Re: [Fractint] Shear Amazement

31 Jul 2003

      The nautibrot6 formula in the .frm file below is evidently of sufficient generality to generate all of the various nautibrot(x) images that were previously posted. So the first thing I want to do is get L'Escargot entered right.

------------------------------parfile-----------------------------

L'Escargot         { ; July 31, '03
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=next.par
  formulaname=nautibrot6 function=conj passes=b
  center-mag=-0.83436/0.180208/0.611899 params=4/1/-1/0
  float=y
  colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\
  zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\
  00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\
  zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\
  zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\
  00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\
  zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\
  zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\
  00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\
  zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\
  zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\
  00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\
  zk0kW0W
  }

-------------------------------endpar-----------------------------

This next image REALLY blows my mind... It's astonishing to me that patterns so strongly associated with the Fibonacci sequence and the golden mean should become utterly predominant, evidently, in a milieu where Feigenbaum's constant usually reigns. Has the former ratio actually entirely supplanted the latter, or do they exert a sort of shared influence, with the fractal perhaps somehow splitting differences between the two? Whatever the case, I about lost track of my time spent cycling diverse color maps through this rather elegant object; the one chosen here is from a recent Lee Skinner par.

------------------------------parfile-----------------------------

Cornucopia         { ; July 31, '03
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=next.frm
  formulaname=nautibrot6 function=exp passes=t
  center-mag=-0.86844/0.124809/0.611899 params=3/-2/-1/0
  float=y
  colors=000000zr1zz1zzC<2>zzz<2>nsjQdrLdtblU<3>Mb8<3>LQ8KM8KJ8<2>\
  I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<\
  4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5\
  _<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0f\
  z0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\
  Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>zzz<3>rw\
  zovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA\
  1NA1<3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5f\
  c0ce7_jFRoNIzb0zj0
  }

-------------------------------endpar-----------------------------

The 'Radiance' image shows that a surprising symmetry is present when a purely imaginary value is assigned to the parameter p1.

------------------------------parfile-----------------------------

Radiance           { ; July 31, '03
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=next.frm
  formulaname=nautibrot6 function=conj passes=b
  center-mag=-2.39562/0.928852/0.2594452 params=0/4/-1/0
  float=y
  colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\
  zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\
  00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\
  zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\
  zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\
  00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\
  zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\
  zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\
  00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\
  zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\
  zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\
  00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\
  zk0kW0W
  }

-------------------------------endpar-----------------------------

This next is a bit whimsical: Save the image as a gif, open it in a small window and drag it about the screen; with the right settings (e.g., 'Show window contents while dragging') and a decent graphics card, you should see some very cool moire effects. This works for most of the others as well.

------------------------------parfile-----------------------------

L'tl_L'es          { ; July 31, '03
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=next.par
  formulaname=nautibrot6 function=conj passes=b
  center-mag=-0.83436/0.180208/0.611899 params=2/1/-1/0
  float=y
  colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\
  zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\
  00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\
  zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\
  zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\
  00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\
  zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\
  zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\
  00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\
  zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\
  zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\
  00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\
  zk0kW0W
  }

-------------------------------endpar-----------------------------

I could not for some reason get this next one to render exactly in the #6 formula, so nautibrot4 is included. (Truly the 'naughtybrots' is what they should be called, since they don't behave at all like proper fractals.) So, OK, go ahead, color-cycle the Hypnoid... I dare ya! (but don't press "Enter" if you do...)

------------------------------parfile-----------------------------

Hypnoid            { ; July 31, '03
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=next.par
  formulaname=nautibrot4 passes=3
  center-mag=+0.98456120553466000/+0.17373634109460730/163.4115
  params=4/1 float=y maxiter=1000 inside=0 outside=fmod
  colors=000CTT<3>8QR7PQ6PP5OP4NO<2>3OO3OP4OP<133>MvpMvpMvq<2>MwqM\
  wqNvp<99>cWc
  }

-------------------------------endpar-----------------------------

------------------------------frmfile-----------------------------

frm:Nautibrot6 {;by Russ Walsmith
  z = 0, c = pixel, k=1, j=p2:
  j=j*(p2)
  k=p1*fn1(k)*j
  z = z^k + c
  z < 1000 }

frm:Nautibrot4 { 
  z = 0, c = pixel, k=1, j=-1:
  j=j*(-1)
  k=p1*conj(k)*j
  z = z^k + c
  z < 1000 }

-------------------------------endfrms----------------------------

Russell Walsmith

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