;     Date: Wed, 20 Nov 2013 19:14:18 -0500
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 20-11-13 (This is a Minibrot [A-8,M-7])
;       Id: <1.5.4.16.20131120191403.2a27cc0a@earthlink.net>
; ---------
; 
; FOTD -- November 20, 2013 (Rating A-8,M-7)
; 
; Fractal visionaries and enthusiasts:
; 
; "This is a Minibrot"
; 
; This phrase is not only the name of today's image, but it is 
; also a harsh fact of the image.  The tiny hole at the center of 
; the scene is a minibrot in the parent fractal that came about 
; when I calculated the expression Z^sqrt(2)+C at a height of 14 
; levels up the hyperladder with no function applied.
; 
; This parent is a shapeless thing, impossible to describe in 
; words, with no resemblance at all to a recognizable Mandelbrot 
; set.  Today's image lies on a filament extending from a mis-
; shapen bud on the northeast side of the parent.
; 
; I chose sqrt(2) as the exponent of Z because the minibrots in 
; this family of fractals are sometimes surrounded by two- and 
; four-way symmetry, making them easier to find, though nowhere 
; near as easy as straight quadratic minibrots.
; 
; I sometimes wonder what separates a minibrot from the countless 
; other holes that parent fractals are often filled with.  As I 
; see it, the difference is that true minibrots do not fill in 
; regardless of how high the maxiter is raised.  Also, minibrots 
; almost always lie in a basin, with the number of surrounding 
; elements increasing without limit as the edge of the open area 
; is approached.  The other holes that fill fractals are often 
; simply random open areas that never fill in, or open areas at 
; the center of bottomless spirals that will fill in with a higher 
; maxiter.
; 
; Most minibrots are of the quadratic variety, even in fractals 
; created by a combination of exponents other than 2.  This 
; quadratic shape appears to be the generalized shape of 
; minibrots, much as parabolas are the generalized shape of curves 
; in the graphs of many functions.  Today's minibrot is of order 
; 1.414... a variety which has no generalized shape at all, and is 
; therefore quite interesting.
; 
; The art rating of an 8 shows that I am quite satisfied with the 
; colors.  The math rating of a 7 was given a boost by the colors. 
; There is little new math stuff in the image however.
; 
; The calculation time of 2-3/4 minutes is slower than I would 
; have preferred, but the FOTD web sites can eliminate the 
; slowness.
; 
; These web sites may be accessed at:
; 
;       <http://www.crosscanpuzzles.com/Archives.html>
; 
; <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
; 
;        <http://www.Nahee.com/FOTD/>
; 
;   <http://user.xmission.com/~legalize/fractals/fotd/about.html>
; 
; The day began with a biting cold temperature of 23F -5C but the 
; clear sky and resulting strong sun bumped it up to 43F +6C by 
; afternoon.  The fractal cats, who are just learning to play 
; together, were too busy chasing each other up and down the 
; fractal hallway to take advantage of the afternoon sunlight 
; flooding their shelf in the southwest window.  The humans, much 
; less playful, spent the day tending to more pressing but less 
; interesting things.
; 
; The next FOTD will be posted when the time is right.  Until 
; whenever that might be, take care, and I admit that fractals are 
; awesome, but are they groovy?
; 
; 
; Jim Muth
; jimmuth@earthlink.net
; 
; 
; START PARAMETER FILE=======================================

This_is_a_Minibrot { ; time=0:02:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident passes=1
  center-mag=+0.864016578592/+0.61309334532/9.9e+007\
  /0 params=1.414213562375/0/14/0 float=y
  maxiter=3200 inside=0 logmap=295 periodicity=6
  colors=0000BY0Dd0Hf0Lt0Qt0Vs2Zs6cq9hqBlqGqoKvoOznR\
  znVznTziRxdQqaOkYNdTLZQLRLKLIIGEHAAG47E02E00I04L09\
  O0BT0GW0KZ0Na0Rf0Wi0Zl0co0ht0kx0oz0tz0xx0zq2vk7qdB\
  lZGhTKcNQZHWVBWQ6VL0TH0RD0QB0OB0NB0LA0KA0IA0HA0E70\
  B40910600200000000000000000000000200900D00H00L00R0\
  0W00`00d00k00o00t10y1WzQYzTYzWYzZYzaYzdZzhZzklnnoq\
  qtsttvxtxztzztzztzztzztzstz`nzIsz1vz0sz0ot0ln6ihDh\
  aKdVRaOZZIfWDnV7tRDvQIxNOyLVzI`zHdzGkzDqzBxz9zz7zz\
  6zz9zzByzDqyGktHcqKWlNQhOIdRB`T6Yz02o6ETEQ7Na0Wl0a\
  o0hs0nv1ty4zz9zzBzz7zy2oq0dh0V`0KT0HO2GK9EGDDDIB9N\
  94T71Y60c40h20i90iD0iH0kL0kQ1kV4lZ7lc9lhBllDflE`lG\
  VlHQlIKlKElL9lN4lO0lQ0lR0lR0fV1aY9Y`ETcKOfRIiYEldA\
  ok6sq1vl4t0T70Y40c10h00n00s00x00v00t04t09t0Dt0Ht0L\
  t0Qt0Vt0Zt0ct0ht0lt0qt0vt0zt0vz0tz0tz0tz0tz0tz0tz0\
  tz0tz0tz0tz0tz0tz0tz4tzBtzILzQOzYRzdVzaWz`ZzZ`zYaz\
  WdzVfzThzRkzOlzNozLqzKszI }

frm:MandelbrotBC3   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)+PI-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a }

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