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fractint-digest         Friday, April 13 2001         Volume 01 : Number 550




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

Date: Wed, 11 Apr 2001 08:21:31 EDT
From: [e-mail]
Subject: (fractint) C-FOTD  11-04-01  (Veiled Objects [7])

Classic FOTD -- April 11, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Today's FOTD is late again . . . no surprise in that.  I'm still
busy.  But I have finally managed to find an image that rates
above a 6.  True, at a rating of 7, it's only a single step
above 6, but it's a start.

I named the image "Veiled Objects" when I noticed that the
smaller features seem to be draped over the larger objects like
a gossamer veil.  To create the image I unpacked number 6 in my
series of 12 MandNewt formulae.  This formula is a random
variation of the Ikenaga function, and the Ikenaga function is a
minor mystery.

The image takes 8-1/2 minutes to render at a low-resolution SF5,
but the highest resolution available is needed to do it justice.
The image may be seen by running the parameter file at the
resolution of your choice, or by downloading the GIF file from:

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

or from:

          <http://home.swbell.net/sdboyd56/fotd/>

once it has been posted.

The fractal weather today was cloudy but dry, with a temperature
of 68F (20C).  The fractal cats approved of the conditions.

That's it for today.  I've got a busy day ahead of me, and it's
time to get to work.  Until next time, take care, and hug at
least one fractal every day.


Jim Muth
[e-mail]


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

Veiled_Objects     { ; time=0:08:38.44--SF5 on a P200
  reset=2001 type=formula formulafile=mandnewt.frm
  formulaname=MandNewt06 passes=1
  center-mag=0.277319/-1.04425/35.70909/1/82.499
  params=-2.37/2.17/-1.56/-1.05/3.29/-3.17 float=y
  maxiter=254 inside=bof60 logmap=yes periodicity=0
  colors=000jwpjwqjwqhuogsmfqlepjdniclgajf`id_gcZeaY\
  c`XbZV`YUZWTXVSWTRUSQSQOQPNPNMNMLLKKJJJIHHGGGEEFCD\
  EBBD9AC78945B67D78F8AH9BJACLBENCFODGQEISFJUGKWHMYI\
  N_JO`KQbLRdMSfNUhOVjPWlQYmRZoS_qTasUbuVcwWexXfxYgr\
  ZdkZadZ_XZXQZVJZSAYRCZQDaNFeKGhHIlEInBJoCKoCKoCLoC\
  LoCMoCMoCNoCNoDOoDOoDPoDQoDQoDRoDRoDSoESoEToEToEUo\
  EUoEVoEWoEWoFXoFXoFYoFYoFZoFZoF_oF_oF`mG`lH`kIajIa\
  hJagKafLbeLbdMbbNbaOc`Oc_PcYQcXRdWRdVSdUTdSUeRUeQV\
  ePWdMYeOWeQVeRTeTSeUQeWPeXOeZMe_LeaJebIedHeeFegEeh\
  CejBekAdj9dj9cj9cj8cj8bj8bi8bi7ai7ai7ai7`i6`i6`h6_\
  h6_h5_h5Zh5Zh4Yh4Yg4Yg4Xg3Xg3Xg3Wg3Wg2Wf2Vf2Vf2Vf1\
  Uf1Uf1Uf1Te3Td4Td5Tc6Tc7Tb8Tb9TaBSaCS`DS`ES_FS_GSZ\
  HSZJSYKSYLRXMRXNRWORWPRVQRUSRUTRTURTVQSWQSXQRYQR_Q\
  Q`QQaQPbQPcQOdPOePNgPNhPMiPMjPLkPLlPKmPKnRMmTNmUOm\
  WQmXRlZSl`UlaVlcWkdYkfZkh_kiajkbjlcjnejpfiqgisiitj\
  ivkhxmhxnhxohkunkunkvojvp
  }

frm:MandNewt06 {; Jim Muth
z=c=(pixel*p1):
a=z^3+(c-p2)*z-c
b=p3*z^2+c-1
z=z-1*a/b
0.000000000000000000000000000001 <= |a|
}

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

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

Date: Wed, 11 Apr 2001 13:28:18 -0000
From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) C-FOTD 11-04-01 (Veiled Objects [7])

>From: [e-mail]
>Subject: (fractint) C-FOTD  11-04-01  (Veiled Objects [7])
>Date: Wed, 11 Apr 2001 08:21:31 EDT
>
>Classic FOTD -- April 11, 2001 (Rating 7)
>
>This formula is a random
>variation of the Ikenaga function, and the Ikenaga function is a
>minor mystery.

