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fractint-digest        Thursday, August 5 1999        Volume 01 : Number 403




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

Date: Tue, 27 Jul 1999 20:13:57 -0500
From: "Damien M. Jones" <[e-mail]>
Subject: (fractint) Fractal-Art '99 Contest

My apologies for those of you already subscribed to the Fractal-Art list,
as you will already know the following.

The Fractal-Art '99 Contest is now under way. It is open to all fractal
artists who wish to participate; you don't have to read a mailing list or
post to a newsgroup, you just need to make fractal images. You can even use
whatever software you like, on whatever kind of computer you like.

Full details on the contest can be found at its web site:

    http://www.fractalus.com/contest99/         USA
    http://www.cribx1.u-bordeaux.fr/contest99/  France

There are no prizes, other than glory, fame, and the respect of your peers,
but please do come and join the fun. Last year's contest was a blast and
most everyone enjoyed themselves.

Now in its second year, the Fractal-Art Contest is an international contest
aimed at promoting fractals as an art form.

Damien M. Jones   \\
[e-mail]  \\  Fractalus Galleries & Info:
                    \\  http://www.fractalus.com/

Please do not post my e-mail address on a web site or
in a newsgroup.  Thank you.

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

Date: Wed, 28 Jul 1999 05:39:34 GMT
From: [e-mail]
Subject: Re: (fractint) Fractal-Art '99 Contest

On Tue, 27 Jul 1999 20:13:57 -0500, you wrote:

>Now in its second year, the Fractal-Art Contest is an international =
contest
>aimed at promoting fractals as an art form.
>
Uh.... Isn't this the 3rd year?

juice --have fun --harm none

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Date: Wed, 28 Jul 1999 10:14:15 -0500
From: "Damien M. Jones" <[e-mail]>
Subject: Re: (fractint) Fractal-Art '99 Contest

Juice,

 - Uh.... Isn't this the 3rd year?

Third year for a contest. Second year for the Fractal-Art Contest, which
isn't restricted to just FractInt. The contest site does list the 1997
FractInt contest first, on the "About" page.

Damien M. Jones   \\
[e-mail]  \\  Fractalus Galleries & Info:
                    \\  http://www.fractalus.com/

Please do not post my e-mail address on a web site or
in a newsgroup.  Thank you.

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

Date: Sun, 1 Aug 1999 09:50:10 +0200
From: "=?iso-8859-1?Q?Luc-Andr=E9_Rey?=" <[e-mail]>
Subject: (fractint) New pages, and beautiful in my site

Hello everybody,

The Fractal Artist Guest of this month is Lee SKINNER.

You find 12 new and original pictures at :
http://www.aour.ch
page "fractales".

En francais, vous trouverez ces pages par le petit bouton jaune en haut de
page.
In english, see the link "english version."




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

Date: Sun, 01 Aug 1999 17:20:47 +0200
From: [e-mail] (Thomas Beyer)
Subject: (fractint) Re: old magnetic1j

Obviously the "look for final attractor"-algorithm (which is ALWAYS
used with magnetic fractals) has been altered between Version 15 and
16.
There are even more differences: (tested with V15.13 and 19.2)

1) V15 adapts the "bailout-value" to the magnification factor. If you
zoom into an attractor, the picture remains nearly the same. V19.2
uses a fixed (but unknown) threshold-value.

2) With V15 the final-attractor-display fails, if magnification
exceeds 20000.

3) V15 doesn't detect cycles as finite attractors (only fixed points).
Try the Julia-set -1 + 0i!

I think the squares displayed in V15 are caused by an incorrect
calculation of the distance.

Circle: sqr(dx) + sqr(dy) < sqr(delta)
Square:  abs(dx) < delta AND abs(dy) < delta

I'll try to verify this by analysing the source code.



On Mon, 19 Jul 1999 17:14:33 EDT, [e-mail] schrieb:

> In Version 14 magnetic types of fractals were introduced in fractint. But
> pictures computed with V14 or V15 looked different from those shown in
> Peitgen's book "The Beauty of Fractals" (BOF).

> between V15.13 and V16.11 (same as 16.1) somebody must have removed the bug
> that made magnetic1j fractals edged! But why was it not mentioned in
> fractint.doc?

> another type of fractals showed the same behavior: simple
> Julias calculated with the function "Look for Finite Attractor=yes".

