Fractal visionaries and enthusiasts:  

I named today's image "Battle in the Deep".  It could be a picture of a squid and lobster locked in mortal combat, or more likely it could be a glimpse of what goes on in a near-Julia aspect of Seahorse Valley of the (-Z)^(1.5)+C Mandeloid.  But whatever it is, the image rates an 8 both for art and math.

A couple very similar images have already appeared as FOTD's several years ago, which keeps today's rating from being even higher.  But don't be put off by the repeat.  Today's FOTD image is certainly worth the few minutes required to set up and run the parameter file.

The outer shape of two touching circles is a Julia set of 'Seahorse Valley' of the parent Mandeloid.  The jagged tannish arms inside the double circle are part of the Mandeloid Seahorse Valley itself, grossly enlarged and distorted by being sliced at such an extreme angle, which is double rotated only 0.01,0.01 degree from the true Julia orientation of 90,90.

The near-proportional enlargement of the Mandelbrot valley is a four-dimensional thing that happens when a shape with two extended dimensions and two small dimensions is cut by a 2-D slice at an angle very close to the plane of the two extended dimensions, and intersects this plane in only one point.  It's impossible to visualize in 3-D space, where two planes must always intersect in a line and only one dimension can be stretched.

The image may be seen by running the included parameter file or by visiting one or all of the FOTD web sites.

The day here at Fractal central began with rain, which continued until mid-afternoon, leading to a cloudy evening with a temperature of 45F +7C.  The new fractal cat Jasmine, who is now looking more like a cat and less like a kitten, is getting more attention from old fractal cat Nicholas, who is starting to notice that she will soon be a lady cat.  The fractal people have known this for several months.  Their concern is more about work and the current world problems.

The next in the near endless series of FOTD fractals will soon be posted, with many more FOTD's still in the pipeline.  Until whenever, take care, and the world apparently makes sense only on the human scale.  When we start to grapple with the extremely large or small, nothing makes sense at all.  Maybe the mystics and New-Agers are right and everything really is an illusion.

Jim (I'm a Boltzmann brain) Muth
jimmuth@earthlink.net


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

Battle_in_the_Deep { ; time=0:02:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot5 passes=t
  center-mag=-0.288401/0/1.25 params=89.99/0/89.99/\
  75/-0.74074/0.00399/0/0/1.5/0 float=y maxiter=1500
  inside=0 outside=tdis periodicity=0 sound=off
  colors=000A0mA0mA0mA1mB2mC4mD7mEAmFDmGGmHJmIMmJPmL\
  SnNVoPXlRYjT_gVadXcbZe_`gXbiVdkSfmPhnNjoKloIjjHifG\
  hbFgZEfVDeRCcNBbJAaF9`B8_77Z37TC8NK8HS9C_9GXDKVGOT\
  JSRNWPQ_NTcLWaNV_PVYRUWTUUVTSXTQZTO`SMbSKdRIfRGhQE\
  jQCwJDqNDkQEfTE`WFWZFQaRHeNJdJKdFLdCMc8Nc4Oc1Pcf06\
  a9AXHDSPGIVDKWFMWHOXJPXLRYNTYOVZQWZSYZU__Wa_Xb`Zd`\
  `fabhadQq`yqfqieiaecP_bRabTcbVeaXgaZiZaia`jc_jeZjg\
  YjiXjkWjmVjoUjqTjsSjuRjwQjyQjvPktPkrPkoPkmPkkPkiPk\
  fPldPlbPl_PlYPlWPlOXmRTlUPlXLk_HkdBkaEkZHkWKkTNkQP\
  kNSkKVkHYkE_kBbk8ek5hkhE4gC3fA1f90cB2`C4ZE6WF8TH9R\
  IBOKDMLFJNGGOIEQKBRM9SNEULJVKNWJSXIXZH`_Ge`FiaEkbH\
  mbKnbNpcQqcTscWtcYpdWmeVjfUggSihRkiQliPmjNnkMolLom\
  JpnIpoHqoGqnJqnMpnPonSnnVmnYkn`tncynfzjizfdvb_sZWq\
  VRoQNmLIkGEhB9d65YCCcIJnOQkUWjVEhSQdRNZJTUMTTQYZMg\
  cJc_GdWDeSAfP8fL5gH2hE0hJ3eN5bS7_W9X_CUdERhGOlIMjL\
  QiOThRWgU_eWbdZecaibdlafo }

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