What the heck is the Ikenaga function?!?!

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

Date: Wed, 11 Apr 2001 13:35:54 -0000
From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Fractint Development

>From: Programmer Dude <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>Subject: Re: (fractint) Fractint Development
>Date: Wed, 04 Apr 2001 10:58:32 -0500
>
>No one has responded to this in a couple days, so I thought I'd take a
>shot at it...

Thanks.

>Andrew Coppin wrote:
>
> > So, you mean that FractInt can as such only use 64KB of memory?
>
>Sort of.
>
>FractInt was born as an MS-DOS program, and MS-DOS ran on Intel chips.
>Intel chips see memory as "segmented" rather than "flat" (as the Motorola
>chips (used in Apple machines) do).  Flat memory looks like one huge
>"address space".  For any memory location from 0000000 to umpteenzillion,
>the memory location just refers to the appropriate point, like milage
>along a road.
>
>In segmented memory, a memory location consists of two numbers: a
>segment and an offset.  The segment is like a rolling window that jumps
>in, IIRC, 256-byte jumps: segment 0 starts at 0, segment 1 starts at 256,
>and so on.  And a segment is a 64-k "window".  The offset refers to any
>location within that 64-k window.
>
>The Intel chips ran programs in an architecture that had four segments:
>a "Code" segment, a "Data" segment, a "Stack" segment and an "Extra"
>segment sometimes used as a second, extended Data segment).  Due to the
>nature of the C language (a primary development language of the day),
>the Stack and Data segments usually had to be identical.  You ended up
>with a 64-K window with your data growing from the bottom upwards and
>your stack growing from the top downwards.  The space in the middle was
>the "heap" and is where you got dynamically allocated memory from.
>
>The "Memory Model" is what various configurations of the segments is
>called.  Remember the old .COM programs?  By definition, they always
>use the "Tiny" memory model.  All segments are identical, and your
>entire program--data and code--must fit in a single 64-K window.
>
>The "Medium" memory model, IIRC, has the stack and data sharing one
>64-K segment, while the code lives in its own 64-K segment.
>
>This doesn't mean the program can't access data outside these segments.
>It can, but outside memory is "far" in the language of Intel memory
>models (opposed to the "near" memory in the data/stack segment).  Because
>the data/stack segment is "framed" by the segment pointers of the Intel
>architecture, you only need 16 bits (64-K) to address it.  But since "far"
>memory is 'somewhere in address space' you need a full address which was,
>at the time, 24 bits usually expressed as two 16-bit values with 8 bits of
>overlap.  Added together, they form a 24-bit address.
>
>The bottom line is that, in your program, you have a mix of "near" data
>and "far" data, and they require different variable types to refer to.

So it's an address space thing? What you're saying is that for certain
address ranges you can miss out a couple of the MSBits? (Hence presumably
smaller/faster code?)

> > What's involved in such a change? Is it just a case of going through the
> > program and changing half a million lines of code on a find-and-replace
> > basis, or does it require an actaul redesign of the code?
>
>I can't speak for the FractInt developers, and I'm not familiar with the
>code.  I can guess it lies between those two ideas.  It's not a simple
>matter of S&R; I'd guess you want to examine every place you need to change
>to see if the change breaks anything.  But it probably does NOT require a
>complete redesign.
>
>Ideally you'd like a compiler that let you treat memory as flat and make
>all your pointers be the same type.  I have no idea if such exists for
>the Intel platforms.

Can't you just treat everything as "far"?

