Fractal visionaries and enthusiasts:  

Today we return to a type of fractal I was working with quite a few years ago.  The image is a scene in a perturbed Z^2+C Mandelbrot set.  It is located at the edge of the inside of a minor bud on the southwest shore line of the main bay.

The half obscured blue and white buds in the background are actually part of the classic M-set itself.  The reddish spiral arms in the foreground are the trails of points that have escaped before being trapped in the remnants of the buds.

What we have here is a demonstration that the points in a perturbed M-set, if they do not escape first, will ultimately fall into the same orbits as points that originate at 0,0.  The points in today's image for example originate at 0.7,0.2.

I named the image "Ghostly Attractor" because of the ghost buds and also because despite my skeptical nature, I find ghosts quite interesting and not at all unlikely to be 'real'.

The art rates a 7, since the image is not all that great.  The math rates a 4.  After all, how unique can the math of the Mandelbrot set be at this point of the fractal era.

The calculation time of just under 2 minutes is slow for a scene in the Mandelbrot set.  The culprit is the maxiter of 250000, which slows things down in the lower part of the image, but this maxiter was necessary to get full definition in the ghost buds.  The web sites can greatly cut the length of the wait to see the image however.

Today here at Fractal Central, which is the almost-real central headquarters of the FOTD, spring gave signs that it was finally ready to arrive.  The brilliant sun, gentle winds, puffy white clouds and temperature of 61F 16C was just what any doctor would have ordered.  The fractal cats soaked up all the sun they could find, and chased each other up and down the hallway when the sun was at the wrong angle, while the fractal humans made the most of the pleasant conditions.

The next FOTD will be posted before too long.  Until that moment of truth arrives, take care, and try to avoid the cognitive instability that arises when we assume something that undermines the argument that justified our assumption in the first place.

Jim Muth
jimmuth@earthlink.net


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

Ghostly_Attractor  { ; time=0:01:50.00 SF5 at 2000MHZ
  reset=2004 type=mandel passes=1 center-mag=-0.5769\
  768387/-0.4519133225/5218/1/146.7/0 params=0.7/-0.2
  float=y maxiter=250000 inside=0 logmap=200
  colors=000yi0xh0xh0xh0xh0uf0re0oc0lb1i`3h_6eY8bWB_\
  VDWUGVSHSRKPRMMPPJOSHMUEKWBJY8H`4Gb3Ee0Df0Bi09k08m\
  08o0Bp6DrEGsMHuUJv`MxhOyoRzvSzzUzzVzzVzzVyzVxzVvyV\
  uyWsyWrxWpxWpxWovWmvYlWYkWWiWUhWRfWReWKeWKcWDbWD`W\
  D_WDYWEWWEVWEUWEUWESWERWGPWGOWGMWGKWIJWKHYHHYHG`FE\
  `CD`FB_C9_98_66Y94YE4WH3WE1WI0V80VA0V80UI0U80UI0S6\
  0SH0S60RH0R60RH1P43PF4P66PF8O89OFBO8BMEDM9EMJFKBFK\
  JGKBGKHHJ9JJHKJ9MHHNH9PHFPG8QGFRG8TGFVE6WEGYE7ZDG`\
  D9aDJcDBdBLfBBfBMg9Fh9Nj9Ik8Om8Jn8Np8Jq6Js6Ht6Hu4H\
  u6Hu6Ju4Ku6Mu6Ou6Pv6Rv6Sv6Uv6Vw6Ww6_w8bx6ex6hx6ky6\
  my6py6ry6sz6uz6vz6xz6yz4yz4yz4yz4yz4yz4yz8yzByzEyz\
  HyzKyzOyzRyzUyzWyz_yzbzzezzhzzkzzkzzkzzkzzkzzkzzkz\
  zkzzkzzkzzkzzkzzkzzkzzkzzkzzkzzyzzyzzyzzyzzyzzyzzy\
  zzyzzyzzyzzyzzyzzyzzyzzyzzyzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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