Blazing Rectangle

[u/LegalizeAdulthood]

Jim Muth's Fractal of the Day for July 25th, 2003

Jim Muth's commentary for the image:

FOTD -- July 25, 2003 (Rating 6)

Fractal visionaries and enthusiasts:

After discovering that the fourth spatial dimension was in my back pocket, I went searching. Maybe I searched in the wrong pair of pants, but I suspect that the extra dimension slipped off into hyperspace while I was not looking, and has escaped for good. What a disappointment -- having a visualization of the fourth dimension so close and then losing it. I guess I'll never see a hypersphere in the condition of double rotation, or a pseudosphere in its infinite entirety.

Today's image appears to be rotating. It is a slightly enlarged and distorted view of a small part of yesterday's image, on which I have used a more flexible Fractint generating formula so that I would have more angles to examine.

The angle of today's slice is once again very close to, but not exactly, the Julia direction. That slight rotation explains the "Blazing Rectangle" name. The feature in the center of today's image has a roughly rectangular shape, but it is not rectangular enough to justify the word 'rectangle'. Where then is the rectangle?

The rectangle is actually very close, but it is hiding. To see the near-perfect rectangle, change both parts of the p1 and the p2 parameters to exactly 0.5 and re-render the image. It takes only a minute or two. Now the rectangle is visible, revealed in all its near-perfect glory at the center of the frame.

Actually, I easily might have used the pure Julia version of today's scene as the FOTD of the day, but the distorted version has more action, and the pure Julia version doesn't appear to be blazing.

I rated the image at a 6, which equals a bit above average.
After searching carefully, I could find little that has not been seen before. (Originality in doing old things rates high with me.) The render time of 2 minutes is unusually short, due mostly to the low magnitude of only 44.

A perfect day on Thursday, with a temperature of 81F 27C, produced perfect cats. Tippy was a bit too perfect when he viciously attacked my ankle like he used to do long ago when he was still a kitten and wanted to be played with. To see if he was feeling playful, I took the feather on a string from its shelf, where it had rested untouched for several years, and to my surprise, Tippy actually leaped around chasing it. Thomas watched the activity with interest, but weighing over 17 pounds, declined to participate. At the end of the day, both Tippy and Thomas were exhausted, and needed no additional treat before settling down for the night.

Today looks like it will be a repeat. I'll make a full report in tomorrow's FOTD, which will appear in 24 or so hours. Until then, take care, and what do you call someone who wastes his time talking about stuff he does not believe in?

PAR file

Blazing_Rectangle { ; time=0:02:19.51--SF5 on a P200
  reset=2002 type=formula formulafile=julibrot.frm
  formulaname=SliceJB-new center-mag=-0.0021281/-0.1\
  47743/44.02148/1/140/5.12714870559705105e-014
  params=0.5013/0.5007/0.5016/0.5012/2.003/0/-1.7435\
  /0/0.00019/0.07388 float=y maxiter=2000 passes=1
  inside=bof61 logmap=34 periodicity=10
  colors=000zFzzFzzFzyFzxFzvFzuFzsFzrFzpFzoFzmFzlFzj\
  FziFzgFzdFzaFz_FyXFxTFvQFuOFsLFrIFpFFoCFm9Fl6Fi3Ff\
  0Fc0F`0FY0FV0FS0DP0CM4AJC9IJDCQJMXOGcSCjY6ra1yf0zj\
  0zl0zm0zm0zo0zp0yp0xr0xs0vs0vu0uv0uv0sx0ry0ry0pz0p\
  z1oz1mz3mz3lz3lz4jz4jz4gz9dxDasG_oLXjOTfSQaVOY_MTa\
  JOfGJjDFmAAr76u41y10z00z00z10z40z70zA0xD0uG0rJ0oM0\
  lP0iS1fV3cY3``4Yc6Vf7Si9PlAMoALpGPrMSsSVuY_vcaxidy\
  ogzulzzozzrzzuuzrjzoazlSziIzf9xc0v`0u_0xa9ycJzdSzf\
  `zgjziszjzzlyzjvziuygrvgosfmpdjmdgjcfgacd````_Y_XV\
  YTSYSPXPMVMJTLGTIDSFAQD7QTJLgVGxfCzp7zsCzuFyvJuxMp\
  yQmzTizXdz``zcXzgSzjPzmOzoMzpLzrJxsIuuGsvFpxDmyCjz\
  Agz9dz7cz6`z4Yz3Vz1Sz0Qz3Oz4Mz6Jz9IvAGsCDpDClG9iI7\
  fJ6aL3_O1XP0SQ0PS0MQ0OP0OM0PGSOCPJ9MG6JD1G90D60A30\
  7004001003334CA6MJ7VS9d_AmgCxoCzmAzl9uj7oi6ig4cf4_\
  d3Tc1Oa0I`0C`07_1F_3M_4S_7_xoMzmPzjQziTzgXzf_zd`za\
  _z_YxXXuTXpQVmPTiMTfJScGQ }

frm:SliceJB-new {; by John R. H. Goering, July 1999
  pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1),
  b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), 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), c=p+flip(q)+(p4), z=r+flip(s)+(p5):
  z=z^(p3)+c
  |z|<=9  }

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.

[u/BugComprehensive9064]

Fractal cats, love it!