there also 
; exists a polytope known as the 24-cell, which would appear to 
; have no corresponding figure in 3-space.
; 
; This appearance is not totally true.  The 24-cell has no 
; corresponding regular figure in 3-space, but it does have a 
; similarly constructed figure -- the rhombic dodecahedron, which 
; consists of 12 rhombic faces, 24 edges and 14 vertices.  
; Curiously, the rhombic dodecahedron is a space-filling figure.  
; In tomorrow's discussion, we shall construct a 24-cell polytope 
; from the ground up, but before then, we have today's fractal to 
; examine.
; 
; Today's image is named "Negative is Positive".  I gave it this 
; name for two reasons -- first: many of my images result from 
; combining negative powers of Z, which is a positive thing, and 
; second: I received a junk e-mail this morning from a spammer, 
; which is nothing unusual.  But this letter was intended to sell 
; an anti-spam program to me.  It began by saying "If you had our 
; product, you would not have received this letter."  My mental 
; reply was, "It's always best to start the day with a laugh."  
; Then, after a moment's consideration, I deleted the e-mail and 
; named today's image.
; 
; Though its name was given in jest, today's image has perhaps a 
; bit more of the negative than the positive about it.  The rating 
; of 4 is quite a comedown from yesterday's, but then, we can't be 
; above average on every day.  And yes, the image was created by 
; combining two negative powers of Z, in this case -3 and -5.
; 
; The parent of today's scene is a rather comical figure 
; resembling a lobster sitting on its blunted tail.  Today's image 
; is located at the tip of an irregular filament near the point 
; where the lobster's right claw joins its body.
; 
; The image renders from the attached parameter file in just over 
; 3 minutes.  The GIF file of the completed image downloads in 
; even less time.  The download may be found at:
; 
;           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; and at:
; 
;           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
; 
; With a temperature of 25F -4C, Wednesday was very cold and windy 
; here at F.C.  Occasional flurries of snow made things even 
; worse.  The F.C. cats spent the entire day indoors, checking the 
; outside conditions several times, but turning around as soon as 
; their sensitive noses felt the chill.
; 
; Today is starting just as cold, and more snow is threatening.  
; The cats will have another unsatisfactory day.  My day will be 
; satisfactory if I find a perfect fractal, which is unlikely.  
; Until next time, take care, and remember that no one is perfect.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

NegativeIsPositive { ; time=0:03:15.26--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+1.23970545929533/-1.269509193680854/9.\
  148861e+009/1/170/7.41674007990883455e-005
  params=1/-3/0.5/-5/0/0 float=y maxiter=1200
  inside=0 logmap=60 periodicity=10
  colors=000OCVPCYQAaT9gV7jW5iX3n`2qd1ph1nl0mp0kt0ix\
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  VvzTCz5FzAGzDHzHJzMLzPMzT }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

; END PARAMETER FILE==================================
; 
;