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fractint-digest        Saturday, March 31 2001        Volume 01 : Number 547




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

Date: Mon, 26 Mar 2001 10:16:41 -0600
From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) Earthquake As Artist

MDrozdis wrote:

>>> ...the article, notice the name of the monk's helper.
>>
>> Thelonius??
>>
>> I don' get it....   ;-(
>
> Thelonius Monk, Jazz Great.

Doh!!!!

Great.  Now I can spend the rest of the week feeling very, very stupid.
I even *own* a couple Monk albums......

:-\

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|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
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------------------------------

Date: Tue, 27 Mar 2001 07:17:12 EST
From: [e-mail]
Subject: (fractint) Missing FOTD

Fractal fans:

Despite my best efforts to continue the FOTD during the current hectic
conditions, I find I am unable to do so without an unacceptable decline
in quality.  In other words, I don't have the time to find the fractals and
write the discussion.  Therefore I must suspend the FOTD until the rush
has passed.  Look for the FOTD to resume around April 3.  There are
still googols of fractals I have not yet found, and lots of fractal
philosophy
I have yet to broach.

Jim M.


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Date: Wed, 28 Mar 2001 12:36:28 -0000
From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) Twenty & One

Arh maaaan, it's my birthday today, and for the first time in months I've
got a completly empty FractInt mailbox today... Not even an FotD... and it's
raining! And I'm sitting at home all by my self... AND I've got to go to
work tonight, and scrub greasy floors on my birthday...

But still, all is not lost... Actually, I'm not writing this messing simply
to bore you all with my unhappyness (for this IRC was invented!) What I'm
really after is fractal formulae, 3 particular ones in fact...

Does anyone here (hello Morgan 8-) know what the generalised Quartic
Mandelbrot formula is?

Next, what about the experiment with the pendulumn and the three magnets?
Can anyone explain to me how I can get fractint to run that simulation? (The
video I saw it on did contain some differential equations, but 1. I do not
really understant such things and 2. I no longer have the video; the library
wanted it back!)

And finally, has anyone ever seen that Mandeloid based on Newton's
Approximation of the Cube Roots of Unity, the one that looks like a figure
of 8 rotated through 90 degrees? What's the formula for that?

Thanks.
Andrew.

PS. It may be raining, I may be all alone, and I may have to go to work
tonight, but I still have FractInt. And LaTeX. It could be much worse! (And
was until yesterday!!!)

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Date: Wed, 28 Mar 2001 17:25:20 +0300 (EET DST)
From: Ville V Sinkko <[e-mail]>
Subject: Re: (fractint) Earthquake As Artist

On Mon, 26 Mar 2001, Programmer Dude wrote:

> Abhishek Roy wrote:
>
> > Hoax. Featured on both slashdot and kuro5hin. Apart from the date of
> > the article, notice the name of the monk's helper.
>
> Thelonius??
>
> I don' get it....   ;-(

The joke is, of course, that it's misspelled. ;) Thelonious Monk, a
jazz pianist. Died 1980-ish. Mighty nice music.

While I'm at it, I might just as well say "Hi" (I just subscribed,
thanks to recently born interest in the F-word) and challenge you
to come up with a fractal picture that represents a thelonious sphere.


+Cinquo


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

Date: Wed, 28 Mar 2001 06:52:11 -0800
From: "Diana L. Dubel" <[e-mail]>
Subject: (fractint) The Fractal Art screen saver is exquisite!

The screen saver is one of the most beautiful things I have seen.  Thanks to
the creators.

Diana

========================================
Diana L. Dubel  :-)

Experience is that marvelous thing that enables you
to recognize a mistake when you make it again.
        -Franklin P. Jones

E-mail - - - [e-mail]
http://home.earthlink.net/~dldubel/

- -----Original Message-----
From: [e-mail]
[mailto:[e-mail]]On Behalf Of Paul N. Lee
Sent: Sunday, March 25, 2001 9:56 AM
To: [e-mail]; [e-mail];
[e-mail]; [e-mail];
[e-mail]
Subject: (fractint) "Fractal Art Screensaver Project" is ready.


Greetings,

I am sending out this notice after receiving an email from Doug
Harrington, explaing that his time has been very limited lately and that
he "would welcome any help" regarding posting a notice of the
availabibility of the new screensaver.

Doug mentioned that he has already "submitted the saver to a couple of
major software sites, ZDNET etc. and still have some to do....", so
hopefully word will soon spread with everybody's help.

