ftp.xmission.com/2014.06.ftp.xmission.com.tar/ftp.xmission.com/pub/lists/fractint/archive/v01.n436

Internet Message Format | 2000-01-13 | 44KB

From: [e-mail] (fractint-digest)
To: [e-mail]
Subject: fractint-digest V1 #436
Reply-To: fractint-digest
Sender: [e-mail]
Errors-To: [e-mail]
Precedence: bulk


fractint-digest        Friday, January 14 2000        Volume 01 : Number 436




----------------------------------------------------------------------

Date: Tue, 11 Jan 2000 00:06:11 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 11-01-00 (Memories) (c)

FOTD -- January 11, 2000

Fractal enthusiasts and visionaries:

Today I had an impure thought.  I found a midget 'brot with a
rather unusual looking outside pattern.  When I saw that
pattern, the devil put an impure thought into my head.  I
wondered what the midget would look like with one of the outside
coloring options other than the purist "iter".

Not really to my surprise, I found that the atan option gave a
quite interesting result, and a few minutes trying different
color palettes produced the striking blue image that is today's
FOTD.

The image reminds me of some vague forgotten thing that happened
long ago.  It's really a mood more than a memory, but the name
"Memories" is the one I settled on.

The parameter file renders in a fast 1-1/2 minutes -- about the
same time it would take to go to:

          <alt.binaries.pictures.fractals>

and download the JPEG file from there, or go to:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and download the image.

The fractal weather was changeable today.  A steady rain all
morning was followed by an almost instant clearing just after
noon.  The temperature of 50F (10C) was well above average but
still not warm enough for the cats, who spent the day by their
favorite radiator.

The philosophy is cooking, but it's not yet finished.  Stay
tuned to see what comes from the oven.  And while the philosophy
is chancy, the fractal for tomorrow is virtually certain.  Until
then, take care and enjoy yourself.


Jim Muth
[e-mail]


START FORMULA==============================================

MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END FORMULA================================================

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

Memories           { ; time=0:01:44.80 on a p200, SF5
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-1.50898713231029800/-2.23909609663967200\
  /426.6895/1/-72.499 params=-2/-2/1/0.9/0/11 float=y
  maxiter=500 bailout=25 inside=0 outside=atan logmap=6
  symmetry=none periodicity=10
  colors=000ej`<3>diadiadiabia<5>aha`ha`hb`fb<2>_fb_fb\
  Yfb<3>XebXeb_eeYedXdbVbaVdaUb`Tb_Ta_R`YQ`XQ_XO_VNYUL\
  XTLXTJVRHUQHUQGTOERNERNCQLAQJ9OH9NH6NG5LE5JE2JC0HA0G\
  A0G90E60C00E50E60E9<3>0EG0EH0EL0EN0EO2EQ<2>2EU5EV5EY\
  <3>6Eb6Ed6Ee9Ef9Eh9Gj<2>AGnAGoCGpCGqCGrCGtEGvEGwEGxE\
  GyGGz<5>HGzHGzJGz<3>JHzJHzJJzJJzJJzJLzJLzJNz<3>JOzJO\
  zJQz<2>JRzJRzJTz<5>JVzJVzJXz<2>JYzJYzJ_z<7>JbzJbzJbz\
  Jdz<4>JfzJfzJfzJhz<9>JlzJlzJlzJnz<12>JszJszJszJtzJtz\
  Jvz<8>JyzJyzJzz<4>JzzJzzJzz<3>JzzsrX<8>ppYppYppY<2>o\
  oYnoYno_no_no_lo_<3>kn_kn_kn_jl_<3>il`il`ik`hk`hk`hk\
  `fk`<2>fj`
  }

END PARAMETER FILE=========================================

START 20.0 PAR-FORMULA FILE================================

Memories           { ; time=0:01:44.80 on a p200, SF5
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-1.50898713231029800/-2.23909609663967200\
  /426.6895/1/-72.499 params=-2/-2/1/0.9/0/11 float=y
  maxiter=500 bailout=25 inside=0 outside=atan logmap=6
  symmetry=none periodicity=10
  colors=000ej`<3>diadiadiabia<5>aha`ha`hb`fb<2>_fb_fb\
  Yfb<3>XebXeb_eeYedXdbVbaVdaUb`Tb_Ta_R`YQ`XQ_XO_VNYUL\
  XTLXTJVRHUQHUQGTOERNERNCQLAQJ9OH9NH6NG5LE5JE2JC0HA0G\
  A0G90E60C00E50E60E9<3>0EG0EH0EL0EN0EO2EQ<2>2EU5EV5EY\
  <3>6Eb6Ed6Ee9Ef9Eh9Gj<2>AGnAGoCGpCGqCGrCGtEGvEGwEGxE\
  GyGGz<5>HGzHGzJGz<3>JHzJHzJJzJJzJJzJLzJLzJNz<3>JOzJO\
  zJQz<2>JRzJRzJTz<5>JVzJVzJXz<2>JYzJYzJ_z<7>JbzJbzJbz\
  Jdz<4>JfzJfzJfzJhz<9>JlzJlzJlzJnz<12>JszJszJszJtzJtz\
  Jvz<8>JyzJyzJzz<4>JzzJzzJzz<3>JzzsrX<8>ppYppYppY<2>o\
  oYnoYno_no_no_lo_<3>kn_kn_kn_jl_<3>il`il`ik`hk`hk`hk\
  `fk`<2>fj`
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Tue, 11 Jan 2000 02:16:06 EST
From: [e-mail]
Subject: Re: (fractint) New ! Improved ! The Franktal Gallery is back !

