Fractal visionaries and enthusiasts:  

Today's image is another 'almost' Julia set.  The parent Julibrot was created by iterating the expression (-Z)^(1.618034)+C.  The area of the image lies deep in the west branch of the valley enclosing the large bud on the northeast shore line of the main bay of the associated Mandeloid.

The image very clearly illustrates the hairline spirals that lie in the Julia sets of the areas just inside Mandelbrot valleys.  The name "Broken Julia Spirals" refers to the spirals on the top side of the grossly enlarged Mandelbrot valley fragment cutting diagonally across the inside of the open area in the image.

These spirals are broken because of the limited resolution of the image, which causes many pixels to totally miss the very narrow body of the spirals and print it as an open area.  This breakup can be eliminated by the process of anti-aliasing, which calculates the image at a higher resolution, slightly blurs the result then shrinks it down.  Unfortunately, the process can be quite time consuming.

The rating of a 7 is FOTD average.  If such images had not been posted so frequently lately, I might have rated the scene as high as an 8.

The calculation time of 7 minutes is a bit excessive.  To save time, I recommend checking one of the FOTD web sites.

Today brought lots of sun to Fractal Central, but the temperature never rose above 30C -1C.  The fractal cat basked in the sun all afternoon, having the best day so far this winter.  The humans passed the very bright day getting organized.

The next FOTD will not be posted before January 20, since I'm going back to Old Fractal Central tomorrow to finish a few things that need to be done.  Until whenever, take care, and since everyone claims to do what is right, why does so much wrong exist in the world?

Jim Muth
jimmuth@earthlink.net


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

BrokenJuliaSpirals { ; time=0:07:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot5 passes=1 periodicity=6
  center-mag=0.10596/0.159292/0.8912656/1/46.75/0
  params=89.8/0/89.8/0/0.3125/0.5702/0/0/1.618034/0
  float=y maxiter=5000 inside=0 logmap=yes
  colors=000B36701812923A33B34C44D55E66F66G77G87H98I\
  98JA9KBALCAMCBNDBOECNFBOECOECPECPEDQEDQEDREEREEREE\
  SEFSEFTEGTEHUEISEJQGKOILMKMKMNIOOGQPFSQEURDWSCXTBY\
  TCbWDgZElaGjcHieIggJfiLdkMcmNaoO`pSYkWWg_UccR_gPWk\
  NSqKNoLOmMOlNOjOPiPPgQPfRPdSQcTQaUQ`VQZVRYWRWXRVYR\
  TZSS_SQ`SPaSNbTMcTKdTJdTLcVNbWPaXR`ZT`_V_`XZbZYc`Y\
  dbXfdWgfVhhUjjUklTlnSnpRorRptQrvPsxOtyOuwNsuNrsNpq\
  NooNnmNlkNkiMigMheMgdMebMd`McZMaXL`VLZTLYRLXPLYNLZ\
  LK_JK`HKaFKaDKbDKbDKbEKcGKdHKeIJeKIeLHeMIeOJePJeRK\
  eSKeTLeVMeWMeXNeZNe_Ob`O``OeUViNamGhq9ou7rw2vyCtqM\
  riVpadnUloHmmMnlQnjUoiYphapfeqeiphoqdmralrZjsWisSg\
  tPfuMduJcvFavC`w9Zz4Xw6Yt7Yr9YoAYlBYjDYgEYdFYbHY_I\
  YYJYZLWZMV_OT_PS`QR`SP`TOaUNaWLbXKbYJb_Hc`GcaFdcDd\
  dCfd9deBbeCaeD_eEZfFXfGWfHUfITfJRgLPgMOgNMgOLhPJhQ\
  IhRGhSGjSFhTFfTFeUFcUEbVE`VEZVEYWEWWDVXDTXDSYDQYDO\
  YCNZCLZCK_CK`CKaCKbCKcCKc }

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