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

Date: Sun, 01 Aug 1999 21:01:11 EEST
From: "Dimosthenis Baikos" <[e-mail]>
Subject: (fractint) Reading email query

Hi all,

Does Fractint Lists Diggests contain all the messages sent in this list?
Thank you for your answer!

P.S. Enjoy your summer vacations. Hope you don't leave messages to pile up
(as I did): Yesterday I returned home and today  read and
saved on disk 74 messages... ( Q-( )


______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com

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

Date: Sun, 1 Aug 1999 21:35:44 -0700
From: "Karin Mattern" <[e-mail]>
Subject: (fractint) Question

This is a multi-part message in MIME format.

- ------=_NextPart_000_00F8_01BEDC65.CFB05500
Content-Type: text/plain;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Hi, everyone!
I just subscribed to this list, mostly because I wanted information. I =
don't know very much about Fractint, or the technical stuff, but I like =
looking at the fractals. I was wondering how to get it to print right. =
Every time I use the Print command, I get ten pages of hieroglyphics. My =
friend got his to print after some difficulties, but he can't remember =
how, and it won't print in colour. I'd appreciate some help!   Thanks.
                                                                         =
                                   Lindsay

- ------=_NextPart_000_00F8_01BEDC65.CFB05500
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 4.72.3110.7"' name=3DGENERATOR>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT color=3D#000000 size=3D2>Hi, everyone!</FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2>I just subscribed to this list, =
mostly because I=20
wanted information. I don't know very much about Fractint, or the =
technical=20
stuff, but I like looking at the fractals. I was wondering how to get it =
to=20
print right. Every time I use the Print command, I get ten pages of=20
hieroglyphics. My friend got his to print after some difficulties, but =
he can't=20
remember how, and it won't print in colour. I'd appreciate some=20
help!   Thanks.</FONT></DIV>
<DIV><FONT color=3D#000000=20
size=3D2>          &nbs=
p;            =
;            =
            &=
nbsp;           &n=
bsp;           &nb=
sp;           &nbs=
p;            =
;           =20
Lindsay</FONT></DIV></BODY></HTML>

- ------=_NextPart_000_00F8_01BEDC65.CFB05500--


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

Date: Sun, 01 Aug 1999 23:44:39 -0500
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Question

Karin Mattern wrote:
>
> Hi, everyone!
> I just subscribed to this list, mostly because I wanted information. I
> don't know very much about Fractint, or the technical stuff, but I
> like looking at the fractals. I was wondering how to get it to print
> right. Every time I use the Print command, I get ten pages of
> hieroglyphics. My friend got his to print after some difficulties, but
> he can't remember how, and it won't print in colour. I'd appreciate
> some help!   Thanks.
>
> Lindsay

Try saving the image as a GIF file and then use some form of image
editor for the printing function.  This is how most everyone does it
when using FractInt.

P.N.L.
- --------------------------------------------------------------
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

Date: Sun, 01 Aug 1999 23:48:29 -0500
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Reading email query

Dimosthenis Baikos wrote:
>
> Does Fractint Lists Diggests contain all the messages
> sent in this list?  Thank you for your answer!

It usually has them all, unless something goes wrong with the system.

>
> P.S. Enjoy your summer vacations. Hope you don't leave
> messages to pile up (as I did): Yesterday I returned
> home and today  read and saved on disk 74 messages... ( Q-( )

Consider yourself very lucky.  I get around 125 per day.  ;-}

P.N.L.
- --------------------------------------------------------------
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

Date: Mon, 02 Aug 1999 05:29:04 -0400
From: davides <[e-mail]>
Subject: Re: (fractint) Question

At 09:35 PM 8/1/1999 -0700, you wrote:

<excerpt><bigger> I was wondering how to get it to  print right. Every
time I use the Print command, I get ten pages of  hieroglyphics. My
friend got his to print after some difficulties, but he can't  remember
how, and it won't print in colour. I'd appreciate some  help!   </bigger>

                             Lindsay

</excerpt>

There is a way via, I think, editing your sstools.ini, but I do not
recall what it is. A work around which I use is to simply save the image
(hit "s" after the image is generated); the image is saved as a .gif
image in your fractint directory. Then open the image and either print it
directly from the associated program, e.g. LViewPro, PSP, etc., or copy
the image and paste it into a word processing program such as WP.


Regards,




[e-mail]

[e-mail]

Back up my hard drive?

How do I put it in reverse?

