[Fractint] 1st Lyapunovs with passes=o...

7 Dec 2004

      The Lyapunov fractal type is one of my favourites.  I attribute this
to being an avid fan of science fiction, and of the "space opera"
feeling that Lyapunovs tend to give me.

I was thrilled a few years ago to discover a version of Lyapunov code
posted to Fractint, because it meant that I could do with it what I
like to do with my favourite fractal types:  modify it, usually by
adding functions here and there.  After much tweaking through a number
of versions, I arrived at several which produced Lyapunov variations
to my liking.  (The choice of a maxiter of 103 is critical to some of
these variations; try 102 for disappoinment, 104 or 105 for some
changes, and higher or lower maxiters for much less interest,
especially with the passes=o mode, see below.)

It took some puzzling through these variations until I reached number
7 before I was rewarded with a version and some parameters for it
which also produced something more than a straight line or two in
passes=o mode.

And now for the main question, related to the latter several of the
pars below:  With this Lyapunov type in passes=o, why can I not zoom
in further than about 1 and still see something being rendered on the
screen?

A further question - sorry, but I've just discovered digital printing
of fractals as actual photographs here in the Republic of Georgia,
maximum size 290 x 465 mm and 300 dpi.  Passes=o, t and possibly other
unusual rendering modes don't work in Disk/Ram Video sizes.  Any
chance of getting this changed?  A large Buddahbrot would look
STUNNING, for example.

Thanks...

Tony Hanmer

Lyapunov2037k      { ; 12 minutes on a 1300Mhz PIII
  reset=2001 type=formula
  formulafile=generalt.frm
  formulaname=Lyapunov02 function=tan/atan
  passes=1
  center-mag=3.19117/3.61002/13.73246/1/90/-3.052882\
  51479236461
  params=0.25/0.5625/0.25/0.5625/0.25/0.5625/10/1.4/\
  1000000/0 float=y maxiter=100 inside=bof60
  outside=mult logmap=yes periodicity=0
  sound=off
  colors=000`00c00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0uW0v\
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  }

Lyapunov2039e      { ; 18 minutes on a 1300Mhz PIII
  reset=2001 type=formula
  formulafile=generalt.frm
  formulaname=Lyapunov02 function=log/sin
  passes=1 center-mag=2.63575/1.93804/0.4813439
  params=0.5/0.5625/0.5/0.5625/0.5/0.5625/10/1.4/100\
  0000/0 float=y maxiter=200 inside=bof60
  outside=mult logmap=yes periodicity=0
  sound=off
  colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\
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  }

Lyapunov2039h      { ; 10 minutes on a 1300Mhz PIII
  reset=2001 type=formula
  formulafile=generalt.frm
  formulaname=Lyapunov02 function=log/sin
  passes=1
  center-mag=-1.37365/-1.43806/1.373246/1/180
  params=0.5/0.5625/0.5/0.5625/0.5/0.5625/10/1.4/100\
  0000/0 float=y maxiter=100 inside=bof60
  outside=mult logmap=yes periodicity=0
  sound=off
  colors=000L00N00P00000T00W00Y00Z00`00c00e80<2>jE0k\
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  }
Lyapunov2041       { ; 20 minutes on a 1300Mhz PIII
                     ; Subtle differences from normal Lyapunovs.
  reset=2001 type=formula
  formulafile=generalt.frm
  formulaname=Lyapunov02 function=log/sin
  passes=1
  center-mag=-1.56796/-1.4745/5.628057/1/180
  params=0.5/0.5625/0.5/0.5625/0.5/0.5625/10/1.4/100\
  0000/0 float=y maxiter=200 inside=bof60
  outside=mult logmap=yes periodicity=0
  cyclerange=104/104 sound=off
  colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\
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  }

Lyapunov7007       { ; 13 minutes on a 1300Mhz PIII
                     ; Boring, but the start of passes=o play.
  reset=2001 type=formula
  formulafile=generalt.frm
  formulaname=Lyapunov07 function=asin/exp
  passes=1 center-mag=0/0/0.06666667
  params=0.66/3/1/0.5/0.35/100/10/1.4/1000000/0
  float=y maxiter=105 inside=zmag outside=255
  logmap=yes sound=off
  colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\
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  }

