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1998-09-02
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From: owner-fractint-digest@lists.xmission.com (fractint-digest)
To: fractint-digest@lists.xmission.com
Subject: fractint-digest V1 #287
Reply-To: fractint-digest
Sender: owner-fractint-digest@lists.xmission.com
Errors-To: owner-fractint-digest@lists.xmission.com
Precedence: bulk
fractint-digest Wednesday, September 2 1998 Volume 01 : Number 287
----------------------------------------------------------------------
Date: Wed, 2 Sep 1998 04:54:32 EDT
From: JimBeau549@aol.com
Subject: (fractint) 10 pars(Lesfrm16)
Now these were really fun! And I'm still not through......
Enjoy~
Jim
~~~~~~~~
members.aol.com/JimBeau549/jim3.htm
" " " /JWeaver285/page1.htm
****************************************************************************
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}
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reset=1960 type=formula formulafile=les_pars.frm
formulaname=Lesfrm16 function=sin/conj passes=1
center-mag=0.0175441/-1.90958e-014/0.8672173/1.0426/-90
params=1/0/1/0 float=y maxiter=10 inside=bof60 outside=real
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_22<14>E01D01C02<7>204005005<9>002002001100100000<2>200
}
LSfrm171 { ; image(c)JimWeaver 9/01/98 t=0:00:39.38 P75@800x600
;
reset=1960 type=formula formulafile=les_pars.frm
formulaname=Lesfrm16 function=conj/sinh passes=t
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G<9>zzzyyv<10>S50<10>zzz<9>KC9<2>G87<16>zX0<14>b42`22_22<14>E01D01C02<7>\
204005005<9>002002001100100000<11>900Z03<11>V52A00
}
LSfrm173 { ; image(c)JimWeaver 9/01/98 t=0:00:38.99 P75@800x600
;
reset=1960 type=formula formulafile=les_pars.frm
formulaname=Lesfrm16 function=conj/sinh passes=t
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22_22<14>E01D01C02<7>204005005<9>002002001100100000<11>900Z03<11>V52A00<\
2>D00<2>G0B<9>zzz<7>xfD000<5>40850A509000kkkwX0
}
LSfrm175 { ; image(c)JimWeaver 9/01/98 t=0:00:41.85 P75@800x600
;
reset=1960 type=formula formulafile=les_pars.frm
formulaname=Lesfrm16 function=conj/sqr passes=t
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005<9>002002001100100000<11>900Z03<11>V52A00<2>D00<2>G0B<9>zzz<7>xfD000<\
5>40850A509000kkkwX0rX6tZ0lP5lP0fH3eF0`92Y50U00
}
LSfrm176 { ; image(c)JimWeaver 9/01/98 t=0:00:41.25 P75@800x600
;
reset=1960 type=formula formulafile=les_pars.frm
formulaname=Lesfrm16 function=conj/sqr passes=t
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}
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;
reset=1960 type=formula formulafile=les_pars.frm
formulaname=Lesfrm16 function=conj/sqr passes=1
center-mag=-0.0468677/-2.22045e-015/0.5361197/1/-90 params=0.5/0/1/0
float=y maxiter=10 inside=bof60 outside=real
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}
LSfrm184_Star02 { ; image(c)JimWeaver 9/01/98 t=0:00:21.48 P75@800x600
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formulaname=Lesfrm16 function=sqr/conj passes=t
center-mag=-0.158569/-3.5083e-014/0.5372222/1/-90 params=1/0/1/0
float=y maxiter=25 inside=bof60 outside=real
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00<2>D00<2>G0B<9>zzz<7>xfD000<5>40850A509000kkk
}
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reset=1960 type=formula formulafile=les_pars.frm
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00306<3>102000100<6>E00G00J00<12>m00<13>A08<11>ZRG`UKcYP
}
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------------------------------
Date: Wed, 2 Sep 1998 10:27:14 +0100
From: Dave <Dave@Quanta.co.uk>
Subject: RE: (fractint) Video Modes
> ----------
> From: GregJ56590@aol.com[SMTP:GregJ56590@aol.com]
> Reply To: fractint@lists.xmission.com
> Sent: 02 September 1998 01:26
> To: fractint@lists.xmission.com
> Subject: Re: (fractint) Video Modes
>
> Isn't the whole idea of having to set parameters based on one's "video
> card" a
> trapping of the late 80's? Why aren't images in Fractint simply
> what they
> are?