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

Date: Mon, 2 Aug 1999 08:26:18 EDT
From: [e-mail]
Subject: Re: (fractint) Question

Dear Lindsay,
   I use Winfract as I don't know DOS so I cannot give you any technical
jargon. You probably know more than I do, but I'll try to help.

Have you saved the fractal first?
Do you have other graphics programs?
Can you open the image in another program and print it from there?
Does your printer work on other images?

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

Date: Sun, 2 Aug 1998 09:34:38 -0700
From: "Terry" <[e-mail]>
Subject: Re: (fractint) Question

- ----- Original Message -----
From: <[e-mail]>
To: <[e-mail]>
Sent: Monday, August 02, 1999 5:26 AM
Subject: Re: (fractint) Question


> Dear Lindsay,
>    I use Winfract as I don't know DOS so I cannot give you any technical
> jargon. You probably know more than I do, but I'll try to help.

Hey, I found out you don't have to "know DOS" to run Fractint. It's pretty
easy.
Even DOS is easy. You don't have to know DOS to run DOS either, but it
helps.
Actually just try to get it going and then experiment with it. The arrow
keys come in pretty handy.  Page up is for zooming. hit C twice for
color-cycling
And the DOS ver. is more powerful (AAR.  AAR!)
ALOha
Terry Erickson
[e-mail]

> Have you saved the fractal first?
> Do you have other graphics programs?
> Can you open the image in another program and print it from there?
> Does your printer work on other images?
>
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>


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

Date: 02 Aug 1999 23:18:52 +0200
From: Erik Eriksson <[e-mail]>
Subject: (fractint) Sierpinski

Hi,

I noticed that the Sierpinski triangle (gasket?) is represented as an
L-system in Fractint. Is it possible to generate this shape the
"dot-by-dot"-way in Fractint? Start in one corner of a triangle;
choose one corner at random; walk halfway towards it and make a dot;
choose a new corner at random; walk halfway towards it and make a dot
... etc?

/ Erik

- --
Erik Eriksson
[e-mail]


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

Date: Mon, 02 Aug 1999 17:37:56 -0500
From: "Damien M. Jones" <[e-mail]>
Subject: Re: (fractint) Sierpinski

Erik,

 - I noticed that the Sierpinski triangle (gasket?) is represented as an
 - L-system in Fractint. Is it possible to generate this shape the
 - "dot-by-dot"-way in Fractint?

Yes. Choose type "ifs", then choose "triangle".

Damien M. Jones   \\
[e-mail]  \\  Fractalus Galleries & Info:
                    \\  http://www.fractalus.com/

Please do not post my e-mail address on a web site or
in a newsgroup.  Thank you.

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

Date: Mon, 2 Aug 1999 19:26:48 -0600
From: "Tim Wegner" <[e-mail]>
Subject: Re: (fractint) Question

Lindsay asked:


<color><param>0000,0000,0000</param>>  I was wondering how to get it to  print right. Every time I

> use the Print command, I get ten pages of

> hieroglyphics. My friend got his to print after some

> difficulties, but he can't  remember how, and it won't print

> in colour. I'd appreciate some  help!


</color>I recommend printing with some other software. Fractint does have
some good prinbter drivers, but printer support is spotty, and the
current authors know knothing about them.


GIF is a universal format, so it is a simple matter to save the image
as a GIF and print with any of hundreds of programs that do a good
job.


Tim


<nofill>

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

Date: Tue, 3 Aug 1999 08:08:45 +0530 (IST)
From: Rajesh P <[e-mail]>
Subject: Re: (fractint) Sierpinski

> Hi,
>
> I noticed that the Sierpinski triangle (gasket?) is represented as an
> L-system in Fractint. Is it possible to generate this shape the
> "dot-by-dot"-way in Fractint? Start in one corner of a triangle;
> choose one corner at random; walk halfway towards it and make a dot;
> choose a new corner at random; walk halfway towards it and make a dot
> ... etc?
>
> / Erik
>

The algorithm is used and the program is available with the book "fractal
Mania". This is a beautiful method. A similar algorithm is used
for creating 'fern', 'castle', etc. You can really observe the changing
location of points every time you run the program yet the figure remains
exactly the same.

                Rajesh P



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Date: Tue, 3 Aug 1999 05:01:37 -0400
From: "James R. McKenzie" <[e-mail]>
Subject: (fractint) Question

I was on this list ages and eons ago and had to leave when my "former" ISP
started changing the e-mail program[s] they used/supported.