Doug Harrington has spent a lot of time and effort on this volunteer
project that was introduced several weeks ago.  He has been
communicating with 49 different artists, at different times, about
different topics, over a 4-6 week to finally resolve all issues that
could be resolved (considering the time and number of individuals
involved).

The basic information about the "Fractal Art Screensaver Project" may be
found at the following URL:

     http://Fractalarts.com/ASF/FASP.html

where you can review the Artists that were involved and retrieve a copy
of this project.  The file is approximately 7-MB in size, but
considering the software and number of images, this is really a great
deal of information packed into a single file.

I hope that this is only the first of many such projects, or even a
series of screensavers showcasing the fractal art of the worldwide
community.

Sincerely,
P.N.L.

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

Date: Wed, 28 Mar 2001 13:42:06 -0600
From: Bob Margolis <[e-mail]>
Subject: Re: (fractint) Twenty & One

Andrew Coppin wrote:

>
> Next, what about the experiment with the pendulumn and the three magnets?
> Can anyone explain to me how I can get fractint to run that simulation? (The
> video I saw it on did contain some differential equations, but 1. I do not
> really understant such things and 2. I no longer have the video; the library
> wanted it back!)
>

Hi Birthday Boy (Birthday Man?);

There was a software package that came out for MS-DOS 11 years ago. It
is called James Gleick's Chaos: The Software and I still have it,
although it's far from being state-of-the-art now. One of the fractal
modules is a program called Magnets and Pendulum. It used many magnets,
not just three, but 16, if you felt like having that number. The book
that accompanied the software discussed the mathematics of the program.
It was also stated in the book, "You can read more about pendulum
systems in James Gleick's Chaos: Making a New Science, pages 40-44. For
more information on sensitive dependence on initial conditions, see
Chaos: Making a New Science, pages 20-23. While the software package
will be hard to find, you may find it easier to locate Chaos: Making a
New Science at an online bookstore, Border's or Barnes and Noble; or try
Amazon.com or Bibliofind.com.

Hope this information is of use to you.

Now go and enjoy your birthday cake.

Cheers,

Bob
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------------------------------

Date: Wed, 28 Mar 2001 19:59:16 EST
From: [e-mail]
Subject: Re: (fractint) Twenty & One

In a message dated 01-03-28 07:38:29 EST, you write:

<< Arh maaaan, it's my birthday today >>
Happy Birthday!! Hope things perk up a bit for some form of mini-celebration.

Sorry, can't help you with the formulas, though.  That Magnet and Pendulum
thing sounds interesting, good luck!

~renrad

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

Date: Wed, 28 Mar 2001 23:55:06 -0600
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Twenty & One

Bob Margolis wrote:
>
> There was a software package that came out for
> MS-DOS 11 years ago. It is called James Gleick's
> Chaos: The Software ......
> While the software package will be hard to find...

Try the following location for the above mentioned software:

    http://www.mathcs.sjsu.edu/faculty/rucker/


Sincerely,
P.N.L.
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------------------------------

Date: Thu, 29 Mar 2001 00:12:57 -0600
From: Bob Margolis <[e-mail]>
Subject: Re: (fractint) Twenty & One

"Paul N. Lee" wrote:
>
>
> Try the following location for the above mentioned software:
>
>     http://www.mathcs.sjsu.edu/faculty/rucker/
>

I forgot all about Rudy Rucker. He and I had a nice phone conversation a
couple of years ago. Anyway, yes, the software is freely available at
his Web site.

Thanks as always, Paul!

Cheers,

Bob
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------------------------------

Date: Wed, 28 Mar 2001 21:35:41 -1000
From: "David Jones" <[e-mail]>
Subject: Re: (fractint) Twenty & One

Cool - looks like fun - just added it to the bookmark
collection! Thanks!