I think you're missing the point - I don't want FRACTINT parameters to
generate better fractals, I want VIDEO CARD parameters to enable me to
see the fractal at a higher resolution, with a greater number of
colours.
> Do the top-notch computerophiles & mathemeticians on this list
> actually
> have 1979 PC's with only a 256 color card??
>
No. We have 1998 PC's with 4MB video cards, capable of displaying in
excess of 16million colours, but feel a bit cheated when the fractal
comes out at only 16 colours with blocky graphics. Fractals are a thing
of beauty to behold, but beauty in this case is constrained by the
limitations of the display card.
Consider listening to your favourite symphony on a transistor radio. How
would you feel if someone said "just accept the music for what it is.
You don't need a modern surround-sound HiFi system to appreciate it"..?
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------------------------------
Date: Wed, 02 Sep 1998 02:59:54 -0700
From: kathy roth <kroth@well.com>
Subject: (fractint) Fractal of the Week
- --------------8224C694A050B64E9FE0F331
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
Sylvie Gallet wrote:
> As every Tuesday, I've uploaded a new Fractal Of The Week to my home
> page:
>
Wow. Now that's ART.
- --------------8224C694A050B64E9FE0F331
Content-Type: text/html; charset=us-ascii
Content-Transfer-Encoding: 7bit
<HTML>
<P>Sylvie Gallet wrote:
<BLOCKQUOTE TYPE=CITE>
<PRE>As every Tuesday, I've uploaded a new Fractal Of The Week to my home
page:</PRE>
</BLOCKQUOTE>
<P>Wow. Now that's ART.
<BR> </HTML>
- --------------8224C694A050B64E9FE0F331--
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------------------------------
Date: Wed, 2 Sep 1998 11:10:41 +0100 (GMT Daylight Time)
From: "Nigel H. J. Long" <n.h.long@soton.ac.uk>
Subject: Re: (fractint) Video Modes
Have you tried searching the WWW for a manufacturer's
home-page? Some of them offer an email help desk. When I
wanted some specific info on my (antique) card I was able
to get quite useful help from the makers themselves.
And yes.... I only have a 256 colour card. It may not be
much - but it's paid for!
- ----------------------
Nigel H. J. Long
n.h.long@soton.ac.uk
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------------------------------
Date: Wed, 2 Sep 1998 09:32:00 -0400 (EDT)
From: kragen@pobox.com (Kragen)
Subject: RE: (fractint) Video Modes
On Wed, 2 Sep 1998, Dave wrote:
> Consider listening to your favourite symphony on a transistor radio. How
> would you feel if someone said "just accept the music for what it is.
> You don't need a modern surround-sound HiFi system to appreciate it"..?
Most modern surround-sound hi-fi systems *are* transistor radios (maybe
with a CD player in there, too.) The alternative is vacuum-tube
amplifiers -- and while there are some people who insist that
symphonies sound better on them, most people would not feel cheated if
they were forced to use a solid-state amp instead. :)
(And isn't it kind of temporally backwards to liken using TrueColor to
using vacuum tubes? :)
Kragen
- --
<kragen@pobox.com> Kragen Sitaker <http://www.pobox.com/~kragen/>
We are forming cells within a global brain and we are excited that we might
start to think collectively. What becomes of us still hangs crucially on
how we think individually. -- Tim Berners-Lee, inventor of the Web
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------------------------------
Date: Wed, 2 Sep 1998 15:23:21 +0100
From: Dave <Dave@Quanta.co.uk>
Subject: RE: (fractint) Video Modes
> Most modern surround-sound hi-fi systems *are* transistor radios
> (maybe
> with a CD player in there, too.) The alternative is vacuum-tube
> amplifiers -- and while there are some people who insist that
> symphonies sound better on them, most people would not feel cheated if
> they were forced to use a solid-state amp instead. :)
>
> (And isn't it kind of temporally backwards to liken using TrueColor to
> using vacuum tubes? :)
>
> Kragen
>
Yeah, point taken - guess I didn't think too hard about the analogy.
However, my comment was intended to point out that a fractal is a
fractal is a fractal, but a fractal viewed at 1280x1024 with 16m colours
looks more stunning than a fractal viewed at 640x480 with 16 colours.
Well... IMHO anyway...