In a message dated 00-01-09 13:21:28 EST, you write:

<< Subj:     (fractint) New ! Improved ! The Franktal Gallery is back !
 Date:  00-01-09 13:21:28 EST
 From:  [e-mail] (Fliguer, Miguel)
 Sender:    [e-mail]
 Reply-to:  [e-mail]
 To:    [e-mail] ('[e-mail]')

 Hola !

 The Franktal Gallery is back !!  It has been extensively
 <snip>
 I'll be glad if ONE of you could repost this message
 to the fractal-art mailing list. Thanks in advance !

 Regards,
 Miguel Fliguer
 Buenos Aires. Argentina
  >>
(***** I"ve forwarded it to the Fractal-art list. Congrats on your gallery,
can't wait to play with the sound pars and see the spirals of which Gumbycat
spoke!
~ren

- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Tue, 11 Jan 2000 02:27:49 EST
From: [e-mail]
Subject: (fractint) 3 cool pars ~

 Here are a few I've enjoyed running across recently,....hope you enjoy as
well.

 Jim Weaver
__________________________________________________________

pkpeaks.gif        { ; image(c)2000 Jim Weaver
  reset=1960 type=formula formulafile=fractint.frm formulaname=ok-36
  function=cotan/cosxx/cosh/cosxx passes=t
  center-mag=1.85462/1.9603/17.86519/1/105 params=0.2/0/0/0 float=y
  maxiter=25 inside=bof60 outside=atan
  colors=D7LC05<21>50UA5WC7WE9X<6>MH_NI_NJ`<5>SNaSObTObTPbUPb<14>aXeaYfaYf\
  bYf<32>njkkjn<23>mqumrvlps<2>gjjeggcef<16>3EI0CG0DH<4>0IJ0JK1LL1NL<5>0ZK\
  0XK0VK<7>02C63C<6>YPI<4>rhAreAqaAqZB<16>C6E20C<3>BAIDCJDBJDAKD8KD5M<22>p\
  ps<17>C04
  }

ok20eps9.gif       { ; image(c)2000 Jim Weaver
  reset=1960 type=formula formulafile=fractint.frm formulaname=OK-20
  function=sin/atan passes=t
  center-mag=-6.86666/-1.29674e-013/0.1440395/1/-90 params=100/0
  float=y maxiter=125 inside=startrail invert=1/-0.1/0 decomp=256
  periodicity=0
  colors=000ozC<2>zz0<15>z1z<15>000<8>0N00Q00T00W00Z0<2>0f0<15>zz0<15>zzz<\
  15>000<12>TN0WO0YQ0`S0aU0<14>zz0<14>jB0i70f70<14>000<15>S5N<15>zz0<14>ZZ\
  8XX8VW8TU8RS8<2>LM6JK6HI6FG6DF5<2>795574354033077<13>4zz<11>kzG
  }

3rdCoast.gif       { ; image(c)2000 Jim Weaver
  reset=1960 type=mandel(fn||fn) function=log/flip passes=t
  center-mag=+1.60533291452199800/-1.33498883875210200/1.18619/1/45
  params=0/0/0.7541600000000001 float=y maxiter=255 inside=bof60
  decomp=256 periodicity=0
  colors=000700<11>`00c00d44<13>zzz<3>snNukDsh3qe0<2>kX0aU0<9>I00<8>000300\
  000003005<5>D0KF0MJ0P<3>Q0ZS0`U2cW4d<2>aGhcKieMkgOmiWokYpmbqoesqjusovupw\
  xvyzzzyvxwpuvosujqseoqbmpYkoWimOgkMeiKc<2>f8Yd4Wc2U`0S<4>R0IP0GN0GL0C<4>\
  B02900700500005<13>00c<15>zzz<15>EEcBBa88Z<2>00S<9>003000022<14>0cc<15>z\
  zz<15>0c0<14>030000200500
  }


- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Tue, 11 Jan 2000 15:52:57 -0800
From: "Dave Hershey (Volt Computer)" <[e-mail]>
Subject: RE: (fractint) Pentium 700

The old MODE command might work.  However, FRACTINT may take control of the
screen mode from DOS and put it back to a text screen.

- -----Original Message-----
From: Jim Shaffer, Jr. [mailto:[e-mail]]
Sent: Sunday, January 09, 2000 3:51 PM
To: [e-mail]
Subject: Re: (fractint) Pentium 700


> I don't "feel" it does. I know it does. I blew the horizontal output
> transistor in a monitor *twice* because I had learned FractInt's keyboard
> controls sufficiently to do about one mode switch per second, sustained
for
> a couple of minutes.

Is there some way that DOS can be made to use a different screen mode than
640x480 for its display, eliminating the need to switch modes between the
control screen and the display screen?

- --
Message to France: Sterilize fascists, not pit bulls.



- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Tue, 11 Jan 2000 17:11:15 -0700
From: Phil McRevis <[e-mail]>
Subject: Re: (fractint) Pentium 700

In article <[e-mail]>,
    "Dave Hershey (Volt Computer)" <[e-mail]>  writes:

> The old MODE command might work.  However, FRACTINT may take control of the
> screen mode from DOS and put it back to a text screen.