Lyapunov_o7001     { ; 12 minutes on a 1300Mhz PIII
                     ; Passes=o; can't zoom past 1...
  reset=2001 type=formula
  formulafile=generalt.frm
  formulaname=Lyapunov07 function=acos/cos
  passes=o
  center-mag=-1.77636e-015/1.77636e-015/0.719912
  params=0.66/3/1/0.5/0.35/100/10/1.4/1000000/0
  float=y maxiter=103 inside=zmag outside=summ
  logmap=yes sound=off
  colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\
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  }

Lyapunov_o7002     { ; 12 minutes on a 1300Mhz PIII
                     ; Passes=o; can't zoom past 1...
  reset=2001 type=formula
  formulafile=generalt.frm
  formulaname=Lyapunov07 function=acosh/cos
  passes=o center-mag=1.67602/0/0.819912
  params=0.66/3/1/0.5/0.35/100/10/1.4/1000000/0
  float=y maxiter=103 inside=zmag outside=summ
  logmap=yes sound=off
  colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\
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  }

Lyapunov_o7003     { ; 12 minutes on a 1300Mhz PIII
                     ; Passes=o; can't zoom past 1...
  reset=2001 type=formula
  formulafile=generalt.frm
  formulaname=Lyapunov07 function=acosh/cos
  passes=o center-mag=1.67602/0/0.819912
  params=0.66/3/1/0.5/0.35/100/10/1.4/1000000/0
  float=y maxiter=104 inside=zmag outside=summ
  logmap=yes sound=off
  colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\
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  }

Lyapunov_o7006     { ; 12 minutes on a 1300Mhz PIII
                     ; Passes=o; can't zoom past 1...
  reset=2001 type=formula
  formulafile=generalt.frm
  formulaname=Lyapunov07 function=flip/log
  passes=o
  center-mag=-1.77636e-015/1.77636e-015/0.719912
  params=0.66/3/1/0.5/0.35/100/10/1.4/1000000/0
  float=y maxiter=103 inside=zmag outside=summ
  logmap=yes sound=off
  colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\
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  }

frm:Lyapunov02 {;"standard" Lambda-Formula,
            ; altered by Anthony Hanmer 2001
   ;abMax = Length of ab-string in the form of: 2^LENGTH - 1
   ;periodicity=no, inside=zmag, outside=ColorNumber
   ;
   ;p1 ... Starting Value / abMax
   ;p2 ... ab-String / Scaling Exponent
   ;p3 ... Scaling Factor / Filter Cycles
   ;p4 ... Zero Level / Divergence Result
   ;p5 ... Bailout
   ;
   x = real(p1), max = imag(p1), ab = real(p2)
   se = imag(p2), sk = real(p3)
   n = imag(p3), z = imag(p4)
   mxi = n + 1 - maxit
   sum = 0:
     n = n - 1
     ab = 2*ab
     IF (ab > max)
       ab = ab - max
       c = imag(pixel)
     ELSE
       c = real(pixel)
     ENDIF
     IF (n < 0)
       sum = sum + fn1(abs(c*(1-2*x)))
       IF (n <= mxi && sum < p4)
         z = fn2(sum/n)^se*sk
       ENDIF
     ENDIF
     x = c*x*(1-x)
   p5 >= abs(x)
   }

frm:Lyapunov07 {;"standard" Lambda-Formula,
            ; altered by Anthony Hanmer 2001
   ;abMax = Length of ab-string in the form of: 2^LENGTH - 1
   ;periodicity=no, inside=zmag, outside=ColorNumber
   ;
   ;p1 ... Starting Value / abMax
   ;p2 ... ab-String / Scaling Exponent
   ;p3 ... Scaling Factor / Filter Cycles
   ;p4 ... Zero Level / Divergence Result
   ;p5 ... Bailout
   ;
   x = real(p1), max = imag(p1), ab = real(p2)
   se = imag(p2), sk = real(p3)
   n = imag(p3), z = imag(p4)
   mxi = n + 1 - maxit
   sum = 0:
     n = n - 1
     ab = 2*ab
     IF (ab > max)
       ab = ab - max
       c = imag(pixel)
     ELSE
       c = real(pixel)
     ENDIF
     IF (n < 0)
       sum = fn2(sum) + (abs(c*(1-2*x)))
       IF (n <= mxi && sum < p4)
         z = fn1(sum/n)^se*sk
       ENDIF
     IF (n > 0)
     sum =  fn1(sum)
     ENDIF
     ENDIF
     x = fn1(c*x*(1-x))
   p5 >= abs(x)
   }