>But then *I* think what you *really* want is to get away from MS-DOS.
>
> > I'd really prefer FractInt to remain a DOS program, or perhaps to have
> > a DOS *and* a Windows version. (...and a Linux/UNIX version, like they
> > do with POV-Ray. Hey... isn't that a Stone Soup project too?)
>
>Don't *think* POV-Ray (great program, BTW) is Stone Soup.  There's actually
>a great concept there.  POV-Ray renders to a disk file normally.  The
>Windows version just happens to have the extra treat of showing you the
>image as it's rendered.  But the heart of POV-Ray is a command line tool
>for rendering 3D scenes into an image file of some type.

Yeah, POV-Ray = utterly cool program!
Actually, the DOS and Amiga verisons show you previouse too (unless you turn
it off).

> >> The other problem is that we do indeed use extended and/or expanded
> >> memory for options other than just disk video.  Saving the on screen
> >> image when switching to a menu comes to mind.
> >
> > If you had more memory to play with, could this be avoided? (I
>understand
> > that disk video can use insane quantities of RAM, but keeping a copy of
> > the video buffer for a normal screen shouldn't be too bad...)
>
>But what I imagine they have to save is the fractal image while the menu
>screens are displayed.  That could be considerable.
>
>Anyway, hope this little data dump helped rather than confused...

Hmm... I remember back on the old 6502 processor found in the legendary C64
there was a "zero page" addressing mode, which only required an 8-bit
address instead of the usuall "absolute addressing" which required a 16-bit
address. I think you're saying the Intel CPU has a "base-offset" register or
something that lets you use shorter addresses (and limits your address
space). Close?

Thanks.
Andrew.

PS. I am now in possetion of the fractint source code. I'll spend some time
failing to understand it later...

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

Date: Wed, 11 Apr 2001 09:54:18 EDT
From: [e-mail]
Subject: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])

Andrew Coppin asked:

>What the heck is the Ikenaga function?!?!

That's the minor mystery!  The function is mentioned in the fractint.frm
file,
but no one seems to know where the function came from or whether it has
any use other than creating fractals.  There is an Ikenaga page on the 'net,
but the owner of that page denies being the function's originator.

Jim M.

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

Date: Wed, 11 Apr 2001 10:03:34 EDT
From: [e-mail]
Subject: (fractint) Re: C-FOTD  09-04-01  (Mandelbrot Mayhem [5])

The Programmer Dude wondered:

>Why should there *be* an ultimate fractal?  Seems kind of limiting...

There is no 'ultimate' fractal.  I intended the statement to be taken
ironically.

Jim M.

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

Date: Wed, 11 Apr 2001 10:13:07 -0500
From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) Fractint Development

Andrew Coppin wrote:

>> The Intel chips ran programs in an architecture that had four segments:
>> a "Code" segment, a "Data" segment, a "Stack" segment and an "Extra"
>> segment (sometimes used as a second, extended Data segment).
>>
>> The "Memory Model" is what various configurations of the segments is
>> called.
>>
>> The "Medium" memory model, IIRC, has the stack and data sharing one
>> 64K segment, while the code lives in its own 64K segment.
>>
>> This doesn't mean the program can't access data outside these segments.
>> It can, but outside memory is "far" in the language of Intel memory...
>
> So it's an address space thing? What you're saying is that for certain
> address ranges you can miss out a couple of the MSBits? (Hence presumably
> smaller/faster code?)

You can miss out on eight of them, yes.

>> Ideally you'd like a compiler that let you treat memory as flat and make
>> all your pointers be the same type.
>
> Can't you just treat everything as "far"?

Yes, and I'm sure this is what the developers would like to do.  It does
require a re-write, since it was NOT done this way originally.  Remember
the age of FractInt; back then speed was an issue (well, it still is),
and universal far addressing was often significantly slower depending on
the compiler, compiler libraries and how you went about it.  As has been
mentioned, even back then, there were MS-DOS "extenders" that could
present a flat address space to the system, but your compiler needed to
know about it to use it.