It does.  Fractint forces a mode switch between text and graphics mode
everytime it wants to alternate between showing graphics and text.
I'm afraid there's no workaround, the code just has to be changed.
- --
<http://www.xmission.com/~legalize/>    Legalize Adulthood!
    ``Ain't it funny that they all fire the pistol,
      at the wrong end of the race?''--PDBT
[e-mail]    <http://www.thewho.net>

- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Wed, 12 Jan 2000 01:39:29 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 12-01-00 (Dancing Mandelbrot) (c)

FOTD -- January 12, 2000

Fractal enthusiasts and visionaries:

Today's fractal shows how much can be done with how little.  It
is a slice through the Seahorse Valley area of the Julibrot, cut
at a remote angle which is impossible to imagine.  The image was
calculated with the under-used ranges and banding features of
Fractint in effect.

There are a grand total of 13, (count them), colors in the
picture.  That is all.  And this in an era where the number of
colors is counted in the tens of millions.  I named the picture
"Dancing Mandelbrot" when I noticed the tortured, stretched and
twisted foreground elements throughout the scene.

The formula by John Goering was posted to the Fractint list a
few months ago.  It's the only formula I am aware of that
actually draws every possible orientation through the four-
dimensional Julibrot figure, though due to the limit of six
variable parameters in Fractint's type=formula fractals, it
lacks the ability to assign a non-zero starting value to Z.

The attached parameter file renders in 3 minutes -- just slow
enough to make a download of the image the better choice.  The
GIF image may be found on Usenet at:

          <alt.binaries.pictures.fractals>

and on the web at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

The fractal weather was quite interesting today.  A clear
sunrise was followed by an unexpected thunder-storm at 11am,
which produced winds of 62mph (100kph).  This was followed by a
sunny afternoon, interrupted by a second squall at 4pm.  It
finally cleared for good at sunset.  All the wind and the
temperature of 48F (9C) kept the fractal cats indoors snuggled
by their radiator.

It was also a good day for philosophy.  My misguided musings
were posted earlier to the Philofractal list.  And now it's time
to shut the shutters, feed the cats and call it a night.  Until
then, take care, and it's a night!


Jim Muth
[e-mail]


START FORMULA==============================================

SliceJB {; 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)+p3, z=r+flip(s):
  z=z*z+c
  |z|<=9
  }

END FORMULA================================================

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

Dancing_Mandelbrot { ; time=0:03:13.16 on a p233, SF5
  reset=2000 type=formula formulafile=julibrot.frm
  formulaname=SliceJB passes=t
  center-mag=-0.449174/-0.139865/7.839261/3.5684/-146.\
  645/17.882 params=0.39/0.39/0.39/0.39/-0.75/0
  float=y maxiter=32767 bailout=25 inside=13
  logmap=25 symmetry=none periodicity=10
  ranges=0/-1/135/140/150/165/195/235/290/390/565/1600\
  /32767
  colors=000GA0KPUZNc<2>gXlj`omer<2>vuxzwzZKm000<240>0\
  00
  }

END PARAMETER FILE=========================================

START 20.0 PAR-FORMULA FILE================================

Dancing_Mandelbrot { ; time=0:03:13.16 on a p233, SF5
  reset=2000 type=formula formulafile=julibrot.frm
  formulaname=SliceJB passes=t
  center-mag=-0.449174/-0.139865/7.839261/3.5684/-146.\
  645/17.882 params=0.39/0.39/0.39/0.39/-0.75/0
  float=y maxiter=32767 bailout=25 inside=13
  logmap=25 symmetry=none periodicity=10
  ranges=0/-1/135/140/150/165/195/235/290/390/565/1600\
  /32767
  colors=000GA0KPUZNc<2>gXlj`omer<2>vuxzwzZKm000<240>0\
  00
  }

frm:SliceJB {; 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)+p3, z=r+flip(s):
  z=z*z+c
  |z|<=9
  }

END 20.0 PAR-FORMULA FILE==================================


- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Thu, 13 Jan 2000 00:47:20 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 13-01-00 (One and Three) (c)

FOTD -- January 13, 2000

Fractal enthusiasts and visionaries:

I named today's picture "One and Three" because it is part of
the fractal that results when Z is added to 3(Z^3), and a
critical plane is drawn.  The parent fractal is an interesting
Mandeloid rotated 90 degrees CW, so that west is down.

The parent fractal has many interesting areas filled with
midgets unlike any that appear in the classic M-set.  Today's
midget lies in an entirely new valley that appears well east of
the East Valley area, in an area that is totally featureless in
the classic M-set.

The pattern around the midget has traces of both the brain-like
features of the East Valley area and the spiky features of the
tip of the Negative tail, but they are mixed together into an
entirely new pattern.

The parameter file runs in 9 minutes, which is slow enough to
cause one to run to the internet to download the JPEG image file
from:

          <alt.binaries.pictures.fractals>

or from:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

The fractal weather today was sunny and mild.  The afternoon
temperature of 50F (10C) was comfortable enough to lure the
fractal cats onto the SW facing porch for a half hour of sun.

The weather was also great for philosophizing, and I did a lot
of it during the afternoon.  But my ideas are still disordered
and it will take a day or two to get them organized.