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------------------------------
Date: Wed, 2 Sep 1998 10:36:13 -0400 (EDT)
From: kragen@pobox.com (Kragen)
Subject: RE: (fractint) Video Modes
On Wed, 2 Sep 1998, Dave wrote:
> Yeah, point taken - guess I didn't think too hard about the analogy.
> However, my comment was intended to point out that a fractal is a
> fractal is a fractal, but a fractal viewed at 1280x1024 with 16m colours
> looks more stunning than a fractal viewed at 640x480 with 16 colours.
Oh, definitely.
Kragen (who thinks that if this weren't the case, no one would bother
to make colormaps)
- --
<kragen@pobox.com> Kragen Sitaker <http://www.pobox.com/~kragen/>
We are forming cells within a global brain and we are excited that we might
start to think collectively. What becomes of us still hangs crucially on
how we think individually. -- Tim Berners-Lee, inventor of the Web
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------------------------------
Date: Wed, 02 Sep 1998 14:04:25 -0400
From: Diosnel Herrnsdorf <diosnel@krauch.com.py>
Subject: Re: (fractint) New Fractal Of The Week
Sylvie Gallet wrote:
> Hi All,
>
> As every Tuesday, I've uploaded a new Fractal Of The Week to my home
> page:
>
> <http://ourworld.compuserve.com/homepages/Sylvie_Gallet/homepage.htm>
>
> I've also created a new gallery that features all the FOTW for July and
> August. This new page has links to my pages at CompuServe but I haven't
> updated the old pages yet and you will have to use the following URL:
>
> <http://members.aol.com/gallets/index.htm>
>
> Enjoy!
>
> - Sylvie
It's really been an enjoyment - both sites. I was just wondering, do you
always choose an image with simmetry for your FOTW?
Regards,
Diosnel
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------------------------------
Date: Wed, 2 Sep 1998 20:28:33 +0200
From: "Dean-Christian Strik" <cstrik.isg@hetnet.nl>
Subject: (fractint) Sylvie's site
Hi Sylvie,
Actually the first time I looked at your site (Compuserve). Very nice images!
[But that's been said time and time again :) ]
I had problems though with accessing Gallet_c.zip, Gallet_d.zip and
wallpapr.zip and the vesa2cfg link. AOL
answered with a simple 'URL not found'.
Christian
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------------------------------
Date: Wed, 2 Sep 1998 14:51:00 -0400
From: "Peter Gavin" <pgavin@mindspring.com>
Subject: RE: (fractint) Fractal risks? and new ways of perceiving Fractals
// >Taste is probably not a high-bandwidth sense.
// >
// No, I wouldn't think so either. Once you specified the relative
// strengths
// of the four taste categories (sour, sweet, etc.) the fine-tuning that
// allows you to distinguish, say, coffee from decaf, is handled
// by the nose
// and volatiles slipping into it via the throat. The other
// channels involved
// would be temperature and texture (which also involve the palate).
Well, you gotta remember, taste isn't just your toungue. About (I'd say)
75% of the sensations/flavors you get while eating are through your nose and
sense of smell, really. Smell, although it doesn't really have a high
bandwidth (IMO), it does have a large spectrum as far as the data goes...
So it would be measured in words or dwords rather than bits per second :)
Peter Gavin
<pgavin@mindspring.com>
// End transmission
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------------------------------
Date: Wed, 2 Sep 1998 21:54:32 +0200
From: "Thore Berntsen" <thbernt@online.no>
Subject: (fractint) New version of Fractint Screen Saver
This is a multi-part message in MIME format.