> Hmm... I remember back on the old 6502 processor found in the legendary C64
> there was a "zero page" addressing mode, which only required an 8-bit
> address instead of the usuall "absolute addressing" which required a 16-bit
> address. I think you're saying the Intel CPU has a "base-offset" register or
> something that lets you use shorter addresses (and limits your address
> space). Close?

Yes.  In fact, it has four (mentioned in the first paragraph above).  It
allows you to use 16-bit addresses with the tradeoff that you only get a
64K address space.  Unlike the 6502, your "segment" can start at any 256
byte boundary in the total address space.

- --
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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

Date: Wed, 11 Apr 2001 13:10:58 -0400
From: Lee Skinner <[e-mail]>
Subject: (fractint) C-FOTD  11-04-01  (Veiled Objects [7])

>> I named the image "Veiled Objects" when I noticed that the smaller
features seem to be draped over the larger objects like a gossamer veil. =
<<

It reminds me of a spacecraft orbiting around a planet.

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

Date: Thu, 12 Apr 2001 08:31:49 EDT
From: [e-mail]
Subject: (fractint) C-FOTD  12-04-01  {Blueberries [5])

Classic FOTD -- April 12, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

With today's fractal, which pictures a midget in the land of
Z^sqrt2+C, we slip back to a rating of 5.  This perfectly
average picture features a perfectly normal, though fractured,
midget that exists in a remote valley of its parent fractal.

I visit the Z^sqrt2 figure frequently because in this figure the
midgets are relatively easy to find compared to the midgets in
other figures with exponents of Z between 1 and 2.  Since 1.4142
is the square root of 2, the midgets in the Z^1.4142 figure
reveal their hiding places by being surrounded with the same
two-way symmetry that reveals midgets in the classic Z^2+C
figure.  But in the Z^1.4142 figure the midgets lie far deeper
and farther apart.

I named the image "Blueberries" when I noticed the berry-like
depressions surrounding the barely visible midget at the center.
There are roughly 9 berries in the outer ring and roughly 13
berries in the smaller inner ring, which is not at all
surprising, since 13/9 equals roughly 1.4142.

The parameter file takes over 23 minutes to render on a 200mhz
Pentium machine.  It will run faster on a faster machine, but
not so fast as to make a download of the GIF image file
superfluous.  That image file may be found on the Web at:

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

and at:

          <http://home.swbell.net/sdboyd56/fotd/>

The fractal weather today featured a steady rain from dawn to
dusk.  The temperature of 52F (11C) combined with the rain to
keep the cats snug indoors in their beds.

Once again we come to the end of the FOTD.  It was a relatively
brief one because I'm still busy.  But eventually I'll catch up,
and then, anything could happen.  Until next time, take care,
and help preserve fractals from extinction.


Jim Muth
[e-mail]


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

Blueberries        { ; time=0:23:16.75--SF5 on a P200
  reset=2001 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1
  center-mag=-1.04105767849226400/-1.142969742678717\
  00/1.290666e+007/1/90 params=1.414213562373/0/100/0
  float=y maxiter=2800 inside=0
  logmap=569 periodicity=10
  colors=000GU0GU0ET0CQ0AO08M06K04I02G00D00D00B00900\
  60050020020000000000000000000000000000000000000000\
  0000000200200400400400600620640840860A80A80AA0CC0C\
  E0CE0EG0EH0GH2GJ2GL2HL4HN4HP6JR6JR8LT8LVALVANXCNZC\
  NZEP`EPbEPbCRdCRdATdATd8Vd8Vd6Vd6Xd4Xd4Ze2Ze2Ze0`e\
  0`e0be0be0be0de0de0eg0eg0gg0gg0gg0ig0ig0kg0kg0kg0m\
  i0mi0oi0oi0oi0qi0qi0si0si0uk0si0sg0qg0qe0oe0od0ob0\
  mb0m`4k`6kZAiZCiXGiVHgVLgTNeTReRTeRXdP`dNbbNebLg`L\
  k`Jm`HqZHsZGvXGxXEzVEzVCzVAzTAzT8zR8zR6zN4zR6zV8zX\
  8z`AzbAzeCzgCzkEzmEzqGzsGzvHxxHvzJuzJszLszLozNmzNk\
  zNizNgvNeuPdsPbqP`mPZkPXiPVgRTdRRbRP`RNZRNZTLXRJXR\
  JXPHVPGYNG`NEcNEfLCiLAfJAcJ8_J6WI6SJ4PK4ML2JM0GN0D\
  O0AP0AQ0AR0AS0AT0AU0AV0AW0CX0EY0GZ0G_0E`0Ga0Gb0Gc0\
  Gd0He0Hf0Hg0Hh0Ji0Jj0Jk2Jl2Lm4Ln6Lo8Lp8NqANrCNsENt\
  EPuGPvHPwJPxJRyLRzNRzPRzPTzRTzTTzVTzVVzXVzZVz`Vz`V\
  zbTzdTzdTzeTzeTzgTzgRziRz
  }