David
[e-mail]

On 28 Mar 01 at 23:55, Paul N. Lee wrote:

> Bob Margolis wrote:
> >
> > There was a software package that came out for
> > MS-DOS 11 years ago. It is called James Gleick's
> > Chaos: The Software ......
> > While the software package will be hard to find...
>
> Try the following location for the above mentioned
> software:
>
>     http://www.mathcs.sjsu.edu/faculty/rucker/


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

Date: Thu, 29 Mar 2001 15:17:16 -0000
From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Twenty & One

>From: "David Jones" <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>Subject: Re: (fractint) Twenty & One
>Date: Wed, 28 Mar 2001 21:35:41 -1000
>
>Cool - looks like fun - just added it to the bookmark
>collection! Thanks!
>
>David
>[e-mail]
>
>On 28 Mar 01 at 23:55, Paul N. Lee wrote:
>
> > Bob Margolis wrote:
> > >
> > > There was a software package that came out for
> > > MS-DOS 11 years ago. It is called James Gleick's
> > > Chaos: The Software ......
> > > While the software package will be hard to find...
> >
> > Try the following location for the above mentioned
> > software:
> >
> >     http://www.mathcs.sjsu.edu/faculty/rucker/

As always, FractInt people prove to be knowledgable people! 8-]

Thanks for the info. Now how about the Newton-Mandeloid and the General
Quartic?

Thanks.
Andrew.

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

Date: Thu, 29 Mar 2001 09:39:37 -0600
From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) Twenty & One

"Paul N. Lee" wrote:

> Try the following location for the above mentioned software:
>
>     http://www.mathcs.sjsu.edu/faculty/rucker/

Rudy Rucker!!  I'm a fan of that guy!  He wrote four (or more?) really
interesting (and different) SF novels.  Been ages since I read them,
and I keep noticing them on the shelf and thinking, "Hmmm, time to read
those again."  Having his name brought up here must be a sign that it
IS time to read those again.

Isn't Rucker the guy who first talked about the L26 system?  I think
it was in his book, MIND TOOLS.  If you consider the alphabet as a
base-26 numbering system, any word is a single number.  If you expand
the base a bit so you can include spaces and punctuation in your
symbols, you can consider entire sentences, paragraphs and even books
as single numbers.  Very, very, VERY large numbers.

But what a cool concept!  I wrote a program once that would take a
short string and return its number.  Wonder what I did with that...

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

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

Date: Thu, 29 Mar 2001 15:47:22 -0000
From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Twenty & One

>From: Programmer Dude <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>Subject: Re: (fractint) Twenty & One
>Date: Thu, 29 Mar 2001 09:39:37 -0600
>
>Isn't Rucker the guy who first talked about the L26 system?  I think
>it was in his book, MIND TOOLS.  If you consider the alphabet as a
>base-26 numbering system, any word is a single number.  If you expand
>the base a bit so you can include spaces and punctuation in your
>symbols, you can consider entire sentences, paragraphs and even books
>as single numbers.  Very, very, VERY large numbers.
>
>But what a cool concept!  I wrote a program once that would take a
>short string and return its number.  Wonder what I did with that...

Yeah, they call it ASCII.  8¼>

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

Date: Thu, 29 Mar 2001 15:54:27 -0000
From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) Fractint Development

I know this one's a recurring theame but...

What's the deal with fractint's current development status? It's ages since
the last "official" release (not the developer's patches). There seems to be
very little happening. Is this true? Or are folk sooo busy developing that
they have no time to tell us about progress?

So, how many peeps are working on this, and what are they trying to do
(there's a whole wedge of things that people have asked for; true-colour
support, hypercomplex/quat parser formulas, more colouring options, more
builtin types, true-colour support...)

And then there's the whole question of porting FI to Windows to escape the
memory limitations of DOS. I've always wondered about this; why is there a
memory problem with DOS but not Windows? Surely FI doesn't do anything that
requires virtual memory (except disk video of course!) Could someone attempt
to explain this to me?

I expect I'm not the only one who's wondering about these things. Thanks in
advance for your answers.

Andrew.

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Date: Thu, 29 Mar 2001 10:20:56 -0600
From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) Twenty & One

Andrew Coppin wrote:

>> If you expand the base a bit so you can include spaces and punctuation
>> in your symbols, you can consider entire sentences, paragraphs and eve=
n
>> books as single numbers.  Very, very, VERY large numbers.
>=20
> Yeah, they call it ASCII.  8=AC>

[BWG]

Yeah, and base-128 numbers get **really** huge fast!!

Watch this!

CHRIS =3D (in decimal ASCII)  67, 72, 82, 73, 83

As a base-128 number:  67 * 128^4 =3D 17,985,175,552
                       72 * 128^3 =3D    150,994,944
                       82 * 128^2 =3D      1,343,488
                       73 * 128^1 =3D          9,344
                       83 * 128^0 =3D             83
                                    --------------
                      "My Number" =3D 18,137,523,411

For a mere five "digit" number!  It boggles the mind to consider the
size of the number of, say, WAR AND PEACE (or the latest Tom Clancy
novel)!!