I kinda remember from way back when something about someone having hand
coded a driver for FRACTINT and the ATI RAGE chip set.  I have a ATI
All-In-Wonder Pro AGP 8mb Vid/mem(Econo-version = not upgradable) and can't
run above 800x600x256.  My old computer which had a generic video card
(Phoenix 32/64 with S3 Virge version chip set) could run FRACTINT @
1024x768x256.  This came into the discussion[s] of the list about the time I
had to quit due to the previously mentioned ISP screw-ups which were over a
year ago.

Can anyone tell me where the driver is and/or who/whom wrote it and how do I
contact them or will they contact me on how to get it?

Whew!  That was a mouth full!


also DAMIEN, is the other list still running?  PLEASE If so put me on it.


BTW, What ever came of the registering of the FRACTINT name as an INTERNET
domain?  Yeah, I was on the list "THAT" far back.


Oh well that it at this time.




L8R






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

Date: Tue, 3 Aug 1999 05:51:49 -0400
From: Barry N Merenoff <[e-mail]>
Subject: (fractint) Re: Sierpinski

Actually, to get a dot-by-dot representation of an EXACT Ifs fractal, the=

adaptive cut method is better. Remember that chaotic iteration is
probabilistic and will always have a small amount of uncertainty.

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Date: Tue, 3 Aug 1999 13:37:25 GMT
From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) In the PAR

I know the very latest version of FractInt is immenent, and I'm shure
everybody concerned is *very* busy, but there is just one little
thing I'd like to see in FractInt. And it probably wouldn't take much
effort. (Ever heard that one before?) I'd like it if I could store
maps, formulas, IFS systems AND parameters in ".PAR" files.

Actually, I already can. I can use a parameter entry which just
contains a "color=" entry, and this works as a map. I can include
"frm:" entries, which function as formulas... But FractInt doesn't
look here when loading pictures. If we could have dedicated features
to do these thing, I'd be very happy.

I like using parameter sets for my formulas; it makes it possible to
set the initial values of the paramiters (p1, etc). It also allows
you to pick the best default colours (something that not even the
built in fractal types do!).

Finally, if there were some special syntax that allowed you to enter
"help" style comments into formulas, and a button to view them, it
might look a bit nicer (although I shouldn't bother with
hyperlinks...)

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

Having dumped all of that, I wonder what the "escher julia" type
would look like if the julia it maps onto used some value other than
C=0. Mmm... Perhaps I could write a little program to load a picture
and then transform it using the Julia mapping function... I'll bet it
would look... interesting... if not actually pretty! Has anyone else
already tried this?

- ---------------------------------
Nam et ipsa scientia potestus est!
(Sir Francis Bacon)
Andrew Orphi Coppin
DMU MK.

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Date: Tue, 03 Aug 1999 10:12:48 -0500
From: "Damien M. Jones" <[e-mail]>
Subject: Re: (fractint) Question

James,

 - I kinda remember from way back when something about someone having
 - hand coded a driver for FRACTINT and the ATI RAGE chip set.

Well you could search the archives for that. :-) Most likely someone
probably used the VESA2CFG program to look up the mode number for various
supported video modes, and added entries to fractint.cfg so that they could
be used.

 - also DAMIEN, is the other list still running?  PLEASE If so put me on
 - it.

Which other list? :-) There are currently three fractal-related mailing
lists running on the icd.com server; fractal-art, ultrafractal, and
philofractal. You can subscribe to any of them by sending "subscribe
listname" (replace listname with the appropriate list name!) in the body of
a message to [e-mail] and you'll be subscribed.

 - BTW, What ever came of the registering of the FRACTINT name as an
 - INTERNET domain?  Yeah, I was on the list "THAT" far back.

The problem is (a) finding someone to pay for it, and (b) finding someone
to host it. If you solve (a) by having a bunch of people "chip in", then
you run into more problems of how to deal with the ownership. (b) is seldom
free, and costs more (usually) than paying for the domain name in the first
place.

Damien M. Jones   \\
[e-mail]  \\  Fractalus Galleries & Info:
                    \\  http://www.fractalus.com/

Please do not post my e-mail address on a web site or
in a newsgroup.  Thank you.