frm:MandelbrotBC = { ; Z = Z^E + C
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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

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

Date: Thu, 12 Apr 2001 19:54:54 -0500
From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])

> That's the minor mystery!  The function is mentioned in the fractint.frm
> file, but no one seems to know where the function came from or whether it
has
> any use other than creating fractals.

From the ikenaga.frm file that came with FRAC'Cetera volume 2 issue 7 (Jon
Horner's publication):

  IKENAGA - Formula originally discovered by Bruce Ikenaga, at Western
Reserve
  University, Indiana.  Documented in Dewdney's `Armchair Universe".

          The Ikenaga set is:    Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C
          where:                      Z(n) = x + yi and C = a + bi

Jonathan



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

Date: Thu, 12 Apr 2001 23:15:35 -0400
From: Bill Jemison <[e-mail]>
Subject: (fractint) Jonathan - puzzling par

Jonathan,

I can't get the following par to generate at any higher res that SF5
(640x480x256).

Is this a bug? or is something going on that I am missing?

***************************************************

billtest           {
                     ;  Version 2001 Patchlevel 6
  reset=3D2001 type=3Dlorenz passes=3Dd
  center-mag=3D+0.00000000000000000/+15.00000000000000000/1.333333/1.3333=

  params=3D0.02/5/15/1 float=3Dy maxiter=3D1000 fillcolor=3D0 inside=3D0
  outside=3D0 cyclerange=3D1/1 sound=3Dbeep/fm orbitdelay=3D1000 showorbi=
t=3Dyes
  colors=3D000pdQ0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKK=
KOO\
  O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>z=
V\
  V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S=
0\
  S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSK=
K\
  S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<=
3\
  >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88=
G\
  8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFB=
G\
  GBFGBDGBCG000<6>000
  }

****************************************************

Bill

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

Date: Thu, 12 Apr 2001 23:42:46 EDT
From: [e-mail]
Subject: (fractint) C-FOTD  13-04-01  (Squirt [6])

Classic FOTD -- April 13, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

It's been another very busy day here at Fractal Central, but not
so busy that I needed to forego my daily fractal search.  It was
however too busy for the enlightening philosophy that you've all
been waiting for.  But there's a long future ahead, and the
philosophy will come at the proper time.  (I don't want to solve
the riddle of the universe too soon -- that would take all the
fun out of it.)

Today's fractal is named "Squirt".  I gave it this name because
the image pictures another midget in the Z^(sqrt2)+C Mandeloid,
and the Fractint abbreviation for 'square root' is 'sqrt', and
if the letters u and i are added to the middle of 'sqrt', the
word becomes 'squirt'.  Another reason is that I often pronounce
'square root' as 'squirt'.

The image, which vaguely resembles an octopus or starfish, is a
bit above average, just enough to deserve the rating of 6 that I
gave it.  These 'squirt' midgets are becoming more interesting
as I develop the knack of finding them.  And the Z^(sqrt2)+C
figure, unlike the familiar Z^2+C figure, is infinite in its
surface extent.

The attached parameter file takes 29 minutes to render on an
aging Pentium running at 200mhz.  Newer and faster machines will
render the image in far less time.  Older, slower ones will take
far longer.