- ------=_NextPart_000_001A_01BDD6BC.441D2B80
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
I have released version 1.70 of Fractint Screen saver today. It can be =
found at :
http://home.sol.no/~thbernt/fintsave.htm
Thore Berntsen
Norway
E-Mail : thbernt@online.no
- ------=_NextPart_000_001A_01BDD6BC.441D2B80
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
<!DOCTYPE HTML PUBLIC "-//W3C//DTD W3 HTML//EN">
<HTML>
<HEAD>
<META content=3Dtext/html;charset=3Diso-8859-1 =
http-equiv=3DContent-Type>
<META content=3D'"MSHTML 4.71.2016.0"' name=3DGENERATOR>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV> </DIV>
<DIV><FONT color=3D#000000 face=3DArial size=3D2>I have released version =
1.70 of=20
Fractint Screen saver today. It can be found at :</FONT></DIV>
<DIV><FONT color=3D#000000 face=3DArial size=3D2></FONT> </DIV>
<DIV> </DIV>
<DIV><FONT color=3D#000000 face=3DArial size=3D2><A=20
href=3D"http://home.sol.no/~thbernt/fintsave.htm">http://home.sol.no/~thb=
ernt/fintsave.htm</A></FONT></DIV>
<DIV> </DIV>
<DIV><FONT color=3D#000000 face=3DArial size=3D2><BR>Thore =
Berntsen</FONT> </DIV>
<DIV><FONT color=3D#000000 face=3DArial size=3D2>Norway<BR>E-Mail : <A=20
href=3D"mailto:thbernt@online.no">thbernt@online.no</A></FONT></DIV></BOD=
Y></HTML>
- ------=_NextPart_000_001A_01BDD6BC.441D2B80--
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------------------------------
Date: Wed, 2 Sep 1998 13:36:38 -0700 (PDT)
From: Ken Childress <kchildre@uccs.jpl.nasa.gov>
Subject: (fractint) Understanding Formulas
I have a question about formulas. If answers can be found in a FAQ,
please point me there, but I haven't uncovered what I've been looking
for so far.
I've been experimenting with formulas and pars done by those on the list
and ones that I've found here and there for several weeks now.
Something that has been intriguing me is how do people come up with the
formulas and coloring methods that they do?
For example, Paul Carlson's balls, spires, etc. formulas are
particularly fascinating. The artistic beauty of Linda Allison's,
Sylvie Gallet's, etc. are amazing. How does one learn to visualize or
estimate what a particular formula will produce? Are there any
tutorials, books, etc. that explain the process one goes through when
writing a formula?
I've read the Fractint formula tutorial and some others that I've found,
and they help somewhat. The problem is, I still find myself at a loss
where to start if I want to try to "roll my own" formula. Any
suggestions from the masters?
Thanks.
Ken...
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Date: Wed, 2 Sep 1998 16:55:53 -0400
From: Sylvie Gallet <Sylvie_Gallet@compuserve.com>
Subject: (fractint) Fractal of the Week
Hi Kathy,
>> Wow. Now that's ART.
Thank you!
Cheers,
- Sylvie
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Date: Wed, 2 Sep 1998 16:55:52 -0400
From: Sylvie Gallet <Sylvie_Gallet@compuserve.com>
Subject: Re: (fractint) New Fractal Of The Week
Hi Diosnel,
>> It's really been an enjoyment - both sites.
I'm glad you enjoyed, thanks!
>> I was just wondering, do you always choose an image with simmetry for
>> your FOTW?
Not at all, for example 980803 doesn't have symmetries.
Cheers,
- Sylvie
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Date: Wed, 2 Sep 1998 16:55:52 -0400
From: Sylvie Gallet <Sylvie_Gallet@compuserve.com>
Subject: (fractint) Sylvie's site
Hi Christian,
>> Actually the first time I looked at your site (Compuserve). Very nice
>> images!
Thank you!
>> I had problems though with accessing Gallet_c.zip, Gallet_d.zip and
>> wallpapr.zip and the vesa2cfg link. AOL answered with a simple 'URL
>> not found'.
I had the same problem the first time I checked the links; then I empti=
ed
my Internet cache and tried again, and this time I got a "server too busy=
,
try again later"... But you know what does "AOL" mean? America Off
Line...
Let me know if the problem persists and I'll email you the files.
Cheers,
- Sylvie
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Date: Wed, 02 Sep 1998 16:40:48 -0500
From: "Damien M. Jones" <dmj@fractalus.com>
Subject: Re: (fractint) Understanding Formulas
Ken,
- I've read the Fractint formula tutorial and some others that I've found,
- and they help somewhat. The problem is, I still find myself at a loss
- where to start if I want to try to "roll my own" formula. Any
- suggestions from the masters?
