Fractal visionaries and enthusiasts:  

I began the day with a question -- when a three-dimensional left hand glove is viewed from the fourth dimension, does it appear as a left or a right hand glove?  A few minutes pondering convinced me that the question is meaningless.  In 4-D space both left and right hand 3-D gloves are the same shape.  They simply lie in different positions.  Now on to the important topic -- the fractal for today.

Today's image has something strangely familiar about it.  In fact, this is the name I gave it.  The familiarity arises because the image is actually a view of the familiar Seahorse Valley of the Mandelbrot set.  The unfamiliarity exists because in today's image the valley is viewed in the Oblate orientation, centered at the point -0.6 on the imag(z) axis.  The scenes of this particular orientation bear no resemblance to either the Mandelbrot or the Julia aspects of the valley.

Seahorse Valley is actually a thing with four spatial dimensions, which means it has six mutually perpendicular planes cutting through it, each of which can be translated in an infinity of perpendicular directions.

With such a familiar object as the source of the image, I could give it no rating.  The calculation time of 5 minutes is longer than I would have preferred, but the new view of an old object that will result will make the effort worthwhile.  Those who do not calculate may view the finished image on the web sites.

Thickening clouds and a temperature of 36F +2C made today less than ideal here at Fractal Central.  The forecast of ice and snow later tonight and tomorrow makes the future look even less ideal.  The fractal cat passed the day in the front window, watching the world go by and in the back window, watching the stray cats go by.  The native humans spent the day watching the work go by.

The next FOTD will be posted when the appropriate time has passed.  Until whenever, take care, and let's give our congress a kick in the butt.  Tell them to pass a law requiring that all our silly disagreements be solved.

Jim Muth
jimmuth@earthlink.net


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

Strangely_Familiar { ; time=0:05:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=1 maxiter=27000
  center-mag=0/0/7.466019/1/-36.75/0 params=0/0/90/0\
  /-0.75/0/0/-0.6/2/0 float=y maxiter=27000
  inside=0 logmap=-13 periodicity=0
  colors=000enldmmclmbkmajn`im_hmZglYfkXekWdjVcjUbiS\
  aiQ`hO_gMZgKYfIWfGVeEUdCSdARc9Qc8Pb7Na5Ma5L`4J`4I_\
  3H_3GZ3EY3DY2CX2AX29W28V17V15U14U13T12T23U24U25U26\
  U37U38U39U3AU3BU4CU4DU4EV4FV5GV5HV5IV5JV5KV6LV6MV6\
  NV6OV4OU6PV7QV9RWARWCSWDTXFTXGUYHVYJVYKWZMXZNX_PY_\
  QZ_SZ`T_`U`aW`aXaaZbb_bbaccbdccdcaca`b_ZaYY`WW_UUZ\
  SSYUQZRO_NM_OK_PJ_PK_QK_QL_RN_SP_TQ_US_UU`VV`WX`XZ\
  `Y_`Za`_c``d`af`biaag`bf`be`bc`bb`ba`b``bZ`bZ`cZ`c\
  Z`cZ`cZadWbeRckMipInuKotMptNqtPqtRrtSstUttVtt_nkci\
  cgdWlZOpUGtP8pS9mV9jYAg`AdcAafBZiBWkBTlDUkEVjGWiHX\
  hJYgKZfG_eC`d8ac4bbIcaNd`Re_WfZ_fYdfXhfZl`YfWXaRWX\
  MVSHUNCTI7SD8YJ9bPAgVBl`CqfEpXFpOGlSHiWHf_IccJ`gJY\
  kKVoKSsNZnQdjSjfVpbXvZYsXYpVZnTZkSZhQ_fO_cM_cLYcQW\
  cVVc_TccSchQcmPcqTcmXcj`cgdcdzcazcZzcXzcUzcSzcOzcK\
  zcHzcLzcPzcTzcXzc`zcdzchzc1zz2zz2zz2zz3zz3zz3zz3zz\
  DzzGzzIzzLzzNzzQzzSzzOzzK }

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