Regardless, the GIF file of the image will soon be posted to:

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

and to:

          <http://home.swbell.net/sdboyd56/fotd/>

The fractal weather today was partly cloudy with an afternoon
temperature of 66F (19C).  These conditions must have suited the
dynamic duo of cats perfectly, since they spent the entire
afternoon basking in the on-again off-again sunshine.  As for
me, I spent the afternoon trying to work my way through the
backlog, having only minor success.

Well, I see it's now time to shut down the fractal place and
call it a night.  Until next time, when I'll return with more
goodies, take care and be ever vigilant for that once-in-a-
lifetime fractal.


Jim Muth
[e-mail]


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

Squirt             { ; time=0:29:41.84--SF5 on a P200
  reset=2001 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1
  center-mag=-0.91532246418772030/+0.387841135413711\
  50/2.102521e+012/1/90 params=1.414213562373/0/120/0
  float=y maxiter=2800 inside=0 logmap=890
  mathtolerance=/1 periodicity=10
  colors=000IgmEzwEzwEzwGzxGzxGzxGzzGzzHzzHzzHzzHzzJ\
  zzJzzJzzJzzKzzJzzJxzJwzJtxJrwJouJlrJkqJhoJfnJckJbi\
  J_hJXeJVcHSbHQ`HNYHKXHJVHGSBEQ8BPBAN77K24J02HH0EH0\
  DH0BH0AJ0BK0BM2DN5DP7EQAESDETGGVHGXKHYNH_QH`TJbVJc\
  YKe`KfcKheMihMkkNlnNloNlnNlnMklMkkMkkKiiKiiJihJihH\
  hfHheHheGfcGfcEfbEfbEe`Ge`Hc_Jc_KcYMbYNbXPbXQ`XS`V\
  T`VV_TX_TY_S_YS`YS`YQbXQcXPeXPfVNhVNiVMkTMlTMnTKoS\
  KqSJrSJtQHuQHwQHwPKuPMuPPuNQtNTtNVtNYrM_rMbrMcqMfq\
  KhqKkoKloJooJqnJtnJunHxlHzlHzlHzlJznJznKxoKwoMtqMr\
  qNqrNorNlrPktPitQhuQeuScwSbwT`xTYxTXxVVzVTzXQzXPzY\
  NzYMz_MzYKzXKzXJzVJzVHzTHzTGxSGxQExQExPDzUDzZPzcUz\
  UPzUEzK8zJ8xJ7tH7qH5lG5iG4eE4bD2_D2YB1YB1XA0_A0`80\
  c50i80iB0fE0cH1`K1YM2XP4TS4QV5NY5K`7Hc4Hb7G`AG_BEY\
  EEYHDXJDVMDTPBSQBSTAQVAPY8N`8Mb8Me7Kh7Ji5Hl5Hn5Go4\
  Eq4Dr4Br4At48u47u45w44x42z42z21z20z20z20z20z20z20z\
  20z20z20z10z20z40z40z50z7
  }

frm:MandelbrotBC = { ; Z = Z^E + C
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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

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Date: Fri, 13 Apr 2001 03:57:28 -0400
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Fractint Development

- ------=_NextPart_001_0000_01C0C3CD.DC545440
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

> Can't you just treat everything as "far"?

Sure, which solves problems of total available memory. But you still get =
problems trying to maintain any contiguous data structure (e.g. array) sp=
anning more than 64kb. With flat memory this is as easy as smaller data s=
tructures.<br clear=3Dall><hr>Get Your Private, Free E-mail from MSN Hotm=
ail at <a href=3D"http://www.hotmail.com">http://www.hotmail.com</a>.<br>=
</p>

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Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> Can't you=
 just treat everything as "far"?<BR></DIV> <DIV>Sure, which solves proble=
ms of total available memory. But you still get problems trying to mainta=
in any contiguous data structure (e.g. array) spanning more than 64kb. Wi=
th flat memory this is as easy as smaller data structures.</DIV> <DIV>&nb=
sp;</DIV> <DIV> </DIV></BODY></HTML><DIV><BR><br clear=3Dall><hr>Get=
 Your Private, Free E-mail from MSN Hotmail at <a href=3D"http://www.hotm=
ail.com">http://www.hotmail.com</a>.<br></p></DIV>

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Date: Fri, 13 Apr 2001 07:56:34 -0500
From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Jonathan - puzzling par

Bill,

> I can't get the following par to generate at any higher res that SF5
> (640x480x256).

