Fractal visionaries and enthusiasts:

In today's FOTD we see the scene I was searching for yesterday when the fractal ship showed up.  I named the image "A Seahorse Goes East" because it combines the features of Seahorse Valley with those of East Valley.

The outer parts of the scene are clearly of an East Valley nature, while the inner parts reflect the appearance of Seahorse Valley when sliced in the Oblate direction, which is determined by the imag(c) and real(z) axes.  The entire image is distorted into a vague triangular shape because it lies at an odd angle in the 4-D Julibrot figure.

(As a matter of curiosity, in the German language, the word 'julibrot' means 'bread of July'.)

Unlike yesterday's image, which was stretched and skewed beyond verbal description, today's image was stretched only a modest 3-1/2 times in the horizontal direction.  The value assigned the real(p4) parameter, which sets real(z) is equal to the real(c) value of the scene in the M-set.  This places the actual location of the scene in what I call the shadow Mandelbrot set, a second Mandelbrot set lurking unsuspected at an angle of 45,45 degrees in the Z^2+C Julibrot.

The rating of a 7 is an improvement over yesterday's miserable rating of 4, but still leaves plenty room for yet more improvement.  The calculation time of a mere 24 seconds will make running the parameter file a breeze.  The task of setting up and running the file may be avoided by viewing the image on the web site.

Strange as it might seem, as the number of hypercube dimensions increases, its diagonal approaches infinity, while the hypervolume of the inscribed hypersphere approaches zero percent of that of the hypercube.

BTW, the formula for the hypervolume of a six-dimensional hypersphere is 1/6(pi^3)*(r^6).

Not a single cloud spoiled the blueness of the sky over Fractal Central today.  The sunrise temperature of 36F +2C was rather chilly, but the unbroken sunshine brought the afternoon temperature to a pleasant 66F 19C, while the near calm winds made the day as close to ideal as we have had in two months.  And the best part is that the near perfect conditions are expected to prevail for a week.

The fractal cats, always seeking perfection, found it on their shelf in the sunny southwest window.  The humans, realizing that perfection never happens, took the day for what it had to offer. The next FOTD will be posted in 24 hours.  Until then, take care, and I agree with the angry young protesters.  We should abolish poverty.  But does anyone know how we might bring about this utopian dream?

Jim Muth
jimmuth@earthlink.net


START PARAMETER FILE=======================================

A_SeahorseGoesEast { ; time=0:00:24.48-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot2 passes=1 center-mag=0/\
  +0.0000003835126177/419409.6/3.4337
  params=0/90/0/90/-1.747855067330428/0/-1.747855067\
  330428/0 float=y maxiter=32767 inside=255 logmap=99
  symmetry=yaxis periodicity=6
  colors=00010S20U30W40Y50_60a70c80e90gA0iA0kA1lC2mE\
  3nH4oJ4pH4oE4mB4j84g84c84_84W75S75P75L64U53c42m3Lu\
  cOzclLhsHmzDrz9wzBzzBzzzO7LNAQLDVKG_IJdHMiJQjKTjLW\
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  XUSQWQJZOC`oC1E3WM5bU6ia8pi9waJrVTnNajGkf6x_9tbBqe\
  DnhFkkHhnLZpJeqHkqFrqExqPng_eZjXQjYOjYMjYKjYJjYHjY\
  FxR5qVAjYEsfQkcMc`IWYEOVAGS61dv5XU8Q2FP6LO9SNCYMFd\
  LIjKLaOOUSQLWS7aWA`VD_UF_TIZSLYRHfIKaMNYQKZaPWaTTa\
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  95fD7dH8bLA_PBYTDVXET`GRdHJWFCNE5ED0T`1XY1_V1bT1eQ\
  1hO5kLAnJFqGKtEPwBUz9Zx8cwAhv7mu7mt7ms6mr6oq5qp5so\
  5un4wm4xl4zk5zk5zk6zj6vj6rj7mi7mi7mi8mh8mh9mh9mg9m\
  gAmgAmgAmc8m_7mW6mS5mP4mL3lH2rD1xA0eBDOCQ6CaDKaKRa\
  RYaYdadkajraksdltfmuhnvjowlpxnqyprzjszdtz_uzXvz_wz\
  bxzeyzhzzkzznzzqzztzzw000 }

frm:SliceJulibrot2   {; draws most 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=sqr(z)+c
  |z|<=9 }

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