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.

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=========================================