That depends on whether you're trying to write a new coloring algorithm, or
a new fractal formula. Most of the formula-writing tutorials cover fractal
formula writing; coloring formula writing is a relatively new topic that is
less well-covered. If you're asking how to come up with the ideas (rather
than the technical details of implementing those ideas) then I'm not sure
anyone can help--I know oftentimes I just dink around with a formula until
I get something that looks promising. Sometimes I get an idea, write a
formula, and it looks like junk. Those get filed away into a dusty,
forgotten drawer. Good stuff get polished up and used for more. :-)
Damien M. Jones \\
dmj@fractalus.com \\ Fractalus Galleries & Info:
\\ http://www.fractalus.com/
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Date: Wed, 2 Sep 1998 14:54:38 -0700 (PDT)
From: Ken Childress <kchildre@uccs.jpl.nasa.gov>
Subject: Re: (fractint) Understanding Formulas
>
> Ken,
>
> - I've read the Fractint formula tutorial and some others that I've found,
> - and they help somewhat. The problem is, I still find myself at a loss
> - where to start if I want to try to "roll my own" formula. Any
> - suggestions from the masters?
>
> That depends on whether you're trying to write a new coloring algorithm, or
> a new fractal formula. Most of the formula-writing tutorials cover fractal
> formula writing; coloring formula writing is a relatively new topic that is
> less well-covered. If you're asking how to come up with the ideas (rather
> than the technical details of implementing those ideas) then I'm not sure
> anyone can help--I know oftentimes I just dink around with a formula until
> I get something that looks promising. Sometimes I get an idea, write a
> formula, and it looks like junk. Those get filed away into a dusty,
> forgotten drawer. Good stuff get polished up and used for more. :-)
I suppose I'm asking about both. I think my problem is that I don't
understand all the issues enough to ask the right questions. :-)
After perusing some of Paul Carlson's formulas, many of his are
different coloring formulas on the classic Mandelbrot formula. I am
definately interested in learning how to write coloring formulas. Wrt
Paul's formuals, I guess I'm asking if one has an idea in advance how to
produce the balls or stalks or whatever, when starting in on the
forumla. I'll have to read Kerry Mitchell's recent messages in more
detail to see what I can glean from them.
Wrt formulas in general, I guess I was wondering if people had in mind
what they were trying to achieve when creating a formula, or if they
just started dinking around, as you mention.
I would also like to make a polite request that those with experience
writing the unique coloring algorithms consider writing a tutorial
and/or documenting their algorithms describing what is going on, if not
already done.
In any case, I appreciate the help and the ability to experiment with
the efforts of others.
Ken...
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Date: Wed, 02 Sep 1998 17:05:55 -0500
From: "Damien M. Jones" <dmj@fractalus.com>
Subject: Re: (fractint) Understanding Formulas
Ken,
- I suppose I'm asking about both. I think my problem is that I don't
- understand all the issues enough to ask the right questions. :-)
Well, that's a start, at least... you know what you don't know. :)
- After perusing some of Paul Carlson's formulas, many of his are
- different coloring formulas on the classic Mandelbrot formula. I am
- definately interested in learning how to write coloring formulas.
Then perhaps this might help:
http://www.fractalus.com/misc/implement.htm
This will explain how to write a coloring algorithm formula for FractInt.
This file:
http://www.fractalus.com/misc/dmj-pub.zip
contains my collection of formulas as well, which like Paul Carlson's and
Kerry Mitchell's formulas, are usually fairly heavily commented.
- Wrt Paul's formuals, I guess I'm asking if one has an idea in advance
- how to produce the balls or stalks or whatever, when starting in on the
- forumla.
Yes. Balls and stalks are in a class of coloring algorithms called "orbit
traps". Basically the idea is to position some shape over the fractal, and
watch each iteration to see whether it falls inside the shape or not. For
more explanations of coloring algorithms in general (and orbit traps
specifically) see this page:
http://www.fractalus.com/misc/algorithm.htm
Hope this helps!
Damien M. Jones \\
dmj@fractalus.com \\ Fractalus Galleries & Info:
\\ http://www.fractalus.com/
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Date: Wed, 2 Sep 1998 15:18:14 -0700 (PDT)
From: Ken Childress <kchildre@uccs.jpl.nasa.gov>
Subject: Re: (fractint) Understanding Formulas
>
> Well, that's a start, at least... you know what you don't know. :)
That's half the battle, no?
> http://www.fractalus.com/misc/implement.htm
>
> http://www.fractalus.com/misc/dmj-pub.zip
>
> http://www.fractalus.com/misc/algorithm.htm
I had read those a while back, and they didn't mean that much to me.
I'll reread them now that I have a bit more of an understanding of
fractals. Thanks for the reminder.
