Fractal visionaries and enthusiasts:  

Today's image shows a slice of a spiral that lies in the Seahorse Valley area of the Z^2+C Julibrot, a fact that is confirmed by the name "The Lost Spiral".  But the image holds no spiral.  Instead, it shows a series of concentric rings which break apart into two separate spirals near the center.

So what is wrong here?  Where is the spiral?  Actually, we are looking at a slice of it.  Everything in the image is a part of the same great spiral, but sliced in an odd direction.  Fractal spirals are four-dimensional things that twist and turn in unimaginable ways, and when sliced in odd directions can produce the most unusual cross-sections.

The full 4-D 'object' that is sliced by today's image does not actually appear on the screen.  It lies in the nearby hyperspace.  The two small spirals at the center are actually two slices of the same hyper-object, which is twisted in 4-D space so that today's image slices through it two times, exactly as a slice through the center of a single donut would produce two apparently separate circles.  The outer rings correspond to the rings produced by a slice through a set of nested spheres.

The image rates a little over a 7.  The plus sign is due to the minor math interest, which adds very little to the artistic worth.

Incidentally, the image has been stretched and skewed to a significant degree to clarify the features.

The coloring detail of the image was created by rendering it with the outside set to 'tdis'.

I would be the first to agree that the calculation time of 7-1/2 minutes is slow.

Have no worry when nothing appears on the screen for a minute or two.  It takes a while for the calculation to reach the rings, which do not intersect the edges of the frame.  All these problems can be avoided however by visiting the web sites.

The day here at Fractal Central began with a very chilly temperature of +5F -15C.  But with clear skies, light winds and an unusually strong sun, it rose to an afternoon high of a rather pleasant freezing.  The fractal cat took full advantage of the sun, spending the entire afternoon on his shelf in the southwest window.  The humans, meanwhile, took it as easy as possible.

The next FOTD will be posted in a minimum of 24 hours, a maximum of who knows what.  Until whenever arrives, take care, and first we have inventions, then the inventions become luxuries, and then the luxuries become one more technology-based necessity that we could not possibly survive without.

Jim Muth
jimmuth@earthlink.net


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

The_Lost_Spiral    { ; time=0:07:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=t
  center-mag=-0.09292496257779437/-0.094383497537425\
  95/104097.2/0.01534/-28.0422538333465177/-74.32609\
  02171528954 params=78.41120639667959/58.8488418225\
  6538/89.81383709219642/-44.26099429303873/-0.7537/\
  0/-0.5/0/2/0 float=y maxiter=3600 inside=0
  outside=tdis periodicity=6 mathtolerance=0.05/1
  colors=000Z8eb7bf6_j6Xn5Ur4Rv3Ow7Qz3Lz9IzEFzKDzPAz\
  V7z_5yb7ye9xhAxkCwnEwqFvtHvwIpqJkkJfeJ``KWVKRPKGGG\
  MKKRONWSRaWUf_Yngkkb`hYQfTFxrRjrSXrTJrU2sZ5rV7qRAq\
  OCpKFoGHoDkaKjbHicFhcCfcAfbEfaIe`Me_QdZUdYYdXacWec\
  UibTmbSqbRucPscOqdNodMmeLkeKjcMkbNl`Pl_QmYRmXTnVUn\
  UWoSXpRYpP_qO`qMarLcrJdsIftGgtFhuDjuCkvBlvJgrRboZY\
  lfThnOeuJbn`7lcAkfDjhGikJhmMgpPfsSeuVdxYcz`YyXSxTM\
  wPGwMDuPAtS8rV5qY3p_4lU4iP5fK5cF5`A9aDDbGHbJKcMOcP\
  SdSQeXVdVZZRaTNcOKcIGcF7cDD`BJR9PG2bI8VKEOMKHJF2NP\
  ARZIVhQapUZqYXraUseStiPumLxwNvpOuiQsbRrWSqQQkTOeWM\
  _ZLVaJPdHJgFDjE8lEiwGdqI_kJVeLQ_NLUJ3JOGOTTSXeWa`X\
  fWXjRYoMYtHZxDZbjiZjkWjmTjoPjqMjsJjtLcuMYvOSwPMxeK\
  XuI5xe3pdCicKbcSWb`PbhIapBaxA`rA_l9_f9Za8ZW8YQ0ZM8\
  YLGYLOYLWXKcXKkXKrXKs_IsaHsdFsfEshCskBsm9so8mn9hm9\
  clAZkAUjBPiBKhCFgCMeFTcHZbJe`LlZNrYPk`NebMZdLTfKMh\
  JGjIJdMMZPPUTROWUJ_XDbV9h }

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

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