> Is this a bug? or is something going on that I am missing?

Here is an excerpt from lorenz.c:

>>
/* BAD_PIXEL is used to cutoff orbits that are diverging. It might be better
to test the actual floating point orbit values, but this seems safe for now.
A higher value cannot be used - to test, turn off math coprocessor and
use +2.24 for type ICONS. If BAD_PIXEL is set to 20000, this will abort
Fractint with a math error. Note that this approach precludes zooming in
very
far to an orbit type. */

#define BAD_PIXEL  10000L    /* pixels can't get this big */
<<

Setting BAD_PIXEL to 20000 does let your par generate.  I suspect that upon
further zooming in, the same thing will happen.  IMO, this qualifies as a
bug.  Although I'm not sure what we would gain by being able to zoom into
these types.  Tim may have more insight into what the problem is.

Jonathan



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Date: Fri, 13 Apr 2001 11:28:54 -0500
From: DeBow Freed <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
Thanks to Jonathan!
<p>A Bruce Ikenaga currently on the Math Faculty at Millersberg, PA last
year denied any knowledge or authorship of the IF's. I was unable to locate
any other "Ikenaga" in the US, Europe or Japan using various Mathematical
Society Membership Records available at this January's Joint Math Meeting
in New Orleans.
<p>Are their <u>two</u> Bruce Ikenaga's, both teaching math at US universities?
Maybe this is akin to expressing surprise that there are 2 John Smith's
selling pork bellies in Chicago, but I don't know common the name Ikenaga
is, nor the joint probability of first name Bruce and being a practicing
Math academic.
<p>Perhaps the "Veiled Object" is really just Ikenaga.
<br>
<p>Freed
<br>
<br>
<p>Jonathan Osuch wrote:
<blockquote TYPE=CITE>> That's the minor mystery!  The function is
mentioned in the fractint.frm
<br>> file, but no one seems to know where the function came from or whether
it
<br>has
<br>> any use other than creating fractals.
<p>>From the ikenaga.frm file that came with FRAC'Cetera volume 2 issue
7 (Jon
<br>Horner's publication):
<p>  IKENAGA - Formula originally discovered by Bruce Ikenaga, at
Western
<br>Reserve
<br>  University, Indiana.  Documented in Dewdney's `Armchair
Universe".
<p>          The Ikenaga set
is:    Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C
<br>          where:
Z(n) = x + yi and C = a + bi
<p>Jonathan
<p>--------------------------------------------------------------
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Date: Fri, 13 Apr 2001 11:38:14 -0500
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])

DeBow Freed wrote:
>
> Are their two Bruce Ikenaga's, both teaching math
> at US universities?

No, it is the same person.  All details may be found at his home page
and the associated web pages (see the page on Biographical Information):

       http://www.millersv.edu/~bikenaga/

Sincerely,
P.N.L.
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Date: Fri, 13 Apr 2001 12:07:16 -0500
From: DeBow Freed <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
Thanks Paul.
<p>Ikenaga's response to my query last year (and I believe his homepage
also lists) one fairly lengthy Adobe-ized set of "classnotes" concerning
Fractals which he (Ikenaga) stated were "trivial".
<p>He also said he had, indeed, heard of a program called "Fractint", which
he liked, and perhaps would take a look at some of last year's pod of Ikenaga-based
FOTD's from Jim (which I forwarded to him) and some the Discussion Group
pages. Subsequently, <i>no mas </i>was ever heard from Dr. Ikenaga<i>.</i>
<p>He twice denied any recollection of having produced anything substantive.
<br>Perhaps we should let him in on the secret.
<p>DeBow
<p>"Paul N. Lee" wrote:
<blockquote TYPE=CITE>DeBow Freed wrote:
<br>>
<br>> Are their two Bruce Ikenaga's, both teaching math
<br>> at US universities?
<p>No, it is the same person.  All details may be found at his home
page
<br>and the associated web pages (see the page on Biographical Information):
<p>       <a href="http://www.millersv.edu/~bikenaga/">http://www.millersv.edu/~bikenaga/</a>
<p>Sincerely,
<br>P.N.L.
<br>--------------------------------------------------------------
<br><a href="http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go">http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go</a>
<p>--------------------------------------------------------------
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Date: Fri, 13 Apr 2001 13:07:04 -0400
From: Bill Jemison <[e-mail]>
Subject: (fractint) Jonathan - puzzling par