While I'm organizing my thoughts, I'd best shut down the fractal
shoppe and call it a day.  Until next time, take care, and how
would you like a series of FOTD's on the fourth and higher
dimensions?


Jim Muth
[e-mail]


START FORMULA==============================================

MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END FORMULA================================================

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

One_and_Three      { ; time=0:09:06.40 on a p200, SF5
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+0.01922126030193131/+0.31616619714983010\
  /177601.2/1/112.499 params=1/1/3/3/0/0 float=y
  maxiter=1400 bailout=25 inside=0 logmap=122
  symmetry=none periodicity=10
  colors=000LDTLDT<2>OJaPLdPPgOUj<3>KkaJp_JtY<3>SdaUab\
  XYc<3>dJg<3>oQm<3>hWZfYWdZS<3>ZdE<5>QQ9ON8NL7<3>HB4K\
  96<3>K2CK1DK3H<3>K8UK9XKA_IBb<3>3Go0Hr5Kn<7>afMehJik\
  F<3>yv1<3>Xe8Qa9JYBCUC<9>9OM9NN9NO<3>8LS<3>ahdingpsj\
  <5>iw`gwZfxX<3>bzR<3>XsfWrjaW3<9>lVImVJnVL<3>rVQQyY<\
  5>De`Aaa8Za<3>0Mc<9>9IV9HUAHT<3>DGQT9Gg36<3>crp<3>Po\
  _LnWInSEmOBmKKhYTcpaZq<3>T`uRavPawNaxPby<3>hdzmdzrdz\
  wazz_z<4>zQz<3>zWzwXz<2>h`zcbz`czZdz<2>bhz<3>PdzMczJ\
  cz<3>H_zHZzGYz<2>FVzFVzHXz<8>VmzR5z
  }

END PARAMETER FILE=========================================

START 20.0 PAR-FORMULA FILE================================

One_and_Three      { ; time=0:09:06.40 on a p200, SF5
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+0.01922126030193131/+0.31616619714983010\
  /177601.2/1/112.499 params=1/1/3/3/0/0 float=y
  maxiter=1400 bailout=25 inside=0 logmap=122
  symmetry=none periodicity=10
  colors=000LDTLDT<2>OJaPLdPPgOUj<3>KkaJp_JtY<3>SdaUab\
  XYc<3>dJg<3>oQm<3>hWZfYWdZS<3>ZdE<5>QQ9ON8NL7<3>HB4K\
  96<3>K2CK1DK3H<3>K8UK9XKA_IBb<3>3Go0Hr5Kn<7>afMehJik\
  F<3>yv1<3>Xe8Qa9JYBCUC<9>9OM9NN9NO<3>8LS<3>ahdingpsj\
  <5>iw`gwZfxX<3>bzR<3>XsfWrjaW3<9>lVImVJnVL<3>rVQQyY<\
  5>De`Aaa8Za<3>0Mc<9>9IV9HUAHT<3>DGQT9Gg36<3>crp<3>Po\
  _LnWInSEmOBmKKhYTcpaZq<3>T`uRavPawNaxPby<3>hdzmdzrdz\
  wazz_z<4>zQz<3>zWzwXz<2>h`zcbz`czZdz<2>bhz<3>PdzMczJ\
  cz<3>H_zHZzGYz<2>FVzFVzHXz<8>VmzR5z
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Thu, 13 Jan 2000 23:39:35 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 14-01-00 (What is Wrong?) (c)

FOTD -- January 14, 2000

Fractal enthusiasts and visionaries:

When I first saw today's fractal, I noticed something strange
about it.  It didn't look quite right.  Then I realized that
something is seriously wrong with the midget in today's picture.

The problem is that the midget has six elements around it in the
outer ring and 12 elements in the inner ring.  This would not be
strange were it not for the fact that the midget is a quadratic
midget, and around all quadratic midgets the elements are
arranged in rings consisting of increasing powers of two.

In my experience, this is unheard of.  All baby brots of order-2
have 2, 4, 8, 16, etc, elements surrounding them, the number
doubling to infinity as the edge of the midget is approached.

The formula behind today's fractal subtracts 0.4Z^(2.5) from Z
before adding C.  My suspicion is that the six elements are
actually 6.25 elements -- a part of the series 2.5, 6.25,
15.625 etc., which would be implied by the Z^2.5 part of the
formula.  But if this is so, where are the discontinuities that
would be expected from a fractional power of Z?  And that inner
ring has 12, not 15.625 elements.

Being a mathematical genius of only modest proportions, I have
no idea of what is going on in this picture, but whatever it is,
it makes a curious picture which is interesting for its
mathematical more than than its artistic merit.

I have named the picture "What is Wrong?" since that is the
question I asked myself when I counted the six obvious elements
around the midget.  Luckily, it will not take too long to view
the problem.  The parameter file calculates in 5-1/2 minutes and
the image downloads in less than half the time.  That image can
be found posted to:

          <alt.binaries.pictures.fractals>

and to:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

The fractal weather was sunny and warm in the morning, with a
noontime temperature of 60F (15.5C), which drew the fractal cats
outdoors.  But it turned sharply colder in the afternoon, and
now at 10:30pm, the fractal thermometer reads 27.8F (-2.3C), and
the cats are snug by their radiator.

