The cover of Mandelbrot's book " Multifractals
and 1/f Noise" has the Pharoah's breast plate. (ref page 126-127 of this
book)
The original IFS of this was done by Dr. Monk, but he has lost the
material and has only a vague idea of how to reconstruct it using 6
transforms.

The fractal challenge is to reconstruct the IFS for the Pharoah's breast
plate in translatable
( at least two recognized computer languages)
Computer code.
To post the result at sci.math, sci.fractals and sci.nonlinear
Respectfully, Roger L. Bagula

tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn

From:	G. A. Edgar
Subject:	Re: The Fractal Challenge
Date:	Fri, 19 Nov 2004 10:09:55 -0500

In article <419E0393.7050102@earthlink.net>, Roger Bagula
wrote:

> The cover of Mandelbrot's book " Multifractals
> and 1/f Noise" has the Pharoah's breast plate. (ref page 126-127 of this
> book)
> The original IFS of this was done by Dr. Monk, but he has lost the
> material and has only a vague idea of how to reconstruct it using 6
> transforms.
>
> The fractal challenge is to reconstruct the IFS for the Pharoah's breast
> plate in translatable
> ( at least two recognized computer languages)
> Computer code.
> To post the result at sci.math, sci.fractals and sci.nonlinear
> Respectfully, Roger L. Bagula
>

See the cover in question at Amazon.com ... I think this link will work:
http://www.amazon.com/gp/reader/0387985395/

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/

From:	Roger Bagula
Subject:	Re: The Fractal Challenge
Date:	Thu, 25 Nov 2004 20:41:48 GMT

Hint: ( these links might help at a number theory professor's site)
http://klein.math.okstate.edu/IndrasPearls/
http://www.math.okstate.edu/~wrightd/INDRA/
Roger Bagula wrote:

> The cover of Mandelbrot's book " Multifractals
> and 1/f Noise" has the Pharoah's breast plate. (ref page 126-127 of
> this book)
> The original IFS of this was done by Dr. Monk, but he has lost the
> material and has only a vague idea of how to reconstruct it using 6
> transforms.
>
> The fractal challenge is to reconstruct the IFS for the Pharoah's
> breast plate in translatable
> ( at least two recognized computer languages)
> Computer code.
> To post the result at sci.math, sci.fractals and sci.nonlinear
> Respectfully, Roger L. Bagula
>
> tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel:
> 619-5610814 :
> alternative email: rlbtftn@netscape.net
> URL : http://home.earthlink.net/~tftn
>
>

--
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn

From:	Roger Bagula
Subject:	Re: The Fractal Challenge
Date:	Sat, 27 Nov 2004 16:42:14 GMT

The Pharaoh's Breastplate Image

http://math.scranton.edu/monks/pubs/pharaoh/pharaoh.html

Above is an image I produced of the Pharaoh's Breastplate fractal, a
limit set of a Kleinian group. I wrote a Maple
program to generate the centers and radii of
the 6734 circles that make up the image. The data was then converted by
another Maple program of mine into a suitable format and read into the
public domain ray tracing program, POV-RAY . The
image has been published on the cover of the book Multifractals and 1/f
Noise (ISBN: 0-387-98539-5) by Benoit Mandelbrot, who helped me with
the selection of the textures and the arrangement of the "stones". The
first published image of the Pharaoh's Breastplate fractal (to my
knowledge) appears in Mandelbrot's book The Fractal Geometry of Nature
(ISBN: 0-7167-1186-9) in Plate 199.

Roger Bagula wrote:

> The cover of Mandelbrot's book " Multifractals
> and 1/f Noise" has the Pharoah's breast plate. (ref page 126-127 of
> this book)
> The original IFS of this was done by Dr. Monk, but he has lost the
> material and has only a vague idea of how to reconstruct it using 6
> transforms.
>
> The fractal challenge is to reconstruct the IFS for the Pharoah's
> breast plate in translatable
> ( at least two recognized computer languages)
> Computer code.
> To post the result at sci.math, sci.fractals and sci.nonlinear
> Respectfully, Roger L. Bagula
>
> tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel:
> 619-5610814 :
> alternative email: rlbtftn@netscape.net
> URL : http://home.earthlink.net/~tftn
>
>

--
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn

From:	G. A. Edgar
Subject:	Re: The Fractal Challenge
Date:	Wed, 24 Nov 2004 15:27:42 -0500

From:	Roger Bagula
Subject:	Re: The Fractal Challenge
Date:	Wed, 24 Nov 2004 23:17:24 GMT

Dear Dr. Edgar,
That's the Dr. Monk data alright but the challenge was:
"The fractal challenge is to reconstruct the IFS for the Pharoah's
breast plate in translatable
( at least two recognized computer languages)
Computer code."