- --=20
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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Date: Thu, 29 Mar 2001 18:39:36 +0200
From: Ulrich =?iso-8859-1?q?Gr=FCn?= <[e-mail]>
Subject: Re: (fractint) Fractint Development

Also schrieben Sie (Andrew Coppin) am Donnerstag 29 MΣrz 2001 17:54:
> I know this one's a recurring theame but...

.. and how about the development for Linux. The current version (20-07)
doesn't do colour cycling (at least not at my system).

                             Ulrich
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------------------------------

Date: Thu, 29 Mar 2001 19:13:57 +0100
From: "Rupert Millard" <[e-mail]>
Subject: Re: (fractint) Twenty & One

Andrew,

> Thanks for the info. Now how about the Newton-Mandeloid and the General
> Quartic?

Is this what you wanted for the Newton-Mandeloid?

KRup2000-41{
;By Rupert Millard
l=pixel
a=l*p1
b=l*p2
c=l*p3
;Solve the cubic equation z^3+bz^2+cz+d=0 - I must be mad
q=(3*b-a^2)/9
r=(9*a*b-27*c-2*a)/54
s=(r+sqrt(q^3+r^2))^(1/3)
t=(r-sqrt(q^3+r^2))^(1/2)
r1=s+t-a/3
r2=-(s+t)/2-a/3+(0,0.5)*sqrt(3)*(s-t)
r3=conj(r2)
;Then the centroid is the point to iterate
z=(r1+r2+r3)/3:
oldz=z
z=z-(z^3+a*z^2+b*z+c)/(3*z^2+2*a*z+b)
|oldz-z|>0.0001}

It iterates Newton's method cubic equation with coefficients proportional to
the coordinates of the pixel (starting at the centroid of the roots of said
equation.) This formula contains minibrots. For proof try:

temp               {
  ; By Rupert Millard ([e-mail]) on Mar 29, 2001
  reset=2001 type=formula formulafile=krup2000.frm
  formulaname=KRup2000-41 center-mag=-2.02977/-1.38778e-015/7.704635
  params=0/0/1/0/1/0 float=y maxiter=500 inside=0 symmetry=none
  cyclerange=0/255 colors=@blues.map
  }

I could make an extended version, for UF as Fractint doesn't have enough
parameters. This would have a constant amount added on to the multiple of
the pixel coordinate (it could be stop a coefficient from being varied.)
Like all my UF formulae you could vary the bailout. It could also be
quartic. Would that produce cubic minibrots? I'll try and find out. Of
course, you're all welcome to try to beat me to it. Its a shame that
Fractint doesn't have the capabilities to handle more than five complex
parameters.

For the general quartic (nb. Requires patch Fractint 20.0.13 or more
recent):

QuarticMandelbrot{
;p1 is multiplier of z^4
;p2 is multiplier of z^3
;p3 is multiplier of z^2
;p4 is multiplier of z
z=c=pixel:
z=p1*z*z*z*z+p2*z*z*z+p3*z*z+p4*z+c
|z|<=128
}

From,

Rupert

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Date: Thu, 29 Mar 2001 18:57:59 -0600
From: "Brian Baske" <[e-mail]>
Subject: RE: (fractint) Twenty & One

You wanna see big, try Goedel numbering...

> -----Original Message-----
> From: [e-mail]
> [mailto:[e-mail]]On Behalf Of Programmer Dude
> Sent: Thursday, March 29, 2001 10:21
> To: [e-mail]
> Subject: Re: (fractint) Twenty & One
>
>
> Andrew Coppin wrote:
>
> >> If you expand the base a bit so you can include spaces and
> punctuation
> >> in your symbols, you can consider entire sentences,
> paragraphs and even
> >> books as single numbers.  Very, very, VERY large numbers.
> >
> > Yeah, they call it ASCII.  8=AC>
>
> [BWG]
>
> Yeah, and base-128 numbers get **really** huge fast!!
>
> Watch this!
>
> CHRIS =3D (in decimal ASCII)  67, 72, 82, 73, 83
>
> As a base-128 number:  67 * 128^4 =3D 17,985,175,552
>                        72 * 128^3 =3D    150,994,944
>                        82 * 128^2 =3D      1,343,488
>                        73 * 128^1 =3D          9,344
>                        83 * 128^0 =3D             83
>                                     --------------
>                       "My Number" =3D 18,137,523,411
>
> For a mere five "digit" number!  It boggles the mind to consider the
> size of the number of, say, WAR AND PEACE (or the latest Tom Clancy
> novel)!!
>
> --
> |_ CJSonnack <[e-mail]> _____________| How's my
> programming? |
> |_ http://www.Sonnack.com/ ___________________| Call:
> 1-800-DEV-NULL  |
> |_____________________________________________|_______________
> ________|
>
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>