Unfortunately, the philosophy remains disorganized, but I'll try
again tomorrow to get it into presentable shape.  If I don't get
my philosophy organized, I'll tell about a four-dimensional man
who has the task of painting the walls of his four-dimensional
room.  Until then, take care, and if you're north of the 30th
parallel, keep warm.  Otherwise, don't lose your cool.


Jim Muth
[e-mail]


START FORMULA==============================================

MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END FORMULA================================================

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

What_is_Wrong      { ; time=0:05:28.78, SF5 on a p200
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+2.09756323075028500/+0.00001748165762026\
  /446531/1/9.999 params=-0.4/2.5/1/1/0/0 float=y
  maxiter=1500 bailout=25 inside=0 logmap=96
  symmetry=none periodicity=10
  colors=000565<7>C4CD4DE3D<2>H3GI2HH2IH2JH2J<10>IFUIG\
  VIIW<2>ILZIM_INZIMZGLW<2>DCMC9GB77<6>L`KNdMOiN<3>TyU\
  <8>EqaCpaAob<3>4le7kfIjfMjf<3>VgfXffZfe<7>n`Yp`Xr_W<\
  2>xYTzYSz_Qz`OzaQ<2>qdSneSkfUhgSehR<5>YnHXoFWpE<2>Ts\
  9St8RsB<13>NlkNlmNkp<2>MjxMjzNiv<6>Pi_PiWPiT<2>QiJQi\
  GRgH<9>ZTI_SI`QIaPIbNIbMI<17>kMfkMhlMi<2>mMmmMnlLl<3\
  >iIpiIqhJr<3>fNveOwdPxdQycRz<4>`_z`az_cz<3>ZkzZmzYoz\
  YqzYszXuzXvz<15>WwzWwzWwz<2>WwzWwzYwz<8>gwz
  }

END PARAMETER FILE=========================================

START 20.0 PAR-FORMULA FILE================================

What_is_Wrong      { ; time=0:05:28.78, SF5 on a p200
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+2.09756323075028500/+0.00001748165762026\
  /446531/1/9.999 params=-0.4/2.5/1/1/0/0 float=y
  maxiter=1500 bailout=25 inside=0 logmap=96
  symmetry=none periodicity=10
  colors=000565<7>C4CD4DE3D<2>H3GI2HH2IH2JH2J<10>IFUIG\
  VIIW<2>ILZIM_INZIMZGLW<2>DCMC9GB77<6>L`KNdMOiN<3>TyU\
  <8>EqaCpaAob<3>4le7kfIjfMjf<3>VgfXffZfe<7>n`Yp`Xr_W<\
  2>xYTzYSz_Qz`OzaQ<2>qdSneSkfUhgSehR<5>YnHXoFWpE<2>Ts\
  9St8RsB<13>NlkNlmNkp<2>MjxMjzNiv<6>Pi_PiWPiT<2>QiJQi\
  GRgH<9>ZTI_SI`QIaPIbNIbMI<17>kMfkMhlMi<2>mMmmMnlLl<3\
  >iIpiIqhJr<3>fNveOwdPxdQycRz<4>`_z`az_cz<3>ZkzZmzYoz\
  YqzYszXuzXvz<15>WwzWwzWwz<2>WwzWwzYwz<8>gwz
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Fri, 14 Jan 2000 11:48:16 GET
From: "Tony \(Anthony\) Hanmer" <[e-mail]>
Subject: (fractint) Colour Map Recognition

Greetings,
I'm wondering if there is any automated way in (or outside) Fractint of
scanning fractal gifs and comparing their colour maps to existing ones - for
either an identical match or the same map but rotated.  Maybe this sounds
lazy, but my collection of colour maps is about 1200 in size...  I know that
one can save colour maps as text and manually read them in a text editor -
I'm thinking of something much faster.  Any ideas?

Tony Hanmer
Tbilisi, Republic of Georgia
______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com


- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Fri, 14 Jan 2000 10:54:31 +0100
From: "Martin Rodenberg" <[e-mail]>
Subject: (fractint) Speed: No cache, no fun (was: Pentium 700)

Hello,
Since a few month I've been lurking around - now it's time to
write a few lines to all you Fractint lovers. It's always hard to
wait for a fractal to be calculated - but if the machine is fast
and the fractal is calculated in a few seconds - I tend to
increase the resolution of the final image until it is hard to wait
for the fractal again.
Hey, I'm very happy about Fractint 20.0 and the large ram/disk
video modes! It is fun to create those giant images *at once* to
have the full resolution for my simple & cheap color printer.

fr_clock           { ; Martin Rodenberg [e-mail]
  reset=2000 type=formula formulafile=fractint.frm
  formulaname=jm_25 function=sinh/log passes=1
  center-mag=+1.01305489025157200/-0.0034013417216\
  4564/124673.3/1.1454/52.778/9.107 params=900/300
  float=y maxiter=900000 colors=@volcano.map
  }

 I've started to use Fractint (that good old 18.1) on a 386/40.
Three years later I bought a P166 machine. The P166 was
about 20-22 times faster than the old 386. A few weeks ago
the P166 was three years old - now I'm sitting here with this
'modern' machine, a P III 500. It is only 8-9 times faster than
the P166. It doesn't like 'old' 16-Bit DOS programs... ;-)

Gregory McClure wrote:
> 3)  Processor / cache:  Now we get to some speed bumps.