> Hope this helps!
Definately. Thanks.
Ken...
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Date: Wed, 2 Sep 1998 18:19:37 -0400
From: Sylvie Gallet <Sylvie_Gallet@compuserve.com>
Subject: Re: (fractint) Understanding Formulas
Ken and Damien,
>> If you're asking how to come up with the ideas (rather than the
>> technical details of implementing those ideas) then I'm not sure
>> anyone can help
I've got interesting results with generalizations of existing formulas =
or
predefined types, but I most often get junk! :-)
- Sylvie
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Date: Wed, 2 Sep 1998 19:19:04 -0500 (CDT)
From: pjcarlsn@ix.netcom.com (Paul and/or Joyce Carlson)
Subject: Re: (fractint) Understanding Formulas
>After perusing some of Paul Carlson's formulas, many of his are
>different coloring formulas on the classic Mandelbrot formula. I am
>definately interested in learning how to write coloring formulas. Wrt
>Paul's formuals, I guess I'm asking if one has an idea in advance how to
>produce the balls or stalks or whatever, when starting in on the
>forumla.
The answer (at least for me) is yes. It would be almost impossible
to "accidentally" come up with a method that produced 3D-like
shapes with each shape consisting of gradations of a particular color.
>Wrt formulas in general, I guess I was wondering if people had in mind
>what they were trying to achieve when creating a formula, or if they
>just started dinking around, as you mention.
When I originally developed the orbit trap technique about 4 or 5
years ago, it involved a lot of experimentation (and was inspired by
Pickover's epsilon cross method, which is also actually an orbit
trap - see below), but once I had the general algorithm developed
for 3D shading, writing formulas for the different shapes was
relatively easy. However, formulas like my four-in-one Julia
sets are not quite so easy, but I still had to know in advance
what I was trying to accomplish.
>
>I would also like to make a polite request that those with experience
>writing the unique coloring algorithms consider writing a tutorial
>and/or documenting their algorithms describing what is going on, if
not
>already done.
I posted this to the list about a year ago:
- ---------------------------------------------------------------
Several people have indicated an interest in how I use orbit traps
to get a pseudo-3D effect in my fractals. The following is an
attempt to explain the methods using as little math as possible.
I guess a good place to start might be to explain how I happened
to develop the 3D Stalks rendering method about 3 or 4 years ago.
I had written a program that plotted fractals using Pickover's
epsilon cross method. With this method, when the orbitting point
lands within a specified distance, "epsilon," of either the real
or imaginary axis, bailout occurs and the screen pixel is plotted
in a color depending on the number of iterations at bailout. The
result is an image consisting of stalks, each stalk being a solid
color. I noticed that if I made epsilon smaller the stalks became
thinner and if larger the stalks became fatter. I then modified
the program so that if the orbit point fell within a distance
epsilon of an axis the pixel was plotted red, but if the point fell
within a distance of one-half epsilon the pixel was replotted green.
The result was red stalks overlaid with green stalks about half
the thickness of the red stalks they were laying on.
These experiments showed me two things: 1) each stalk represents
a single iteration count at bailout, and 2) it was possible to
vary the color of the stalk depending on where within epsilon
the orbit point fell. My first 3D Stalks image used only shades
of yellow - from bright yellow if the point fell exactly on one of
the axes to dark yellow if the point fell a distance epsilon away
from an axis, with intermediate shades of yellow for points falling
between those two extremes. I used 250 shades of yellow, the
brightest at colormap index 1 and the darkest at colormap index 250
and the rest varying linearly in between (I usaully save colormap
index 0 for black since this is the overscan or border color). My
program computed how close the orbit point fell to an axis and if
it was within epsilon the distance was saved in a variable "dist."
Then the ratio dist/epsilon was computed (call it "ratio") and used
to compute an index into the colormap as follows:
index = 1 + ratio * 249
This gives values of index from 1 to 250 since ratio varies from
zero to one. The resulting image consisted of yellow stalks, each
stalk being dark yellow at the edges and bright yellow in the center,
giving the stalks a 3D appearance since, everything else being equal,
bright portions of an image appear closer to the observer than dark
portions.