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Date: Thu, 29 Mar 2001 19:33:11 -0600
From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Fractint Development

Andrew,

> What's the deal with fractint's current development status? It's ages
since
> the last "official" release (not the developer's patches). There seems to
be
> very little happening. Is this true? Or are folk sooo busy developing that
> they have no time to tell us about progress?

I am currently working on the true color support for the DOS version.  There
seems to be a problem with the routines that Bert Tyler added.  At any rate,
I'm having difficulty getting the images to appear correctly colored on the
screen.  I'll let you know when it is fixed.

The memory limitations stem from two sources.  One is that Fractint is
compiled in the medium memory model.  This means that memory usable for near
data is limited to 64KB unless some form of swapping is done.  This memory
includes the stack space, and we are banging up against this limit
constantly.  And, no it isn't a simple matter to just change the memory
model.  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.

I'll let all the other developer's respond to your question themselves.

Jonathan



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Date: Thu, 29 Mar 2001 19:38:20 -0600
From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Fractint Development

Ulrich,

> .. and how about the development for Linux. The current version (20-07)
> doesn't do colour cycling (at least not at my system).

If you are in a true color mode, that's the nature of the beast.  If you are
in a 256 color mode, then we broke it and I'll take a look at it.

Strangely, the Neomagic chip in my laptop does color cycling in true color
modes.  Unfortunately, it uses its own choice of colors.

Jonathan



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Date: Thu, 29 Mar 2001 19:11:15 -0800
From: Mark Christenson <[e-mail]>
Subject: (fractint) Web space help

My Web site is down right now; it's a long story as to how
and why, so I will skip the saga for now.  What I need now
is some data.

Someone was nice enough, a year or so ago, to direct me
to a service that provided "unlimited" Web server space for
five dollars US per month.  If you're out there, or are someone
with similar information, please pass it along.  I can't hope to
find the original message in the mountain of e-mail.


TIA,
        Bud


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Date: Thu, 29 Mar 2001 18:50:14 -0600
From: Bob Margolis <[e-mail]>
Subject: Re: (fractint) Twenty & One

Programmer Dude wrote:


> Isn't Rucker the guy who first talked about the L26 system?

Actually it was the L27 system, with 0 standing for a space, and A to Z
being 1 through 26.

>  I think it was in his book, MIND TOOLS.

It was and still is. :-)

Bob = 1865
Dude = 94154
Paul = 315534
FractInt = 68752031869

Bob
- --
*******************************************************
  We interrupt this program to bring you loud static.
*******************************************************


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Date: Thu, 29 Mar 2001 15:17:16 -0000
From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Twenty & One

>From: "David Jones" <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>Subject: Re: (fractint) Twenty & One
>Date: Wed, 28 Mar 2001 21:35:41 -1000
>
>Cool - looks like fun - just added it to the bookmark
>collection! Thanks!
>
>David
>[e-mail]
>
>On 28 Mar 01 at 23:55, Paul N. Lee wrote:
>
> > Bob Margolis wrote:
> > >
> > > There was a software package that came out for
> > > MS-DOS 11 years ago. It is called James Gleick's
> > > Chaos: The Software ......
> > > While the software package will be hard to find...
> >
> > Try the following location for the above mentioned
> > software:
> >
> >     http://www.mathcs.sjsu.edu/faculty/rucker/

As always, FractInt people prove to be knowledgable people! 8-]

Thanks for the info. Now how about the Newton-Mandeloid and the General
Quartic?

Thanks.
Andrew.

_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.


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Date: Fri, 30 Mar 2001 09:35:17 -0600
From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) Twenty & One

Bob Margolis wrote:

>> Isn't Rucker the guy who first talked about the L26 system?
>
> Actually it was the L27 system, with 0 standing for a space, and A to Z
> being 1 through 26.