Indeed!
The above .PAR ran several times from (clean) PLAIN DOS:

Today I've played a little with my machine. The Clock of my board
may be set to different speeds by BIOS. I've tried this and
calculated an index [Pixel per second per 100 MHz CPU].

Those of you who like benchmarking will be interested in the
following table:

CPU          FSB          PCI          F3 (320*200)        SF4  (640*400)
333          66.8         33.4        6:03.23 [52.9]        25:53.85 [49.5]
375          75.0         37.5        5:31.31 [51.5]        23:37.25 [48.2]
500         100.3         33.4        4:02.00 [52.9]        17:15.75 [49.4]
515         103.0         34.3        4:01.23 [51.5]        17:11.99 [48.2]
525         105.0         35.0        3:56.84 [51.5]        16:52.28 [48.2]
560         112.0         37.3        3:41.84 [51.5]        15:49.00 [48.2]
500         100.3         33.4     2:24:34.27[1.48]      - {*1}
500         100.3         33.4      4:08.10 [51.6]     17:40.99 [48.2]{*2}

{*1}= CPU L1 and L2 Cache disabled
{*2}= CPU L1 Cache enabled, L2 Cache disabled

To wait for an Image nearly 2 1/2 hours at 320*200 gives back the old
adventure-feeling - those 386/40-times...

On the other hand... one of these extreme expensive refrigerators running
an Athlon at 1 Ghz will perhaps spend about only 8 Minutes or
less for SF4...

Greetings, Moon





- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Fri, 14 Jan 2000 16:29:22 GMT
From: "Rupert Millard" <[e-mail]>
Subject: Re: (fractint) Colour Map Recognition, I'll write a program

>From: "Tony \(Anthony\) Hanmer" <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>Subject: (fractint) Colour Map Recognition
>Date: Fri, 14 Jan 2000 11:48:16 GET
>
>Greetings,
>I'm wondering if there is any automated way in (or outside) Fractint of
>scanning fractal gifs and comparing their colour maps to existing ones -
>for
>either an identical match or the same map but rotated.  Maybe this sounds
>lazy, but my collection of colour maps is about 1200 in size...  I know
>that
>one can save colour maps as text and manually read them in a text editor -
>I'm thinking of something much faster.  Any ideas?
>
>Tony Hanmer
>Tbilisi, Republic of Georgia
>______________________________________________________
>Get Your Private, Free Email at http://www.hotmail.com
>
>
>--------------------------------------------------------------
>Thanks for using Fractint, The Fractals and Fractint Discussion List
>Post Message:   [e-mail]
>Get Commands:   [e-mail] "help"
>Administrator:  [e-mail]
>Unsubscribe:    [e-mail] "unsubscribe fractint"

Hi Tony (and everyone else),
                            Over the weekend, I'll see if I can write a
program to do just that, perhaps a program like orgform would be handy, I'm
sure lots of my maps are duplicates.
                        From,
                            Rupert
______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com


- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Fri, 14 Jan 2000 11:56:21 EST
From: [e-mail]
Subject: Re: (fractint) Colour Map Recognition, I'll write a program

In a message dated 1/14/2000 11:31:20 AM Eastern Standard Time,
[e-mail] writes:

<<  Over the weekend, I'll see if I can write a  program to do just that,
perhaps a program like orgform would be handy, I'm  sure lots of my maps are
duplicates. >>

If you do so, I'd love a copy of the program.

- --Bob Carr--(Ocala, FL)

- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Fri, 14 Jan 2000 08:14:32 -0800
From: "Angela Wilczynski" <[e-mail]>
Subject: Re: (fractint) Colour Map Recognition

Tony....

If you have UltraFractal, you can open any number of fractint maps in UF to compare
them and will see them in UF's gradient editor.  It's very easy to pick out
duplicates or near-duplicates.

Angela aka wizzle

"Tony (Anthony) Hanmer" wrote:
>
> Greetings,
> I'm wondering if there is any automated way in (or outside) Fractint of
> scanning fractal gifs and comparing their colour maps to existing ones - for
> either an identical match or the same map but rotated.  Maybe this sounds
> lazy, but my collection of colour maps is about 1200 in size...  I know that
> one can save colour maps as text and manually read them in a text editor -
> I'm thinking of something much faster.  Any ideas?
>
> Tony Hanmer
> Tbilisi, Republic of Georgia

- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

Date: Fri, 14 Jan 2000 09:47:47 -0800
From: Gregory McClure <[e-mail]>
Subject: (fractint) New variation on an old theme...

=A92000 Greg McClure

I was first introduced to fractals by the Scientific American article
back in 1986.  I wrote a simple VMS Basic program to produce the
set on my graphics terminal.  After hours of play with the standard
formulas using the square function, I decided to try SIN.  It was then
on to writing a program that could use the clustering capability of VMS
to add multiple CPUs to the task.  Shortly after that effort, I learned
about Fractint and stopped work on my VMS programs.

Many of the direct variations of the Mandelbrot/Julia sets hardcoded
in Fractint have the basic forms:

[the function f(z(n)) takes on a variety of forms, some with and some
without corresponding Julia functions]

Mandelbrot:                         Julia:
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D               =
  =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
z(0)   =3D p1 + pixel                 z(0)   =3D pixel
z(n+1) =3D f(z(n))                    z(n+1) =3D p1*f(z(n))

[p1 is perturbation]                [p1 is Mandelbrot point]

The problem I encountered was: pixel is not added into each Mandelbrot
iteration step, therefore I could not reproduce any of the SIN plots I
had created with my VMS Basic program.  Then I learned about using
FORMULAS, and I was able to reproduce them again.

( Special note:
  Fractint V18.0 introduced the (fn||fn) formulas.  These functions
  DO use pixel and p1; by setting the function shift value to 0 and
  second function to sin (first function is effectively defeated this
  way) I was FINALLY able to produce my original SIN fractal from my
  VMS fractal days!  However, the first iteration is not identical to
  the standard Mandel, so the colors are assigned differently.  Set
  the function shift value to 0 and second function to sqr; you will
  see the difference.  Because of this and because the GregsMandel and
  GregsJulia contain multiplication factors (P2) I have kept the ~M1
  formulas in the list.  For P2 =3D (1+0i), the (fn||fn) fractals are =
much
  faster!. )

Over the years I have created the GregsMan series of formulas, which
use the following basic forms:

Mandelbrot:                         Julia:
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
            =
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D
z(0)   =3D p1 + pixel                 z(0)   =3D pixel + f(z(pixel)) + =
p1
z(n+1) =3D f(z(n)) + pixel            z(n+1) =3D f(z(n)) + p1

Note the addition of pixel in the first iteration for the Mandelbrot
series and the addition of one cycle in the first iteration for the
Julia series.  This reproduces the expected plots of the standard
Mandelbrot and Julia engines in Fractint.

Because my Mandelbrot formulas add in the pixel in each repetition,
and my Julia formulas similarly add in p1, the standard Mandelbrot
and Julia set can be reproduced in many of the formulas (as described
in each formula, sometimes several different ways).  All Mandelbrot
formulas have corresponding Julia set formulas.

The last parameter entry is a combination of bailout value and bailout
type.  The real portion is the bailout value, the imaginary portion is
the bailout type (0 =3D MOD, 1 =3D REAL, 2 =3D IMAG, 3 =3D OR, 4 =3D =
AND,
5 =3D MANH, and 6 =3D MANR)

These formulas are copyrighted.  I figured, if others can copyright
formulas and parameter files on a copyrighted freeware program, why
can't I? :-)  Actually, you can use or modify any of these formula or
parameter files as long as the original formula copyright and
authorship are mentioned (i.e. you can treat this just like Fractint
itself).

The file GREGSMAN.PAR is a sample set of parameters using the
GREGSMAN.FRM formulas.  Most of these are translations of my SIN
fractals from VMS days.

The file GMANTEST.PAR is my test set of parameters to show that I can
reproduce the Mandelbrot and Julia sets with the GregsMan.FRM formulas,
and that they look identical to the MANDEL and JULIA fractals for
consistency.  I included the time to create each set (compare to 2.3
sec for standard Mandel on my Pentium 166Mhz, floating point on, 1024 x
768 resolution, 1023 iterations).

I always use p1 for the perturbation offset (Mandel-type) and for the
Mandel point (Julia-type).  I always use p3 for the bailout value and
type.  So only p2 is available as a modification parameter for the
fractal formula iterations.  I have tried to take advantage of math
equivalencies to reduce the number of formulas in a particular formula
series, for example a (p2*fn1 + fn2) formula can be reproduced by
switching fn1 and fn2 and using the (fn1 + p2*fn2) formula, and
sqr(p2*fn1) is the same as p2*p2*sqr(fn1).  Someday, when additional
parameter values are added to the formula function (p4, p5, etc) I can
reduce the number of formulas!  If that ever happens, I will come out
with a new reduced set of equivalent formulas.  However, these formulas
have an uncanny ability to multiply in my head as I consider different
configuration sets, so that reduction will be short-lived.  I am
already working on 3- and 4-function sets using the same basic format,
the shear number of combinations is staggering.

Agreed, with the advent of Fractint V20.0, I SHOULD be able to reduce
the number of formulas in half, but there is a bug in this version that
causes several of these formulas, when combined, to produce zero color
blank screens instead of the expected fractal images.  I have tried
the suggested command line parameter DEBUG=3D90, some formulas STILL
don't work.  So I am releasing this set until the bug is fixed.  When
this bug is fixed, I will release the revised set of formulas taking
advantage of the ismand=3Dxxx parameter.

The specific iteration formulas in GregsMan.FRM are:

All Mandel formulas: z(0) =3D p1 + Pixel
All Julia formulas:  z(-1) =3D Pixel
Julia formulas: replace "Mandel" with "Julia", and "pixel" with "p1"
                z(0) is first be calc'd by applying formula to z(-1)

1- and 2-function formulas: (GREGSMAN.FRM)

 Standard function series:
  GregsMandelM1:  z(n+1) =3D p2*fn1(z) + pixel

  GregsMandelM2:  z(n+1) =3D p2*[fn1(z)+fn2(z)] + pixel
  GregsMandelM3:  z(n+1) =3D fn1(z) + p2*fn2(z) + pixel

 Power function series:
  GregsMandelP1:  z(n+1) =3D fn1(z)^p2 + pixel

  GregsMandelP2:  z(n+1) =3D [fn1(z) + fn2(z)]^p2 + pixel
  GregsMandelP3:  z(n+1) =3D fn1(z) + fn2(z)^p2 + pixel

  GregsMandelP4:  z(n+1) =3D fn1(z)^p2 + fn2(z)^p2 + pixel

 Squared function series:
  GregsMandelS1:  z(n+1) =3D sqr[p2*fn1(z)] + pixel

  GregsMandelS2:  z(n+1) =3D sqr{p2*[fn1(z) + fn2(z)]} + pixel
  GregsMandelS3:  z(n+1) =3D sqr[fn1(z) + p2*fn2(z)] + pixel
  GregsMandelS4:  z(n+1) =3D p2*{fn1(z) + sqr[fn2(z)]} + pixel
  GregsMandelS5:  z(n+1) =3D p2*fn1(z) + sqr[fn2(z)] + pixel
  GregsMandelS6:  z(n+1) =3D fn1(z) + p2*sqr[fn2(z)] + pixel

  GregsMandelS7:  z(n+1) =3D sqr[p2*fn1(z)] + sqr[p2*fn2(z)] + pixel
  GregsMandelS8:  z(n+1) =3D sqr[fn1(z)] + sqr[p2*fn2(z)] + pixel

 Exponent function series:
  GregsMandelE1:  z(n+1) =3D p2*e^fn1(z) + pixel
  GregsMandelE2:  z(n+1) =3D e^[p2*fn1(z)] + pixel

  GregsMandelE3:  z(n+1) =3D e^{p2*[fn1(z) + fn2(z)]} + pixel
  GregsMandelE4:  z(n+1) =3D e^[fn1(z) + p2*fn2(z)] + pixel
  GregsMandelE5:  z(n+1) =3D fn1(z) + e^[p2*fn2(z)] + pixel
  GregsMandelE6:  z(n+1) =3D p2*{e^[fn1(z) + fn2(z)]} + pixel
  GregsMandelE7:  z(n+1) =3D p2*[fn1(z) + e^fn2(z)] + pixel
  GregsMandelE8:  z(n+1) =3D p2*fn1(z) + e^[fn2(z)] + pixel
  GregsMandelE9:  z(n+1) =3D fn1(z) + p2*e^fn2(z) + pixel

  GregsMandelEA:  z(n+1) =3D p2*[e^fn1(z) + e^fn2(z)] + pixel
  GregsMandelEB:  z(n+1) =3D e^fn1(p2*z) + e^fn2(p2*z) + pixel
  GregsMandelEC:  z(n+1) =3D e^[fn1(z)] + e^[p2*fn2(z)] + pixel
  GregsMandelED:  z(n+1) =3D e^fn1(z) + p2*e^fn2(z) + pixel

 Logarithm function series:
  GregsMandelL1:  z(n+1) =3D p2*ln[fn1(z)] + pixel
  GregsMandelL2:  z(n+1) =3D ln[p2*fn1(z)] + pixel

  GregsMandelL3:  z(n+1) =3D ln{p2*[fn1(z) + fn2(z)]} + pixel
  GregsMandelL4:  z(n+1) =3D ln[fn1(z) + p2*fn2(z)] + pixel
  GregsMandelL5:  z(n+1) =3D fn1(z) + ln[p2*fn2(z)] + pixel
  GregsMandelL6:  z(n+1) =3D p2*{ln[fn1(z) + fn2(z)]} + pixel
  GregsMandelL7:  z(n+1) =3D p2*{fn1(z) + ln[fn2(z)]} + pixel
  GregsMandelL8:  z(n+1) =3D p2*fn1(z) + ln[fn2(z)] + pixel
  GregsMandelL9:  z(n+1) =3D fn1(z) + p2*ln[fn2(z)] + pixel

  GregsMandelLA:  z(n+1) =3D p2*{ln[fn1(z)] + ln[fn2(z)]} + pixel
  GregsMandelLB:  z(n+1) =3D ln[fn1(p2*z)] + ln[fn2(p2*z)] + pixel
  GregsMandelLC:  z(n+1) =3D ln[fn1(z)] + ln[p2*fn2(z)] + pixel
  GregsMandelLD:  z(n+1) =3D ln[fn1(z)] + p2*ln[fn2(z)] + pixel

 Function of function series:
  GregsMandelF1:  z(n+1) =3D p2*fn1[fn2(z)] + pixel
  GregsMandelF2:  z(n+1) =3D fn1[p2*fn2(z)] + pixel
  GregsMandelF3:  z(n+1) =3D fn1[fn2(z)^p2] + pixel
  GregsMandelF4:  z(n+1) =3D fn1[fn2(z)]^p2 + pixel

 Miscellaneous function series:
  GregsMandelZ1:  z(n+1) =3D fn1(z)^fn2(z) + fn3(z)^p2 + pixel
  GregsMandelZ2:  z(n+1) =3D fn1(z)^fn2(-z) + fn3(z)^p2 + pixel
  GregsMandelZ3:  z(n+1) =3D fn1(z)^p2 + fn2(z)^(-p2) + pixel
  GregsMandelZ4:  z(n+1) =3D {fn1(z) || fn2(z) || fn3(z)} + pixel
  GregsMandelZ5:  z(n+1) =3D fn1{fn2(z) || fn3(z) || fn4(z)} + pixel

Enjoy,

[e-mail]

P.S.  The .PAR and .FRM files follow in seperate messages.

  The Kwisatz Haderach,
=DF  Gregory J. McClure

- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

------------------------------

End of fractint-digest V1 #436
******************************