The next step was to break the colormap into two color ranges, index
1 to 125 light yellow to dark yellow, index 126 to 250 light blue
to dark blue. The yellow range was used if bailout occurred on an
even iteration, the blue range if on an odd iteration, ie,
if even, index = 1 + ratio * 124
if odd, index = 126 + ratio * 124
or, in general:
index = 1 + range_num * colors_in_range + ratio * (colors_in_range-1)
where range_num varies from zero to the number of color ranges minus
one.
This illustrates the basic pseudo-3D orbit trap method:
If an orbit point falls within the trap, compute the ratio of the
distance from the orbit point to some point Q in the trap divided by
the maximum distance from point Q to the boundary of the the trap
(this guarantees that the ratio will be from zero to one, inclusive)
and use that ratio to index into a color range.
Orbit traps can have many forms. The main requirement is that the
test for the orbit point falling in the trap can't take too long to
execute since the test must be done every iteration. Simple closed
areas like circles and squares make good orbit traps since it is easy
to test if the orbit point falls within them and it is also easy to
compute the ratio using the center of the area as point Q. Plane
curves expressed in parametric form also make good orbit traps
except in this case the trap is a narrow constant width band with the
curve at its center (ie, for a circle the band would be a ring).
A formula I posted some time ago using an astroid curve illustrated
this: the argument of the iterated variable (the counter-clockwise
angle from the positive real axis to the orbit point) is computed
and used to compute the coordinates of point Q on the plane curve.
If the orbit point is within the specified distance of point Q,
compute the ratio and color index as above.
Sometimes for special effects I'll use color ranges in which the
colors do not vary linearly. Sometimes I'll have the darkest shade
at both ends of the range with the brightest shade in the center of
the range. Sometimes I'll use the ratio squared which emphasizes
the colors towards the beginning of a range. Because the ratio
is always from zero to one, it can be raised to any positive power
and still be from zero to one.
The same general method of using a ratio between zero and one to
index into a color range is not limited to orbit traps. In my
Atan method, for example, I use a ratio of angles.
To use these methods with Fractint I had to find a way to get
Fractint to use the computed colormap index. I do this in my
formulas by iterating some variable other than z and by keeping
my own iteration counter. Then when the point falls in the
orbit trap I set z equal to the colormap index minus the number of
iterations. This works when outside=summ is used which adds
the number of iterations to z.
That's all I can think of for now. I'll be glad to answer any
questions.
Paul Carlson
- --------------------------------------------------------------
Hope this helps.
Paul
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Date: Wed, 2 Sep 1998 19:52:10 -0700 (MST)
From: Kerry Mitchell <lkmitch@primenet.com>
Subject: Re: (fractint) Understanding Formulas
When I come up with a new coloring scheme, I generally try to verbalize
what I'm after, then write a formula that will do that. For example, when
I came up with the triangle method coloring, I wanted a method that would
show something different than just iteration number or polar angle. I
went back to my complex analysis books and remembered the triangle
inequality. So, my coloring method came from, "how does the iterate tend
to fall within the bounds given by the triangle inequality?" I think it
looks better than it sounds. :-) Another example is the "principal root"
coloring, in which I asked, "how often is the previous iterate the
principal root of the next squaring?"
The point is that I try to have some idea of what I'm after when I start.
Usually, the idea fleshes itself out along with the formula. Today, I
wrote a formula in response to a point Damien made about the (now ongoing)
fractal contest. We were talking about image processing, and Damien
mentioned that he made a formula the gives the "embossing" effect often
found in image processing software. So, I decided to come up with a
formula that does embossing.
To do this well, I think one needs to have a fairly good background in the
math behind the fractals, as well as a good grasp of the formula syntax
paired with the intricacies of Fractint's coloring methods. I started out
writing formulas that simply transformed the "z" variable, and let
Fractint's coloring methods go from there. Now, fairly aware of what
Fractint can do, I write formulas that, when used with specific Fractint
features (e.g., decomp=256, inside=zmag, outside=real), I get what I want.
Above all, I think, is practice. Try rolling your own and get a feel for
what they can and cannot do. Look at other people's work and try to
deconstruct it or make similar (or better) versions. Generalizing other
peoples' work is good, too. It gives you a good sense of how things work,
and expands the field of possibilities for other artists.
Oh yeah, have fun. :-)
Kerry
- -------------------------------------------------------------------------------
Kerry Mitchell lkmitch@primenet.com www.primenet.com/~lkmitch/
- -------------------------------------------------------------------------------
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