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

Date: Tue, 03 Aug 1999 22:36:29 +0200
From: Theo Bakker <[e-mail]>
Subject: Re: (fractint) Sierpinski

Erik Eriksson wrote:
>
> Hi,
>
> I noticed that the Sierpinski triangle (gasket?) is represented as an
> L-system in Fractint. Is it possible to generate this shape the
> "dot-by-dot"-way in Fractint? Start in one corner of a triangle;
> choose one corner at random; walk halfway towards it and make a dot;
> choose a new corner at random; walk halfway towards it and make a dot
> ... etc?
>
> / Erik
>
>
> Erik Eriksson
> [e-mail]
>
> Typically I also tried to play this "chaos game" with FractInt, but didn't succeed. The random number generator incorporated in FractInt only generates a new number after each complete iteration. Which is bullocks (>>) for the Chaos game.
I've written a routine in Maple though (obviously DEAD SLOW), but I
don't suppose that's what you want. In fact I'm writing a dutch manual
for FractInt to which I added an appendix about the chaos game,
Hutchinson operators and so on. In it I put the very same question to
the readers. If you make it work, please inform me!

Gretings,

Theo.
>
>
>
>

- --
Theo Bakker                     [e-mail]
H. Roland Holstlaan 29          UIN 8400214 (ICQ)
2162 JE Lisse
0252-413775

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Date: Tue, 03 Aug 1999 22:42:32 +0200
From: Theo Bakker <[e-mail]>
Subject: Re: (fractint) Sierpinski

"Damien M. Jones" wrote:
>
> Erik,
>
>  - I noticed that the Sierpinski triangle (gasket?) is represented as an
>  - L-system in Fractint. Is it possible to generate this shape the
>  - "dot-by-dot"-way in Fractint?
>
> Yes. Choose type "ifs", then choose "triangle".
>
> Damien M. Jones   \\

Hai Damien,

Suppose you had a rough night when you wrote this reply.
Never mind. Don't slep too well myself lately.

Greetings; have fun

Theo.
- --
Theo Bakker                     [e-mail]
H. Roland Holstlaan 29          UIN 8400214 (ICQ)
2162 JE Lisse
0252-413775

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Date: Tue, 03 Aug 1999 22:52:13 +0200
From: Theo Bakker <[e-mail]>
Subject: Re: (fractint) Re: Sierpinski

Barry N Merenoff wrote:
>
> Actually, to get a dot-by-dot representation of an EXACT Ifs fractal, the
> adaptive cut method is better. Remember that chaotic iteration is
> probabilistic and will always have a small amount of uncertainty.
>
>Hi Barry,

In fact it's not difficult to prove that this probabilistic method in
fact produces the gasket (given enough time and discarding the first few
points). Obviously both the ifs and .frm variation (which in fact uses
the same operator) have quicker and better results. But that's not the
fun of it, really ...

Greetings,

Theo.

- --
Theo Bakker                     [e-mail]
H. Roland Holstlaan 29          UIN 8400214 (ICQ)
2162 JE Lisse
0252-413775

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Date: Wed, 4 Aug 1999 21:21:52 +0200
From: "kanak" <[e-mail]>
Subject: (fractint) someone is interested in ...

This is a multi-part message in MIME format.

- ------=_NextPart_000_0011_01BEDEBF.5F248020
Content-Type: text/plain;
    charset="iso-8859-1"
Content-Transfer-Encoding: 7bit

carissimi frattalizzatori:

I made a little utility that

create a .MAP with the colors
of a chosen sequence faded eachother
(and fading the last into the first one)

it is an handmade perl script
and you need to be perl-IZED to use it

perl [Practical Extraction and Report Language]
is a free prog language easily available in the net)

ask me questions
or tell me if someone is interested in this




P.S.
try allfad.map with AtomicGlow ...


kanak
$_ = join "", reverse (split /\s+|[A-Z]|'/,
"hacker'S - lONG perIOD - rUN'TILL theY'LL noTICE a - stRAWBERRY juICE");
s/\-/ /gi and s/([jp])/\u$1/gi and print;


