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fractint-digest          Friday, May 21 1999          Volume 01 : Number 390




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

Date: Tue, 18 May 1999 18:55:24 -0400
From: Lee Skinner <[e-mail]>
Subject: (fractint) We haven't AL

Bresslau,

>> I know it's not a great difference, but it _is_ technically more
eficient to use the guessing method. Am I right in supposing that you use=

the 1 pass method because it's beautiful to see image _scrolling_ down th=
e
screen? <<

Any of the guessing methods will often guess wrong.  Passes=3D1 is used t=
o
insure more accuracy in the rendering on an image, particularly for very
chaotic images.

Lee

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

Date: Tue, 18 May 1999 19:10:46 -0700
From: "Jay Hill" <[e-mail]>
Subject: Re: (fractint) Choose yur picture before downloading the par.

Deleting much header and footer  :-) =20

I get a vision of clicking my way through a fractal mall where I=20
get messages like "Add to cart" and then finally I go to the=20
check out counter and to get my pars. The box boy says=20
"plastic or paper" ah er "email or download" and packs up=20
the pars into a single par file, then zips em up.  Then I can=20
click to download (ftp like) or get it in email as an attachment.=20
I think I'm getting VONS and Amazon mixed up here - oh well,
I read that Amazon just bought a grocery store.

Jay

- ----------
> From: Jack Baker <[e-mail]>
> To: [e-mail]
> Subject: Re: (fractint) Choose yur picture before downloading the par.
> Date: Monday, May 17, 1999 8:42 PM
>=20
> Pretty good idea, and it really would not be to hard to do.  Just gotta=
 get=20
> the web space and time to get it done.  Perhaps on a server like xoom.c=
om???=20
>   Anyway, a simple CGI would probably be fine, and all that would be=20
> necessary for the graphics would be a thumbnail.  The user could downlo=
ad=20
> any pars that they were intrigued by and view the larger graphic at the=
ir=20
> leisure.  Anybody out there want to jump on board here?????
>=20
> -Jack
>=20
>=20
>=20
> I just had an idea:
> what if there where a site where you could see a preview of the pars yo=
u
> were going to download? Somethng like a thumbnail page with checkboxes =
for
> each picture. you like the picture, you check it. Then you post the for=
m and
> a par file with all the pars for the pics you checked is created specia=
lly
> for you.
> This was the idea. I downloaded lots of huge par files with hundreds of
> pictures without havin a hint to what they contained. My pars are reall=
y a
> mess and I don=B4t have time to process each of them to see what comes =
up.
> Maybe if I could download only what I wanted, I could still have a beau=
tiful
> collection of fractals without having the trouble to select them one by=
 one
> after they were generated.
> I don=B4t know nothing about web deisgn /programming, and I don=B4t kno=
w if this
> is a good idea. But if anybody likes it, please use it.
> Bresslau
>=20
>=20

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

Date: Tue, 18 May 1999 21:18:39 -0600
From: Phil McRevis <[e-mail]>
Subject: Re: (fractint) We haven't ALL gone to UF

Solid guessing is good for sets that are "connected" (the M-set has
been proved connected, but not necessarily locally connected, I
believe).  "Connected" has a specific mathematical meaning, but just
think of it as the concept of the interior of the set being one single
piece that can't be partitioned into multiple disjoint areas.

There are julia sets that are "totally disconnected" meaning that they
can be separated into an infinite collection of disjoint pieces.
Solid guessing makes many mistakes when used to render a totally
disconnected fractal.  Solid guessing is an approximation; for
connected sets like the classic M, the approximation is valid.  For
disconnected sets, the approximation will produce many errors in the
rendering.  (The solid guessing algorithm will conclude that a chunk
of the image is a constant color, when in fact there is a little
island of fractal hiding in the middle that was missed by solid
guessing.)

You can always compare passes=1 (or even passes=3, since passes=1,2,3
all result in the same picture, only the pixels are computed in a
different sequence) to passes=g to see if there is any difference on
your particular fractal.
- --
<http://www.xmission.com/~legalize/>    Legalize Adulthood!
    ``Ain't it funny that they all fire the pistol,
      at the wrong end of the race?''--PDBT
[e-mail]    <http://www.eden.com/~thewho>

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

Date: Wed, 19 May 1999 10:30:44 +0200
From: "Randall Britten" <[e-mail]>
Subject: RE: (fractint) We haven't ALL gone to UF

Where can one obtain the proof that the M-set is connected?