Thanks Jonathan (although I don't have a clue as to what you are talking =

about <g>) As you may have surmised, my reason for zooming into this =

type fractal is strictly for sound-generation purposes.
  =

************************

> I can't get the following par to generate at any higher res that SF5
> (640x480x256).

> Is this a bug? or is something going on that I am missing?

Here is an excerpt from lorenz.c:

>>
/* BAD_PIXEL is used to cutoff orbits that are diverging. It might be =

better
to test the actual floating point orbit values, but this seems safe for =

now. A higher value cannot be used - to test, turn off math coprocessor a=
nd
use +2.24 for type ICONS. If BAD_PIXEL is set to 20000, this will abort
Fractint with a math error. Note that this approach precludes zooming in
very far to an orbit type. */

#define BAD_PIXEL  10000L    /* pixels can't get this big */
<<

Setting BAD_PIXEL to 20000 does let your par generate.  I suspect that up=
on
further zooming in, the same thing will happen.  IMO, this qualifies as a=

bug.  Although I'm not sure what we would gain by being able to zoom into=

these types.  Tim may have more insight into what the problem is.

Jonathan



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Date: Fri, 13 Apr 2001 12:20:48 -0500
From: DeBow Freed <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
To all-
<p>Before I disseminate more misinformation than usual, Dr. Ik's "classnotes"
[his phrase] on "Self-SimilarFractals" are available at the homepage address
provided by PNL in the form of a <u>Mathematica 2.1 Notebook</u> [<b>not
Adobe</b>, as I previously stated], which I did not have the ability to
convert to legible text at the time.
<p>When I heard nothing further from Dr. Ikenaga, I (obviously mistakenly)
assumed he knew his own work better than I ever would, gave up the search
for archaic versions of Mathematica software with which to translate his
2.1 Notebook, and took the man at his word.
<p>Funny, wonder what the real genesis of the functionals was.
<p>Freed
<br>
<p>DeBow Freed wrote:
<blockquote TYPE=CITE>Thanks Paul.
<p>Ikenaga's response to my query last year (and I believe his homepage
also lists) one fairly lengthy Adobe-ized set of "classnotes" concerning
Fractals which he (Ikenaga) stated were "trivial".
<p>He also said he had, indeed, heard of a program called "Fractint", which
he liked, and perhaps would take a look at some of last year's pod of Ikenaga-based
FOTD's from Jim (which I forwarded to him) and some the Discussion Group
pages. Subsequently, <i>no mas </i>was ever heard from Dr. Ikenaga<i>.</i>
<p>He twice denied any recollection of having produced anything substantive.
<br>Perhaps we should let him in on the secret.
<p>DeBow
<p>"Paul N. Lee" wrote:
<blockquote TYPE=CITE>DeBow Freed wrote:
<br>>
<br>> Are their two Bruce Ikenaga's, both teaching math
<br>> at US universities?
<p>No, it is the same person.  All details may be found at his home
page
<br>and the associated web pages (see the page on Biographical Information):
<p>       <a href="http://www.millersv.edu/~bikenaga/">http://www.millersv.edu/~bikenaga/</a>
<p>Sincerely,
<br>P.N.L.
<br>--------------------------------------------------------------
<br><a href="http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go">http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go</a>
<p>--------------------------------------------------------------
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End of fractint-digest V1 #550
******************************