;     Date: Wed, 19 Oct 2011 09:46:32 -0400
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 18-10-11 (Down in the Boondocks [All math])
;       Id: <1.5.4.16.20111019094638.1197d506@pop.earthlink.net>
; ---------
; 
; FOTD -- October 18, 2011 (Rating All Math)
; 
; Fractal visionaries and enthusiasts:
; 
; Today's image rates All Math.  The mathematical interest is just 
; about all it has going for it.  The image itself is little more 
; than a passing scene in an infinite world of fractals.  And the 
; calculation time of nearly 2 hours is far beyond reason.  In 
; addition, the exponent of Z that created the image is 1.0005, so 
; close to unity that no one in his right mind would enter it as a 
; parameter with any expectation at all of finding much more than 
; smooth and straight band edges.
; 
; Questioning my own sanity, I did enter this value as the 
; exponent of Z, and in addition I felt fairly confident of 
; finding something of interest.  Today's image is what popped up 
; where nothing should exist.
; 
; The scene is neither a Julia set nor a Mandelbrot set, but 
; something in between.  The detail in the image is not the 
; organized chaos that makes most fractals so interesting.  The 
; detail in today's image consists of countless discontinuities 
; arranged into half-orderly elements.  If any part of the image 
; is zoomed into, a flat featureless area will ultimately be 
; arrived at.  In ordinary fractal chaos, the chaotic features 
; continue without limit.
; 
; The name "Down in the Boondocks" refers to the exponent of Z, 
; which is by far the closest to unity of any FOTD fractal so far.
; 
; A price must be paid for seeing detail in a fractal so close to 
; unity however.  The price is the need of a very high maxiter, 
; resulting in a calculation time of 1-3/4 hours, which is tedious 
; indeed for such an unartistic image.  But help has arrived in 
; the form of the FOTD web sites.
; 
; All the tedious calculating may be avoided by viewing the 
; finished image on the FOTD web site at:
; 
;       <http://www.crosscanpuzzles.com/Archives.html>
; 
; It may be seen in high definition at:
; 
; <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
; 
; The original, now classic web site may be accessed at:
; 
;       <http://www.Nahee.com/FOTD/>
; 
; The day began with clouds here at Fractal Central, but the 
; clouds cleared off before noon, leading to an afternoon of 
; sunshine, balmy south breezes and a temperature of 70F 21C.  
; With rain and colder weather forecast, today might have been the 
; last near-perfect day of the fall.
; 
; The fractal cats passed a good part of the day sharing the new 
; chair.  The humans disagreed a bit about politics (as is 
; standard) but the day passed uneventfully.  The next FOTD will 
; be posted in 24 hours.  Until then, take care, and liberal 
; thinkers know that conservative policies are the cause of the 
; problems, while conservative thinkers know that liberal policies 
; are the cause of the problems.  Neither side appears able to 
; recognize that their conflicting views of the solution are also 
; a part of the problem.
; 
; 
; Jim Muth
; jimmuth@earthlink.net
; 
; 
; START PARAMETER FILE=======================================

DownInTheBoondocks { ; time=2:05:44.73-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot5 passes=1 maxiter=120000
  center-mag=+2.723099067722828/+0.02123607283229285\
  /6919/1/5/0 params=37.5/0/37.5/0/1.1513/0/0/0/1.00\
  05/0 float=y inside=0 logmap=-15900 periodicity=9
  colors=000zdCzeEzfGzgIzhKziMzjOzkQzmSznUzoWzpYzq_z\
  razsbzs_zsXysUwsRurOsqOqpOooNmnNkmNilMgkMfjMeiLdhL\
  cgLbfKaeK`dK_cJZbJYaJX`IWZIVXIUVHTTHSRHROGQLGPIHOF\
  GNDKMDKLFKKIKJKKINKHPKUKzTKzTKzTKzTKzTKzTKzTKzSKzS\
  KzSKzSKzSKzSKzSKzRKzRKzRKzRKzRKzRKzRKzRKzQKzQKzQKz\
  QKzQKzQKzQKzPKzPKzPKzPKzPKzPKzPKzOKzOKzOKzOKzOAzOA\
  zOAzOAzPAzQAzRAzSAzSAzTAzUAzVAzWAzWAzXAzYAzZ1z_1z_\
  2z`2za3zb3zc4zc4zd4ze5zf5zg6zg6zh7zi7zj7zk8Wk8Yl9_\
  m8an6co4eq2gr0is0ku0mv0ox0qz0sy0ux0ww0ww0ww0ww0ww0\
  ww0ww0ww0ww0ww0uw0sw0qw0ow0mw0kw0iw1gw1ew2ew2ew3ew\
  4fw4gw5gw5hw6hw6iw7iw7jw8kw8kw9lwAluAmsBmqBnoComCo\
  mDpmDpmEqmEqmFrmEsmFrmFqmFpmGomGomGnmHmmHlmHlmIkmI\
  jmIimJimJhmJgmKfmKfmKemLdmLcmMczOazQ`zS_zUZzWXzYWz\
  _VzaUzcTzeRzgQziPzkOzmMznLzpKzpJzpIzpGzpFzpEzpDzpB\
  zpAzp9zp8zp7zp5zp4zp3zp2zp1zp2zp2zpfzpezpezpdzpczp\
  czpbzpazpazp`zp`zp_zpZzpZ }

frm:SliceJulibrot5   {; 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), esc=imag(p5)+9
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=(-z)^(real(p5))+c
  |z|< esc }

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