- -------------------------
Randall Britten



- -----Original Message-----
From:    [e-mail]
[mailto:[e-mail]] On Behalf Of Phil McRevis
Sent:    Wednesday 19 May 1999 05:19
To:    [e-mail]
Subject:    Re: (fractint) We haven't ALL gone to UF


Solid guessing is good for sets that are "connected" (the M-set has
been proved connected, but not necessarily locally connected, I
believe).  "Connected" has a specific mathematical meaning, but just
think of it as the concept of the interior of the set being one single
piece that can't be partitioned into multiple disjoint areas.

There are julia sets that are "totally disconnected" meaning that they
can be separated into an infinite collection of disjoint pieces.
Solid guessing makes many mistakes when used to render a totally
disconnected fractal.  Solid guessing is an approximation; for
connected sets like the classic M, the approximation is valid.  For
disconnected sets, the approximation will produce many errors in the
rendering.  (The solid guessing algorithm will conclude that a chunk
of the image is a constant color, when in fact there is a little
island of fractal hiding in the middle that was missed by solid
guessing.)

You can always compare passes=1 (or even passes=3, since passes=1,2,3
all result in the same picture, only the pixels are computed in a
different sequence) to passes=g to see if there is any difference on
your particular fractal.
- --
<http://www.xmission.com/~legalize/>    Legalize Adulthood!
    ``Ain't it funny that they all fire the pistol,
      at the wrong end of the race?''--PDBT
[e-mail]    <http://www.eden.com/~thewho>

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

Date: Wed, 19 May 1999 13:00:36 GMT
From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) Fractal Noise

So how does one actually *calculate* some fractal noise (with any
exponent)? It sounds fasinating.

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

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

Date: Wed, 19 May 1999 11:47:26 -0600
From: Phil McRevis <[e-mail]>
Subject: (fractint) Re: Connectedness of M

In article <000801bea1d1$e4e2d3e0$[e-mail]>,
    "Randall Britten" <[e-mail]>  writes:

> Where can one obtain the proof that the M-set is connected?

According to "Chaos and Fractals", by Peitgen, Jurgens and Saupe, pg.
849:

    "[...] the Mandelbrot set is connected.  This is known since 1982
    through a paper of Douady and Hubbard, in which they showed that
    the encirclement of the Mandelbrot set always generates domains
    which are bounded by circle-like curves.  If the encirclement is
    properly manufactured it can be shown that the bounding curves are
    in fact equipotentials of the Mandelbrot set."

The paper mentioned in that paragraph is given as

    A. Douady, J. H. Hubbard, "Iteration des polynomes quadratiques
    complexes", CRAS Paris 294 (1982) 123-126.

All my other references quote the result from this paper and refer you
to the paper fro the proof.
- --
<http://www.xmission.com/~legalize/>    Legalize Adulthood!
    ``Ain't it funny that they all fire the pistol,
      at the wrong end of the race?''--PDBT
[e-mail]    <http://www.eden.com/~thewho>

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

Date: Tue, 18 May 1999 20:27:07 +0930
From: "Wayne Kiely" <[e-mail]>
Subject: Re: (fractint) We haven't ALL gone to UF

Tony,

>... Some recent work.

And nice work at that.  I especially liked bm007 (the fractured chaotic edge) and cn002.

Regards,

Wayne


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

Date: Thu, 20 May 1999 00:20:40 EDT
From: [e-mail]
Subject: (fractint) quickie pars

We haven't All...but its damn close isn't it?
A couple pars and a couple formulas

Im not a prolific par generator and more often than not I get hooked on the
geometry or logic rather than the art but sometimes it just looks good.

Tony Hanmer....BM007 was my favorite, looked great

Edgy_infinity      { ; (c) R Parracho May 05, 1999 t=  0:07:10.56 66mhz
  reset=1960 type=formula formulafile=rsp_may.frm
  formulaname=rsp_may002 passes=1 center-mag=0.618064/1.33263/11.44689
  float=y logmap=14 periodicity=0
  colors=000300700900<3>P30S40X60`70<3>qE0uF0zI0zK0zM0zP0zS0zU0zW0zZ0za0ze\
  0<2>zm0zp0zt0zv0zy0zv2zt4<2>zjAzgCzeEzaGzZIzWKzUMzSOzPQ<2>zIWuFY<2>iAcd8\
  e`7gX6iS4k<3>D1s90u70w30y000000300700900<3>P30S40X60`70<3>qE0uF0zI0zK0zM\
  0zP0zS0zU0zW0zZ0za0ze0<2>zm0zp0zt0zv0zy2zv4zt6<2>zjCzgEzeGzaIzZKzWMzUOzS\
  QzPS<2>zIYuF_<2>iAed8g`7iX6kS4m<3>D1u90w70y300000000300700900<3>P30S40X6\
  0`70<3>qE0uF0zI0zK0zM0zP0zS0zU0zW0zZ0za0ze0<2>zm0zp0zt0zv2zy4zv6zt8<2>zj\
  EzgGzeIzaKzZMzWOzUQzSSzPU<2>zI_uFa<2>iAgd8i`7kX6mS4o<3>D1w90y70030000000\
  0300700900<3>P30S40X60`70<3>qE0uF0zI0zK0zM0zP0zS0zU0zW0zZ0za0ze0<2>zm0zp\
  0zt2zv4zy6zv8ztA<2>zjGzgIzeKzaMzZOzWQzUSzSUzPW<2>zIauFc<2>iAid8k`7mX6oS4\
  q<3>D1y
  }

rsp_modular        { ; (c) R Parracho May 10, 1999 t=  0:01:27.61 66mhz
  reset=1960 type=formula formulafile=rsp_may.frm
  formulaname=rsp_may005 center-mag=-0.453568/0/0.6666667
  params=7/0/5/0 float=y maxiter=256 inside=2 outside=summ
  periodicity=0
  colors=000000<12>jvVLT`MaSZyR6PDa8qSJ55mTD9`SWo2s6bDrj0GMjxmivjfj6pufUJu\
  icIpZXhSJpOveYBBJhaDTf`ssHPqxS2j34edF2On7bGZyybYD1V9vWSGoLa9P9ohGAKvnDMY\
  77Iz7FqhsKdVPZsBLuThIkAE6_G_WB915xV9LTS96G7AAzQ4Dg1SuPbeNxWVd7IenotvwotD\
  bWv3Vx`LDJIG_GhTpy8`VBLs2MZFCTjLFh74fctO8QK2WUx0II9kLWn6`DUzOZXuiYh9zAta\
  kf9i1DthXY_wSHEgE3g6nElMsci9hh7QqklDPb5zJPS16b94jXGShd03VeE19Q6EEJHPuq0F\
  QWntah4etJBwPzlSJHDcYRMRbycCp5FrcXfUEhYqV1VW9P`u87iuCwRTqQuWUSIHk75gFl53\
  INF2F1zrjqmlO5pgfJ8F67fsZv5Qv2Gf6xSSx1Xiu9T6P18ZtHKJzFx5mbf``eZ7fU8d`Zgs\
  RejoWtpSI0XaRyeIIqu4UpYnn_MXPl3j52go0sUkb8k2fUJtmHootfi7It7zfp7hcvK1A7`u\
  fK3X3tRL5ZRg7McUs7TxhuRDszeLHlgKGETxnQZzyLkdR2oHOrRMl9Wbatjca0LO7WzGF9EH\
  EHrZ6qnvZp229gtO_JbrSy2V3ofKbIyab2kKQz7rDdKw6h8r`pJu4oM5qn_3FyKNvHUre`IT\
  6zKywMiWPBofkglYH9fNNNm
  }

serps_mand1        { ; (c) R Parracho May 13, 1999 t=  0:04:41.22 66mhz
  reset=1960 type=formula formulafile=rsp_may.frm
  formulaname=rsp_may007 passes=1 center-mag=-0.983412/0.3238/13.33333
  params=8/0/4/0 float=y inside=2 periodicity=0
  colors=000000<7>hPU<6>xdi<8>7ST<6>69W<2>NPVTVUZ`TdfTjlSprRvxQ<27>gQWfOXg\
  OchOjiPq<13>cpvbswcrw<13>sYwuWxuWw<13>yY`zZZzZZ<13>zVgzUhxVi<13>XpxVrzUr\
  w<14>0d8<15>eHuhFyhFy<28>wOgxPfxPd<15>oL0<13>iVuhWziTz<3>oGypGypHz
  }