C++, Basic, Mathematica, MatLab, Maple...
Any varifiable computer language that runs on more than one system.

All I care about is that the method isn't lost.
G. A. Edgar wrote:

>In article <419E0393.7050102@earthlink.net>, Roger Bagula
> wrote:
>
>
>
>>The cover of Mandelbrot's book " Multifractals
>>and 1/f Noise" has the Pharoah's breast plate. (ref page 126-127 of this
>>book)
>>The original IFS of this was done by Dr. Monk, but he has lost the
>>material and has only a vague idea of how to reconstruct it using 6
>>transforms.
>>
>>
>>
>
>Interesting. Here it is...
> http://www.math.ohio-state.edu/~edgar/BPlate/index.html
>
>
>

--
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn

From:	David C. Ullrich
Subject:	Re: The Fractal Challenge
Date:	Thu, 25 Nov 2004 06:16:00 -0600

On Wed, 24 Nov 2004 23:17:24 GMT, Roger Bagula
wrote:

>Dear Dr. Edgar,
>That's the Dr. Monk data alright but the challenge was:
>"The fractal challenge is to reconstruct the IFS for the Pharoah's
>breast plate in translatable
>( at least two recognized computer languages)
>Computer code."

So the "challenge" was not to find the IFS? A perfectly
clear and unambiguous description of the IFS doesn't count,
the challenge is to write the actual code?

This would be a much better challenge for a CS 101 class
than for sci.math.

>C++, Basic, Mathematica, MatLab, Maple...
>Any varifiable computer language that runs on more than one system.
>
>All I care about is that the method isn't lost.
>G. A. Edgar wrote:
>
>>In article <419E0393.7050102@earthlink.net>, Roger Bagula
>> wrote:
>>
>>
>>
>>>The cover of Mandelbrot's book " Multifractals
>>>and 1/f Noise" has the Pharoah's breast plate. (ref page 126-127 of this
>>>book)
>>>The original IFS of this was done by Dr. Monk, but he has lost the
>>>material and has only a vague idea of how to reconstruct it using 6
>>>transforms.
>>>
>>>
>>>
>>
>>Interesting. Here it is...
>> http://www.math.ohio-state.edu/~edgar/BPlate/index.html
>>
>>
>>

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

David C. Ullrich

From:	Roger Bagula
Subject:	Re: The Fractal Challenge
Date:	Thu, 25 Nov 2004 15:10:16 GMT

Most of this information was available.
The definition isn't clear to those who know nothing of
Klein groups, Møbius transforms and
half plane transforms.
It isn't a "linear" affine IFS, so defining circles
as this does , doesn't specify their transformations
An actual mathematical definition of the transforms that can be
"performed" is necessary.
Thus, a working program is preferred.
Dr . Mauldin gave a definition like this of the appolonian gasket:
It wasn't adequate for most people to construct a working program.
It was actually clearer than this one is!
If it was easy , it would already be on the Internet.
Roger Bagula wrote:

> Dear Dr. Edgar,
> That's the Dr. Monk data alright but the challenge was:
> "The fractal challenge is to reconstruct the IFS for the Pharoah's
> breast plate in translatable
> ( at least two recognized computer languages)
> Computer code."
>
> C++, Basic, Mathematica, MatLab, Maple...
> Any varifiable computer language that runs on more than one system.
>
> All I care about is that the method isn't lost.
> G. A. Edgar wrote:
>
>> In article <419E0393.7050102@earthlink.net>, Roger Bagula
>> wrote:
>>
>>
>>
>>> The cover of Mandelbrot's book " Multifractals
>>> and 1/f Noise" has the Pharoah's breast plate. (ref page 126-127 of
>>> this book)
>>> The original IFS of this was done by Dr. Monk, but he has lost the
>>> material and has only a vague idea of how to reconstruct it using 6
>>> transforms.
>>>
>>>
>>
>>
>> Interesting. Here it is...
>> http://www.math.ohio-state.edu/~edgar/BPlate/index.html
>>
>>
>>
>

--
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn

From:	Lee Rudolph
Subject:	Re: The Fractal Challenge
Date:	25 Nov 2004 10:21:48 -0500

Roger Bagula writes:

....
>If it was easy , it would already be on the Internet.
....

Hell, if it was , it
would already be on the Internet, too!

Lee Rudolph

From:	Philo D
Subject:	Re: The Fractal Challenge
Date:	5 Dec 2004 06:58:32 -0800

See some nice pictures of a similar Kleinian group limit sets in the
December Notices.
free on line.... http://www.ams.org/notices/200411/200411-toc.html
see the paper of David J. Wright.