Ah, yes!  I *knew* that "L26" didn't sound right.

>>  I think it was in his book, MIND TOOLS.
>
> It was and still is. :-)

Fascinating book!


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

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Date: Fri, 30 Mar 2001 21:41:19 +0200
From: Michael Weitzel <[e-mail]>
Subject: (fractint) Fractint Development: The Ljapunow Type

Hi :-)

In 1995 when I was still in school I read an article (by Mario Markus), about
Ljapunow diagrams in the german science magazine "Spektrum der Wissenschaft".
Last week, while cleaning up my desktop, it fell into my hands and I wrote a
small program to display these diagrams...

* Ljapunow diagrams absolutely *need* true-colour. :-)
  colouring the images there are (imho) two methods
  1. calculate the whole image, store the exponents fp-number for every
     pixel. After calculation, use a linear (or non-linear) function and the
     min and max values for the exponent to colour the image. The image can't
     be displayed while calculation runs.
  2. use a scaleable function that produces values in a fixed interval - 0..1
     for example. These values can be rescaled to fit into the
     Screens/X-Servers colour depth. I made good experiences with the
     Gauss-curve g(x) = exp(-(a*x)^2) and its complement h(x) = 1 - g(x).

     Parameter a can be used for scaling the curves width. The decision, if
     the exponent lambda is <0 or >=0 gives additional interesting information
     about the image:

    if (lambda>0.)
    {
        red = (int)(255. * (1-exp(-lambda*lambda*.2)));
        gre = (int)(255. * exp(-lambda*lambda*4.));
        blu = (int)(255. * (1-exp(-lambda*lambda*.8)));
    }
    else
    {
        red = (int)(255. * (1-exp(-lambda*lambda*.5)));
        gre = (int)(255. * exp(-lambda*lambda*40.));
        blu = (int)(255. * (1-exp(-lambda*lambda*.2)));
    }

     Has someone thought about a different way to colour these images?
     I would be interested :-)

* The logistic equation is fast to calculate ... but other equations are
  perhaps more interesting. I tried out

      f(x) = b*sin^2(x+r)

  it describes something about the optic stability of liquid cristals
  (whew;-). b is a fixed parameter; r is the periodic A-B sequence. I produces
  wonderful repeating textures (is 'procedural textures' the correct english?
  ... like those textures used for backgrounds in HTML files). In the article
  are 4 more equations given I have not tried out yet... (if someone is
  interested in an example, I can put some screenshots on my homepage)

* Fractint's way to specify the A-B-order is too complicated and unhandy for
  the normal user.

* I've had a look at xlyap (included in the xscreensaver package, only
  logistic equat., only 256 colours) ... it does some incredible speed-up
  (it looks like Fractint's boundary tracing for the complex-number fractals)
  perhaps one could find out how this works...






Thanks to the Stonesoup Group for the wonderful Fractint! :-))
- --
   Michael                  LDKnet / LDK/LUG / Unix-AG
     *Weitzel* /LinuX --- email: michael(at)ldknet.org

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Date: Sat, 31 Mar 2001 10:58:01 -0800
From: Mark Christenson <[e-mail]>
Subject: (fractint) (belated) new Web gallery

As I continue the search for a new home for my fractals,
it seems that my site has risen from the dead.  How long
it will remain up is uncertain, but here's the announcement
that was slated for last week:

I have added Fractint Gallery 6, with my Fractal Art 2K
entries (which most of you have already seen) and a series
of evolving gravijul spirals.

http://www.hooked.net/~mchris/fractals.htm
        -or-
http://www.wenet.net/~mchris/fractals.htm

Enter through Fractint Galleries or What's New.


Aloha,
        Bud


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Date: Sun, 01 Apr 2001 00:44:34 +0200
From: Guy Marson <[e-mail]>
Subject: Re: (fractint) Fractint Development: The Ljapunow Type

At 21:41 30.03.2001 +0200, you wrote:
>Hi :-)
>
>In 1995 when I was still in school I read an article (by Mario Markus), about
>Ljapunow diagrams in the german science magazine "Spektrum der Wissenschaft".
>Last week, while cleaning up my desktop, it fell into my hands and I wrote a
>small program to display these diagrams...

Hi fractinters,

Does somebody know the Lyapunow-formula written for the Parser similar to
the build-in type, or a place (url or so) to find this formula?

Cheers,

Guy




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End of fractint-digest V1 #547
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