;     Date: Fri, 12 Mar 2010 22:13:56 -0500
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 13-03-10 (Misplaced Surprise [?])
;       Id: <1.5.4.16.20100312221522.2b3f8110@pop.mindspring.com>
; ---------
; 
; FOTD -- March 13, 2010 (Rating ?)
; 
; Fractal visionaries and enthusiasts:
; 
; Today's image holds not only the promised surprise but a mystery 
; as well.  I named it "Misplaced Surprise" because the minibrot 
; in the upper right seems strangely out of place.
; 
; Yesterday's image is an East-Valley-type Julia set.  This is 
; evident by its appearance.  Today's image shows the same scene 
; from a viewpoint double-rotated only 0.001,0.001 degree from the 
; Julia direction.  (Double rotation is another story.)  Despite 
; such a tiny rotation, the resulting image has lost all resem-
; blance to a Julia set, and more closely resembles a non-critical 
; Mandelbrot scene.  But wait!  This is impossible!  What is a 
; near-perfect Mandelbrot minibrot doing in a fractal that is so 
; close to being a Julia set?
; 
; Actually, the minibrot is far from perfect.  A closer examina-
; tion will reveal that it is perturbed, but the fact that it is 
; there at all makes the image so exceptional.
; 
; When I began rotating the scene toward the Mandelbrot orienta-
; tion, I had one of the biggest surprises of my fractal career.  
; A near-perfect Mandelbrot midget unexpectedly appeared amidst 
; the degenerating Julia features.  This is striking because, due 
; to the four-dimensional shape of Mandelbrot elements in the 
; Julibrot, with 2 infinitely extended dimensions and 2 compact 
; dimensions, Mandelbrot features supposedly cannot appear in a 
; Julia set.
; 
; Another thing I notice in the image is the missing elements.  In 
; the pure Julia version, 32 striped red elements surround the cen-
; ter.  In today's almost-Julia version I see only 24.  I have no 
; idea what happened to the missing elements, though I suspect a 
; second radiant center lies off the screen some distance to the 
; left.
; 
; I have no answers to these fractal paradoxes, nor do I expect to 
; think of any.  I guess it will forever remain one of those unex-
; pected things that make fractals so interesting.
; 
; Since the image is of purely mathematical interest, and would 
; have little artistic worth to the 'look ma I'm an artist' type 
; of fractalist, I rated it at a question mark.
; 
; The calculation time of 1-2/3 minutes for all this surprise and 
; mystery is quite a bargain.  Those who are not bargain hunters 
; may view the image on the new FOTD web site at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; The weather here at Fractal Central took a turn for the worse 
; Thursday night, and Friday dawned with cloudy skies and light 
; rain.  Friday brought continued clouds, intermittent rain and a 
; temperature of 50F 10C.  These conditions did not please the 
; fractal cats, who wanted more sun.  Unfortunately, with rain 
; forecast for at least 3 more days, the cats will remain unhappy.
; 
; My day was fair enough.  If all goes well and no antiquing 
; expedition arises on Saturday, the next FOTD will be posted in 
; 24 hours.  Until then, take care, and be with the fractal elite.
; 
; P.S. My almost-useless AOL e-mail address may be discontinued in 
; a month or so.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE=======================================

Misplaced_Surprise { ; time=0:01:39.89-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=t float=y
  center-mag=-0.00021870072691744/-0.000080784627994\
  88/3194.472/1/-7.5/0 params=89.999/0/89.999/0/0.27\
  58107881858941/-0.006746958379780152/0/0/2.003/0
  maxiter=6000 inside=255 logmap=310 periodicity=0
  colors=000000XJaMCPB6CvGeFMQ7BDz82S51E20zEPS9GE48T\
  UqJK_9AIaFgPATC5E8maeqz2`q1Rc1IR09DrtxdehRSUDUzVKz\
  F6Sry4di3RV2DF1kisWU`GFIlxG_hCOU8CF4ixpNUQdz0zO0KG\
  0A80Ah06U03F0WvEGT7e08BrglGwZVoLih8xaGmRObGWT5faAz\
  zFzzKe_DMj7LI6qU`_KOIACoqTQREURYKIMA9BdIQUDJK9DA46\
  tZoqHX_BMI5B`xpvuDgf9TT6EE3aRzJDVBmg7XT3GE1Ul0M_0F\
  O07CkPQWGHG88pONbIHQCBD65UuzaT1SL0JE0970EyqAic7VR3\
  FDaQxSJhJDU96FwXTUGEhnyNwFFcA7K5peXQLGDB08704304Db\
  8z94V4LjGEVA7F5EVK9KD4A6jZRCZq9Qc6HR38D`8qI4R6_gtH\
  FS87pD9Z86H43fYHWPCLH8A842Ly1AVig6UT4FE2q4M9Ib6DT4\
  9J2499vL6gF4TA2E5NTBHL8BE5572Q82J61D41620tg4SM2L2H\
  E1B705gtaMSJte1eV0SL0EA02Rg1IT09ECMO6BCEOMp_BZO7HC\
  3itOYeINSCBE6upGfbCTQ8ED41g9hzz0MUzr2jqK0fFzOABC57\
  bdUEQhAJU7Dc36_RLOIEC970`50O30C1Da_8PO4CCZG6NA4B52\
  _MgRGXIBM95Bk7oW4YG2HhheSDDI88944vlOi_RNIDt2fa1SJ0\
  Es78e56S34E12ZunAgH7XCzzz }

frm:SliceJulibrot4   {; draws all 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=z^(p5)+c
  |z|<=9 }

; END PARAMETER FILE=========================================
; 
; 
; 
; _______________________________________________
; Fractint mailing list
; Fractint@mailman.xmission.com
; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint