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fractint-digest       Tuesday, December 23 1997       Volume 01 : Number 040




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

Date: Sun, 21 Dec 1997 19:20:10 -0600
From: "Paul N. Lee" <[e-mail]>
Subject: (fractint) "Top Three" Images

Greetings,

We had twenty-six (26) ballots on this round of voting:

And without further ado, here are the "Three":

  Place  Image Name

     1.  PRESLAR2
     2.  SGALLET2
     3.  LINDAA03

Thank you for voting.

Merry Christmas, Cheerful Hanukkah, Joyful Kwanzaa, Glad Solstice and a
Happy New Year.

P.N.L.

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

Date: Sun, 21 Dec 1997 20:21:55 EST
From: Clamcake <[e-mail]>
Subject: (fractint) Lebesgue measure

Hi,
Can someone possibly tell me what it means for a set to have a positive or  a
zero Lebesgue measure and perhaps provide some examples of sets that do and
sets that do not. Thank you.

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

Date: Sun, 21 Dec 1997 21:21:01 -0500
From: Lee Skinner <[e-mail]>
Subject: (fractint) 3DStalks_Julia&MonkFace

Paul Carlson asked me to post this message for him, as he is currently
having problems sending mail to this mailing list.
Lee Skinner
Message from Paul Carlson follows:
- -----------------------------------------------------------------------
Here is a heavily commented .frm file that describes how my
3D Stalks rendering method works, along with a .par file
that uses it do produce one of my favorite fractals.

The 3D Stalks method is an extension of Clifford Pickover's
Epsilon Cross method.  In the 3d Stalks method, an index into
one or more ranges of colors is computed based on the ratio
of the distance of the trapped point from the nearest axis to
1/2 the width of the "trap."

3DStalks_Julia (ORIGIN) {; Copyright (c) Paul W. Carlson, 1997
    ;****************************************************
    ; Always use floating point math and outside=3Dsumm.
    ;
    ; Parameters:
    ;   p1 =3D the value of complex constant c in the equation
    ;   real(p2) =3D a factor controlling the width of the stalks
    ;              (this is actually 1/2 the width of the "trap")
    ;   imag(p2) =3D bailout value for |w|
    ;   real(p3) =3D number of color ranges
    ;   imag(p3) =3D number of colors in each color range
    ;
    ; Note that the equation variable is w, not z.  Always
    ; initialize z to zero.
    ;****************************************************
    w =3D pixel
    c =3D p1
    z =3D 0
    bailout =3D 0
    iter =3D 0
    range_num =3D 0
    ;****************************************************
    ; In the accompanying par file, mnkyface.par,
    ; we have 2 color ranges with 98 colors in each range
    ; for a total of 196 colors. The first range starts at
    ; color 1.  Pixels will use color 0 when |w| < bailout.
    ; Other values can be used here as long as the product
    ; of num_ranges times colors_in_range is less than 255.
    ; Color 0 is reserved for the background color and color
    ; 255 can be used for the inside color.
    ;****************************************************
    num_ranges =3D real(p3)
    colors_in_range =3D imag(p3)
    ;****************************************************
    ; Real(p2) controls the width of the stalks.
    ; These values will usually be in the range 0.001 to 0.5
    ;****************************************************
    stalk_width =3D real(p2)
    index_factor =3D (colors_in_range - 1) / stalk_width:
    ;****************************************************
    ; The equation being iterated.  Almost any equation
    ; that can be expressed in terms of a complex variable
    ; and a complex constant will work with this method.
    ; This line in the formula is the only one that needs
    ; to be changed for other equations.
    ; This example uses the "magnet2j" equation.
    ;****************************************************
    w=3D((w^3+3*w*(c-1)+(c-1)*(c-2))/(3*w*w+3*w*(c-2)+(c-1)*(c-2)+1))^2
    ;****************************************************
    ; Find which axis the orbit point is closest to.
    ;****************************************************
    IF (abs(real(w)) <=3D abs(imag(w)))
        min_dist_to_axis =3D abs(real(w))
    ELSE
        min_dist_to_axis =3D abs(imag(w))
    ENDIF
    ;****************************************************
    ; If the orbit point is within stalk_width of an axis,
    ; set z to the index into the colormap and set the bailout flag.
    ; Also, prevent bailout on the first two iterations.
    ;****************************************************
    IF (min_dist_to_axis < stalk_width && iter > 1)
      z =3D index_factor * min_dist_to_axis + range_num * colors_in_range=
 + 1
      bailout =3D 1
    ENDIF
    ;****************************************************
    ; Cycle through the range numbers (0 thru num_ranges - 1)
    ; With two color ranges, even iterations use color
    ; range 0, odd iterations use color range 1.
    ;****************************************************
    range_num =3D range_num + 1
    IF (range_num =3D=3D num_ranges)
        range_num =3D 0
    ENDIF
    ;****************************************************
    ; Since we are using outside=3Dsumm, we have to subtract
    ; the number of iterations from z.
    ;****************************************************
    iter =3D iter + 1
    z =3D z - iter
    ;****************************************************
    ; Finally, we test for bailout
    ;****************************************************
    bailout =3D=3D 0  && |w| < imag(p2)
}

MonkeyFace           { ; Copyright (c) Paul W. Carlson, 1997
  reset=3D1930 type=3Dformula formulafile=3Djlstalks.frm
  formulaname=3D3DStalks_Julia passes=3D1
  corners=3D-3.153125/-1.332708/6.993125/8.358438
  params=3D-0.25/0/0.1/10000/2/98
  float=3Dy maxiter=3D200 inside=3D255 outside=3Dsumm
  colors=3D000Vzz<96>0GGzVz<96>F0G000<57>000
  }

I'll be glad to answer any questions about these.
Paul Carlson
- ------------------------------------------------------------------
                email   [e-mail]

WWW Fractal Galleries   http://sprott.physics.wisc.edu/carlson.htm
                        http://fractal.mta.ca/fractals/carlson/
                        http://www.cnam.fr/fractals/carlson.html
- ------------------------------------------------------------------

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

Date: Sun, 21 Dec 1997 19:27:46 -0800
From: "Ester" <[e-mail]>
Subject: Re: (fractint) "Top Three" Images

The contest page has been updated.

http://www.geocities.com/CapeCanaveral/Lab/3825/TopTen97.html

The final version of the Contest Construction Kit(TM) will be ready
in a week or two.  Then we can file this one away and who knows....

Great show guys and gals!

Jay
PS.  Isn't Janet the one I browbeat into joining the contest....
Hmmmmm???

- ----------
> From: Paul N. Lee <[e-mail]>
> To: The Fractals and Fractint Discussion List
<[e-mail]>
> Subject: (fractint) "Top Three" Images
> Date: Sunday, December 21, 1997 5:20 PM
>
> Greetings,
>
> We had twenty-six (26) ballots on this round of voting:
>
> And without further ado, here are the "Three":
>
>   Place  Image Name
>
>      1.  PRESLAR2
>      2.  SGALLET2
>      3.  LINDAA03
>
> Thank you for voting.
>
> Merry Christmas, Cheerful Hanukkah, Joyful Kwanzaa, Glad Solstice and a
> Happy New Year.
>
> P.N.L.
>
> -


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

Date: Sun, 21 Dec 1997 21:49:13 -0600
From: Janet Preslar <[e-mail]>
Subject: Re: (fractint) "Top Three" Images

Jay wrote:

> The contest page has been updated.
> http://www.geocities.com/CapeCanaveral/Lab/3825/TopTen97.html

<snip>

> PS.  Isn't Janet the one I browbeat into joining the contest....
> Hmmmmm???

Yep! That's me! A week ago I was rendered speechless by making the top te=
n. Now
I'm in shock. I am greatly surprised and humbled =97 with so many wonderf=
ul images
to choose from, I had no idea mine would even be noticed. As several peop=
le said
before the voting began, it is a huge honor just to be in the company of =
such
great fractal artists, from whom I've learned so much in the twelve month=
s since
I saw my very first fractal. Thanks for everything you've taught me.

Best wishes to all for a happy holiday!
Janet



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

Date: Mon, 22 Dec 1997 00:13:33 -0500
From: "Brian E. Jones" <[e-mail]>
Subject: Re: (fractint) "Top Three" Images

Hi Janet,

Congratulations!!!

Have a Merry Christmas!

Brian
http://ourworld.compuserve.com/homepages/Brian_E_Jones


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

Date: Sun, 21 Dec 1997 23:56:07 -0600
From: Janet Preslar <[e-mail]>
Subject: Re: (fractint) "Top Three" Images

Thanks!

You, too! (Have a Merry Christmas!)

Janet


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

Date: Mon, 22 Dec 1997 01:35:59 -0500
From: Michael Sager <[e-mail]>
Subject: (fractint) Happy Holidays

Hi everyone - I'm really glad I joined this list, the contest images
were great eye-candy and I find the discussions interesting.  I haven't
contributed much to the list, so I figured I'd send something now,
before I go home from Rutgers University for Christmas.  Here are come
parameters for the contest formula that I've come up with since the
contest.  I hope everyone enjoys them - my roommate did!  I'll try to
contribute a little more next semester, but I don't know - I'll be
taking 20 credits.  Justin K.- thanks for correcting my contest pars!
- -Mike Sager

  metallic             { ; Whoa...trippy
  reset=1960 type=formula formulafile=contest.frm
  formulaname=contest4
  center-mag=+0.32934353054332530/+0.00354225486261372/4943346
  params=0/0 float=y maxiter=2048 inside=0 outside=atan
  colors=00z00VVVV00UUUU00TSSS00SRRR00QQQQ00PPPP00OOOO00\
  NMMM00LLLL00KKKK00JJJJ00IHHH00HGGG00FFFF00EEEE00DDDD00\
  CBBB00AAAA00999900888800777700555500444400333300222200\
  0<3>00111100222200333300444400555500555500666600777700\
  888800999900AAAA00AAAA00BBBB00CCCC00DDDD00EEEE00FFFF00\
  FFFF00GGGG00HHHH00IIII00JJJJ00KKKK00LLLL00LLLL00MMMM00\
  NNNN00OOOO00PPPP00QQQQ00QQQQ00RRRR00SSSS00TTTT00UUUU00\
  VVVV00VVVV00WWWW00XXXX00YYYY00ZZZZ00____00____00````00\
  aaaa00bbbb00cccc00dddd00eeee00eeee00ffff00gggg00hhhh00\
  iiii00jjjj00jjjj00kkkk00llll00mmmm00nnnn00oooo00oooo00\
  pppp00qqqq00rrrr00ssss00tttt00tttt00uuuu00vvvv00wwww00\
  xxxx00yyyy00zzzzzzz00zyyy00yxxx00xwww00wvvv00vttt00tss\
  s00srrr00rqqq00qppp00onnn00nmmm00mlll00lkkk00jjjj00ihh\
  h00hggg00gfff00eeee00dccc00cbbb00baaa00a```00____00ZYY\
  Y00YXXX00XWWW
  }

Spirals            { ; Spiky Spiral Things
  reset=1960 type=formula formulafile=contest.frm
  formulaname=contest4
  center-mag=+0.32934346263812660/+0.00354215599061105/9966424
  params=0/0 float=y maxiter=2048 inside=0 outside=atan
  colors=0000800A00C80KE2202402442482A42A842046246646A48\
  04C84SK4`U60066268468868C6A06A26CG6E66EA6EC6IE86086888\
  48A88AA8C48GC8I0A00A64A80AA8ACAACCACGAMGC40CC2CECCEECE\
  ICOKCWQE60EA0EE4EE8EG0EGEEGGEKIEKMEM8G40G60GA6GC2GIGGM\
  KGQSIA0IC8IE4IOKIb`KA8KC4KE0KG6KKEKQOKSEKU4KUWKWUME2MS\
  OMffOA0OK6OKAOUUO`QQA0QC6QI6QIAQQKQSCSM2SOASYYSY`SdbSf\
  UUI6UMAUWYUYQU`GWOCWSEWbbWbfWjlYK0YMAYS4YSCYbQYbUYdGYd\
  d`OC`WM`YG`bd`dWbUIbhhbj`bprdQ8dS0d`Qd`UdbKdfhdjSfUGfW\
  8fhjfhnfllhO4h`MhllhnnhpjjYMj`Cjb4jfWjhbjlrjvtlS8lU0l`\
  MlbEljSlphlpplrbnpvnrrpWCpdQpfEphSpnWpnlpttpxrpzvpzzrY\
  Er`6rdMrh4rndrprrtzrvvrzltYEtlStrxttltxxvdEvjWvlKvnAvn\
  YvptvrlvtfvtrvtzvvhvvnvxzvzvvzzxbExfGxrvxvhxvtxvxxxWxx\
  pzjGzjOzrWztQztfzvfzvpzvrzvzzxjzxrzxvzxzzzrzzvzzxzzzB6\
  5ywz310zzzusyxbFLB8CEJxruzxz300jlqACHzvrpzvfhmzvy46Bnp\
  u249sqwvps020040064
  }

Rug                { ; Looks like some kind of fancy rug
  reset=1960 type=formula formulafile=contest.frm
  formulaname=contest4

center-mag=-1.64687943103130100/-0.00000000004144189/4.667908e+007/1.364\
  3/42.063/7.942 params=0/0 float=y maxiter=1024 inside=0 outside=atan
  colors=0000200400640800A00C80KE2202402442482A42A842046\
  246646A4804C84SK4`U60066268468868C6A06A26CG6E66EA6EC6I\
  E8608688848A88AA8C48GC8I0A00A64A80AA8ACAACCACGAMGC40CC\
  2CECCEECEICOKCWQE60EA0EE4EE8EG0EGEEGGEKIEKMEM8G40G60GA\
  6GC2GIGGMKGQSIA0IC8IE4IOKIb`KA8KC4KE0KG6KKEKQOKSEKU4KU\
  WKWUME2MSOMffOA0OK6OKAOUUO`QQA0QC6QI6QIAQQKQSCSM2SOASY\
  YSY`SdbSfUUI6UMAUWYUYQU`GWOCWSEWbbWbfWjlYK0YMAYS4YSCYb\
  QYbUYdGYdd`OC`WM`YG`bd`dWbUIbhhbj`bprdQ8dS0d`Qd`UdbKdf\
  hdjSfUGfW8fhjfhnfllhO4h`MhllhnnhpjjYMj`Cjb4jfWjhbjlrjv\
  tlS8lU0l`MlbEljSlphlpplrbnpvnrrpWCpdQpfEphSpnWpnlpttpx\
  rpzvpzzrYEr`6rdMrh4rndrprrtzrvvrzltYEtlStrxttltxxvdEvj\
  WvlKvnAvnYvptvrlvtfvtrvtzvvhvvnvxzvzvvzzxbExfGxrvxvhxv\
  txvxxxWxxpzjGzjOzrWztQztfzvfzvpzvrzvzzxjzxrzxvzxzzzrzz\
  vzzxzzzB65ywz310zzzusyxbFLB8CEJxruzxz300jlqACHzvrpzvfh\
  mzvy46Bnpu249sqwvps
  }

Hairs              { ; No comment
  reset=1960 type=formula formulafile=contest.frm
  formulaname=contest4
  center-mag=+0.46824853276622360/+0.87638302029325500/37.7397/1/-35
  params=0/0 float=y maxiter=2048 inside=epsiloncross outside=atan
  decomp=256
  colors=000000000000<3>B93we3GE5<14>uoJ<29>n`2n_1mZ0lY0\
  <197>000
  cyclerange=1/8
  }

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

Date: Sun, 21 Dec 1997 22:55:40 -0800
From: "Ester" <[e-mail]>
Subject: (fractint) Happy Holidays snowman

Here is another snowman.

Jay

SnowMan350            { ; Snowman 350  Jay Hill 1997
  reset=1960 type=mandel
  center-mag=-3.12933/9.04832e-015/8.195459/0.9657/90 params=0/0
  float=y maxiter=256 inside=250 outside=summ invert=1/-3.5/0
  colors=0cwBOzmuzrfzGuiUmzXuzcbzluzQ\
  kzltz<2>ktydeyjty<93>RfoRfoRfp<13>Ucw\
  UcwUcwUbwTbw<90>11w00w00u<26>004zzz000000000AwKAvK
  savename=snow350
  }



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

Date: Mon, 22 Dec 1997 02:08:34 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) Tip of the Day

If you do a decomp image, esp. a 256 decomp image, and your entire palette
is NOT being used: turn off logmap :-)


- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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Date: Mon, 22 Dec 1997 02:10:11 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) High precision transcendental functions

I'm working on a high-precision math library that includes transcendental
functions: exp, log, arbitrary powers, roots, trig.

I have reasonably nice fast convergent calculations for the library's
recalculation of pi and e to biogger precision whenever more precision is
needed. Pi turns out to work out faster using Newton to solve sin(x)=0 for
the initial value x=3, using a Maclaurin series for sin, than using
1-1/3+1/5-1/7... e is had from 1/n!.
I also have good convergent Taylor series for cos (and obviously sin),
sinh, cosh, and thus tan, sec, csc, cot, tanh, csch, coth, and sech.
Exp works nicely, and sin^-1 and cos^-1 do also.
sinh-1 and cosh-1 are evaluated in terms of logs.

The trouble is here: my atan converges quite slowly. (It uses a Maclaurin
series about 0 for |x|<=1 and for |x|>1, evaluates atan(-1/x)-pi/2, in
which |-1/x|<=1.) So does my log (Newton's method to solve e^y-x=0,
with |x|>e handled as -log(1/x)... but a Maclaurin series about 1 with the
same -log(1/x) trick to handle x>1 promised to be even slower).
And I am not aware of a converging series or iteration for csc-1, sec-1,
tanh-1, csch-1, or sech-1, nor cot-1 and coth-1. At least, cot-1 x is just
pi/2-tan-1 x, and I can probably link csc-1 and sec-1, coth-1 and tanh-1,
and csch-1 and sech-1 similarly.

So, can anyone provide:

  * Iterative methods to converge quickly for all x to
    * tan-1 x
    * tanh-1 x
    * sec-1 x
    * sech-1 x
    * ln x
  * Information about whether my sin-1 and cos-1 Maclaurin series, or
    those for sin, cos, exp can be improved upon (all are expanded about 0
    currently), or the Newton method for pi?


- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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

Date: Mon, 22 Dec 1997 02:16:48 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) ProtoMatter

The current state of things:

* Design decisions:
  ProtoMatter will be written mostly in Java. Before you all freak out,
  read on: the built in fractal types will, of course, be written as JNI
  (Java Native Interface) methods written in C/asm. High speed performance
  will thus be available for Win95/NT and Unix platforms using DLLs or other
  native dynamic libraries. Formula types will compile into Java, and thus
  run at speeds similar to Fractint formula types, which use an
  interpreter or bytecode compiler themselves.
  Plugin architecture: Plugins will be available as .class/DLL pairs, the
  .class portable, the DLL platform dependent.
* Platforms:
  Any platform supporting Java will be supported. High precision
  (deepzoom) math will be supported on all platforms. High speed native code
  will be supported on any platform which supports a Java runtime capable of
  loading native methods, and for which the appropriate DLL type file for
  the fractal class is located in the library path at run time. (Java
  versions of the same algorithms will run otherwise.)
* Scripting: Some kind of scripting language for parameter files and more
  will exist. It may consist of a java runtime environment capable of
  on-the-fly compilation.


- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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Date: Mon, 22 Dec 1997 03:08:27 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Autozooming, was: M-set field lines?

Path of shallowest ascent: Will enter whirlpool. Ditto steepest.

Heuristic tricks:

First, model an exponential random variable. (See a text on probability
theory and statistics for algorithms about how to convert uniform random
numbers such as rand() gives into exponential ones.)
Use your ranexp() to obtain a time. Go for that time up a shallow ascent,
then switch to a steep one or to a random direction of motion. Follow that
for a SHORT time. Then perhaps go back to step 1, or perhaps terminate.


Other ideas: Start at full M-set. Inspect some points. Pick one on the set
and one not on, pick halfway point, choose it and out if in, or it and in
if out. Repeat subdividing to home in on M boundary in current image.
After a few such divisions stop and center a zoom there. Repeat for a
while. (Exp variable again?) Then find highest dwell point in image such
that there is NO member of M within a significant distance, center a zoom
there, then keep zooming at highest dwell... look for M to reappear, then
a midget has been found, if so repeat from step 1.

- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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Date: Mon, 22 Dec 1997 03:21:25 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Colors of Infinity

Lee Skinner writes:
[stuff]

Congrats!

Just don't bore them to death with a 2^180 deepzoom... not unless they
supply you with an Alpha/Risc 400MHz or something. :-)


- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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Date: Mon, 22 Dec 1997 03:23:26 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Clouds Over Shiprock

>I really wanted to view the fractal "Clouds Over Shiprock"
>( I like Shiprock!) but got an error message when I tried to
>generate the fractal.  I have solved this problem for most
>of the others.  I put clouds as a .par file and the formula as
>a .frm file but when I tried to run it it said "oops I couldn't
>understand the argument pixinv."

Did you try it on the latest Fractint, 19.6?


- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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Date: Mon, 22 Dec 1997 06:16:44 EST
From: JulianPA <[e-mail]>
Subject: (fractint) Christmas Ornament

> Wizzle <[e-mail]> writes:
>Subject: (fractint) Christmas Ornament
>
>I think I have a winner here!!!  I was messing around with Jill Lawson's
>gif's this morning and managed to produce this Christmas image using one of
>her files by adding a color map of mine....

Angela,
I think you have a winner too.  I love the spherical 3D shape!

I've attached a par for the same image with a slightly different shadowing.
You may like it better or worse according to your taste.

Julian

>Jim Smith <[e-mail]> writes:
>Subject: Re: (fractint) Christmas Ornament (refering to Wizzle's original
image)
>
>Very, very nice! Anyone have any suggestions on how to keep the background
>from 'flickering" when it is color-cycled? Xfractint 3.02 under X11R6 at 8bpp
>(sorry, old display).

Jim,
I changed the inside color from 1 to zero.  The background will remain a
constant color, and shouldn't flicker anymore.

Julian

- -------------------
Julian Adamaitis

Fractelligent Designs
visit "Julian's Fractal Page"
http://members.aol.com/julianpa
[e-mail]

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

ornament-$         { ; Re-Coloring of Wizzle's Image Posted to Fractint List
                     ; by Julian Adamaitis
  reset=1960 type=mandelfn function=ident
  center-mag=-0.00219726999999992/-0.00041961500000021/0.2032378/1/90
  params=0/0 inside=0 invert=4.5/0/0 decomp=128
  colors=111Z56<4>l56o56s55w64<13>zwU<9>885<15>3wU<15>0A4<20>000100300<12>\
  P03R03T03V03X03Z04<11>w08<9>X56<4>6A0<7>1wU<15>0A03C2992<2>UA0<15>xzc<13\
  >KA0000<46>000330<13>110
  }


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


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Date: Mon, 22 Dec 1997 12:35:50 EST
From: KivrynH <[e-mail]>
Subject: Re: (fractint) "Top Three" Images

Hi Janet,

Congratulations and happy holidays.  Do you have a web page?  If so, could you
please post it?  Thanks

Kivryn

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Date: Mon, 22 Dec 1997 12:37:38 -0600
From: Janet Preslar <[e-mail]>
Subject: Re: (fractint) "Top Three" Images

KivrynH wrote:

> Hi Janet,
>
> Congratulations and happy holidays.  Do you have a web page?  If so, could you
>
> please post it?  Thanks

Thanks. My web page is http://www.ParkeNet.org/jp

Janet


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Date: Mon, 22 Dec 1997 15:20:45 -0500
From: Sylvie Gallet <[e-mail]>
Subject: Re: (fractint) "Top Three" Images

Hi All,

  Congratulations, Janet!

  Thanks for all these wonderful images and for Jay's and Paul's work.

  Merry Christmas to all of you!

        - Sylvie

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Date: Mon, 22 Dec 1997 11:26:10 -0700
From: Rich Thomson <[e-mail]>
Subject: Re: (fractint) High precision transcendental functions

Paul, interesting that you should ask about this as I was beginning to
explore along the same lines.  However, I've never delved much into
the details of implementing transcendental functions.  When looking
around at various places (I was looking at assembly code for digital
signal processors, namely TI's TMS320C50 for instance), lots of the
programs given referred to things like the "Handbook of Elemental
Functions" (or something like that; I can dig out the exact title if
you like).

Basically I got the impression that everything was done with power
series.  However, these programs didn't discuss the convergence
characteristics of the series for various ranges of argument.  (I have
a feeling that to handle "any argument" as you requested, that you
might need to select one algorithm from a collection of several
depending on the argument.)  I have those files at home (I picked up
a TMS320C50 evaluation kit for $60 this year), so I can get the name
of the referenced book if it would help.

Paul Derbyshire wrote:
> So, can anyone provide:
>
>   * Iterative methods to converge quickly for all x to
>     * tan-1 x
>     * tanh-1 x
>     * sec-1 x
>     * sech-1 x
>     * ln x

For the trig functions can you avoid special series by using trig
identities?  I imagine you've already looked into that...

>   * Information about whether my sin-1 and cos-1 Maclaurin series, or
>     those for sin, cos, exp can be improved upon (all are expanded about 0
>     currently), or the Newton method for pi?

I think for this one needs to consult a book like the one I mentioned
above.  This is an interesting aspect of computation, because to my
knowledge, noone has implemented full trig support for arbitrary
precision floating point.  I think most implementations depend on the
fact that only a few iterations (and polynomial terms) are needed to
achieve 8 or 16 decimal digits of accuracy.

I just asked around the office (there's a bunch of math guys around
here) and the general consensus is that trig functions are all
implemented as a taylor series expansion around 0 (a MacLaurin series
as you are using).  It may be possible to improve upon a Taylor
series, but I don't know.  If I find out anything further, I will be
sure to send a message to fractint.  Also, if you find out anything
further, Paul, would you be so kind as to report your results to the
fractint list?  Thanks.
- --
  ``Between stimulus and response is the will to choose.''  -- Steven Covey
 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
     3D Paint: The Power to Create in 3D;        Rich Thomson
     email me for more info                [e-mail]

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Date: Mon, 22 Dec 1997 17:17:17 -0500
From: Jack Valero <[e-mail]>
Subject: Re: (fractint) "Top Three" Images

I just saw the results of the contest.
Congratulations Linda and Sylvie.
And a special congratulations to you, Janet!
Once again the list members have demonstrated
their excellent taste!


Regards - Jack

visit our fractal gallery: http://www.globalserve.net/~jval/

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Date: Mon, 22 Dec 1997 12:05:40 -0700
From: Rich Thomson <[e-mail]>
Subject: Re: (fractint) Lebesgue measure

In article <[e-mail]> ,
    Clamcake <[e-mail]>  writes:
> Can someone possibly tell me what it means for a set to have a positive or  a
> zero Lebesgue measure and perhaps provide some examples of sets that do and
> sets that do not. Thank you.

The standard "middle thirds" Cantor set construction on the real line
has zero Lebesgue measure.

The unit interval [0,1] has a Lebesgue measure of 1.0.

The intervals (a,b), [a,b), (a, b], and [a,b] have Lebesgue measure of
b-a.

The one-dimensional Lebesgue measure corresponds to length.
The two-dimensional Lebesgue measure corresponds to area.
The three-dimensional Lebesgue measure corresponds to volume.
etc.

For more details, I recommend reading "Fractal Geometry", by Kenneth
Falconer.  It covers Lebesgue measures.
- --
  ``Between stimulus and response is the will to choose.''  -- Steven Covey
 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
     3D Paint: The Power to Create in 3D;        Rich Thomson
     email me for more info                [e-mail]

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Date: Mon, 22 Dec 1997 12:33:36 -0700
From: Rich Thomson <[e-mail]>
Subject: Re: (fractint) Christmas Ornament

In article <[e-mail]> ,
    Wizzle <[e-mail]>  writes:
> I think I have a winner here!!!

Very nice... the edges look great when anti-aliased....  If you can
stand to download the 809K PNG, check it out...
<URL: http://www.xmission.com/~legalize/fractals/>
- --
  ``Between stimulus and response is the will to choose.''  -- Steven Covey
 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
     3D Paint: The Power to Create in 3D;        Rich Thomson
     email me for more info                [e-mail]

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Date: Mon, 22 Dec 1997 16:28:44 -0600
From: Janet Preslar <[e-mail]>
Subject: Re: (fractint) "Top Three" Images

Sylvie Gallet wrote:

>Congratulations, Janet!

And to you. You are an inspiration!

Jack Valero wrote:

> I just saw the results of the contest.
> Congratulations Linda and Sylvie.
> And a special congratulations to you, Janet!
> Once again the list members have demonstrated
> their excellent taste!

Thanks for your kind words.

Janet
[e-mail]
http://www.ParkeNet.org/jp


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Date: Mon, 22 Dec 1997 17:29:19 EST
From: T R Moe <[e-mail]>
Subject: (fractint) top three

congratulations to Janet, Sylvie, and Linda. Nice work all the way around.

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Date: Mon, 22 Dec 1997 14:52:51 -0800
From: kathy roth <[e-mail]>
Subject: Re: (fractint) Clouds Over Shiprock

Paul Derbyshire wrote:

> >I really wanted to view the fractal "Clouds Over Shiprock"
>
>
> >  I put clouds as a .par file and the formula as
> >a .frm file but when I tried to run it it said "oops I couldn't
> >understand the argument pixinv."
>
> Did you try it on the latest Fractint, 19.6?
>
> --
>     .*.  Friendship, companionship, love, and having fun are the reasons for
>  -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
>     `*'  Send any and all mail with attachments to the hotmail address please.
> Paul Derbyshire [e-mail] [e-mail]
>
> -
> ------------------------------------------------------------
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> Post Message:   [e-mail]
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Date: Mon, 22 Dec 1997 15:06:44 -0800
From: kathy roth <[e-mail]>
Subject: Re: (fractint) Clouds Over Shiprock

Paul Derbyshire wrote:

> >>I really wanted to view the fractal "Clouds Over Shiprock"
>
>
> >>I put clouds as a .par file and the formula as
> >>a .frm file but when I tried to run it it said "oops I couldn't
> >>understand the argument pixinv."
>
> >Did you try it on the latest Fractint, 19.6?

Yes, and I am wondering if that is part of what the problemis.  Are some of the
pars being written on earlier versions?
     Sorry about sending the previous partial message accidentally.
I hope you all have a wonderful holiday.

>
>




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End of fractint-digest V1 #40
*****************************