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    name="allfad.map"
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7    0    0
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31    0    0
39    0    0
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55    0    0
63    0    0
71    0    0
79    0    0
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151    255    0
143    255    0
135    255    0
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47    255    0
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31    255    0
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7    255    0
0    255    0
0    247    7
0    239    15
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0    223    31
0    215    39
0    207    47
0    199    55
0    191    63
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0    167    87
0    159    95
0    151    103
0    143    111
0    135    119
0    127    127
0    119    135
0    111    143
0    103    151
0    95    159
0    87    167
0    79    175
0    71    183
0    63    191
0    55    199
0    47    207
0    39    215
0    31    223
0    23    231
0    15    239
0    7    247
0    0    255
4    0    255
8    0    255
12    0    255
16    0    255
20    0    255
24    0    255
28    0    255
32    0    255
36    0    255
40    0    255
44    0    255
48    0    255
52    0    255
56    0    255
60    0    255
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68    0    255
72    0    255
76    0    255
80    0    255
84    0    255
88    0    255
92    0    255
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100    0    255
104    0    255
108    0    255
112    0    255
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120    0    255
124    0    255
128    0    255
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120    0    239
116    0    231
112    0    223
108    0    215
104    0    207
100    0    199
96    0    191
92    0    183
88    0    175
84    0    167
80    0    159
76    0    151
72    0    143
68    0    135
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56    0    111
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40    0    79
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32    0    63
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0    0    0
0    0    0

- ------=_NextPart_000_0011_01BEDEBF.5F248020--


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

Date: Wed, 4 Aug 1999 17:24:17 -0700
From: "Karin Mattern" <[e-mail]>
Subject: (fractint) Thanks

This is a multi-part message in MIME format.

- ------=_NextPart_000_003B_01BEDE9E.2E832BE0
Content-Type: text/plain;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Thanks for all the help on how to print. It works great if I save it and =
print it from another program.
                                                                         =
                               Lindsay

- ------=_NextPart_000_003B_01BEDE9E.2E832BE0
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    charset="iso-8859-1"
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<!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 4.72.3110.7"' name=3DGENERATOR>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT color=3D#000000 size=3D2>Thanks for all the help on how to =
print. It=20
works great if I save it and print it from another program.</FONT></DIV>
<DIV><FONT color=3D#000000=20
size=3D2>          &nbs=
p;            =
;            =
            &=
nbsp;           &n=
bsp;           &nb=
sp;           &nbs=
p;            =
;       =20
Lindsay</FONT></DIV></BODY></HTML>

- ------=_NextPart_000_003B_01BEDE9E.2E832BE0--


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

Date: Thu, 5 Aug 1999 15:55:06 GMT
From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) Feigenbaum's Number

I have a question about Feigenbaum's Number. They say it's about
4.669... Does anyone know how you actually calculate it? Is it
rational? (I suspect not!) Just curiouse.

- ---------------------------------
Nam et ipsa scientia potestus est!
(Sir Francis Bacon)
Andrew Orphi Coppin
DMU MK.

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Date: Thu, 5 Aug 1999 15:14:00 -0700
From: "Kerry Mitchell" <[e-mail]>
Subject: Re: (fractint) Feigenbaum's Number

Andrew,

Feigenbaum has 2 constants named after him.  I believe the 4.669... one is
the alpha constant.  It's been calculated to many (20+) places, and I don't
believe it's rational (although I haven't seen a proof).

A direct (but not terribly efficient) way to calculate it is to use the
structure of the Mandelbrot set.  The main cardioid is centered on 0, that
is, 0 is the "c" point such that c=0 (obviously).  The large disk just left
of the cardioid is centered on -1.  That is, c=-1 satisfies c^2 + c = 0.
To the left of that disk is another, smaller, centered somewhere about
- -1.28.  That point satisfies (c^2 +c)^2 + c = 0.  The sequence of disks
getting smaller off to the left have centers that satisfy the appropriate
iteration of z^2 + c = 0, where z is the result of the previous iteration.

For any group of 3 adjacent centers, form the ratio:
(c_current - c_previous)/(c_next - c_current).  As the disks get smaller
and smaller and you converge on the Feigenbaum point (-1.4something), this
ratio will converge on alpha.

Kerry

- -----------------------------------------------------------------
Kerry Mitchell
[e-mail]   http://www.primenet.com/~lkmitch/
- -----------------------------------------------------------------

- ----------
> From: Andrew Coppin <[e-mail]>
> To: [e-mail]
> Subject: (fractint) Feigenbaum's Number
> Date: Thursday, August 05, 1999 8:55 AM
>
> I have a question about Feigenbaum's Number. They say it's about
> 4.669... Does anyone know how you actually calculate it? Is it
> rational? (I suspect not!) Just curiouse.
>
> ---------------------------------
> Nam et ipsa scientia potestus est!
> (Sir Francis Bacon)
> Andrew Orphi Coppin
> DMU MK.
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
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> Unsubscribe:    [e-mail] "unsubscribe fractint"

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End of fractint-digest V1 #403
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