web_spinner        { ; (c) R Parracho May 13, 1999 t=  0:03:48.60 66mhz
  reset=1960 type=formula formulafile=rsp_may.frm
  formulaname=rsp_may008
  center-mag=+0.33521126760563420/+0.05198329853862181/98.03922
  params=2/0/4/0 float=y inside=2 periodicity=0
  colors=000000<12>jvV<4>yyb<6>j0G<10>BBJ<16>Kyw<17>7hc1SuPbeNxWVd7Ienotvw\
  otDbWv3Vx`LDJIG_GhTpy8`VBLs2MZFCTjLFh74fctO8QK2WUx0II9kLWn6`DUzOZXuiYh9z\
  Atakf9i1DthXY_wSHEgE3g6nElMsci9hh7QqklDPb5zJPS16b94jXGShd03VeE19Q6EEJHPu\
  q0FQWntah4etJBwPzlSJHDcYRMRbycCp5FrcXfUEhYqV1VW9P`u87iuCwRTqQuWUSIHk75gF\
  l53INF2F1zrjqmlO5pgfJ8F67fsZv5Qv2Gf6xSSx1Xiu9T6P18ZtHKJzFx5mbf``eZ7fU8d`\
  ZgsRejoWtpSI0XaRyeIIqu4UpYnn_MXPl3j52go0sUkb8k2fUJtmHootfi7It7zfp7hcvK1A\
  7`ufK3X3tRL5ZRg7McUs7TxhuRDszeLHlgKGETxnQZzyLkdR2oHOrRMl9Wbatjca0LO7WzGF\
  9EHEHrZ6qnvZp229gtO_JbrSy2V3ofKbIyab2kKQz7rDdKw6h8r`pJu4oM5qn_3FyKNvHUre\
  `IT6zKywMiWPBofkglYH9fNNNm
  }

rsp_mandradius     { ; (c) R Parracho May 19, 1999 t=  0:13:56.90 66mhz
  reset=1960 type=formula formulafile=rsp_may.frm
  formulaname=rsp_may011 passes=1 center-mag=-0.613881/0/0.6666667
  params=0.25/0 float=y maxiter=256 periodicity=0
  colors=000000<7>hPU<6>xdi<8>7ST<6>69W<2>NPVTVUZ`TdfTjlSprRvxQ<27>gQWfOXg\
  OchOjiPq<13>cpvbswcrw<13>sYwuWxuWw<13>yY`zZZzZZ<13>zVgzUhxVi<13>XpxVrzUr\
  w<14>0d8<15>eHuhFyhFy<28>wOgxPfxPd<15>oL0<13>iVuhWziTz<3>oGypGypHz
  }

rsp_juliradius     { ; (c) R Parracho May 19, 1999 t=  0:03:44.04 66mhz
  reset=1960 type=formula formulafile=rsp_may.frm
  formulaname=rsp_may012 center-mag=0/0/0.6666667
  params=0.15/0/-0.768/0.13 float=y maxiter=256 periodicity=0
  colors=000000<7>hPU<6>xdi<8>7ST<6>69W<2>NPVTVUZ`TdfTjlSprRvxQ<27>gQWfOXg\
  OchOjiPq<13>cpvbswcrw<13>sYwuWxuWw<13>yY`zZZzZZ<13>zVgzUhxVi<13>XpxVrzUr\
  w<14>0d8<15>eHuhFyhFy<28>wOgxPfxPd<15>oL0<13>iVuhWziTz<3>oGypGypHz
  }

rsp_mandradiusz    { ; (c) R Parracho May 19, 1999 t=  1:15:32.28 66mhz
  reset=1960 type=formula formulafile=rsp_may.frm
  formulaname=rsp_may011 passes=1
  center-mag=0.105572/0.571056/5.464481 params=0.25/0 float=y
  maxiter=256 periodicity=0
  colors=000000<7>hPU<6>xdi<8>7ST<6>69W<2>NPVTVUZ`TdfTjlSprRvxQ<27>gQWfOXg\
  OchOjiPq<13>cpvbswcrw<13>sYwuWxuWw<13>yY`zZZzZZ<13>zVgzUhxVi<13>XpxVrzUr\
  w<14>0d8<15>eHuhFyhFy<28>wOgxPfxPd<15>oL0<13>iVuhWziTz<3>oGypGypHz
  }

frm:rsp_may002{
    z=10*pixel
    a=z, an=1, n=i=0,
    :
    i=i+.5, n=a-i,
    an=an*n/(z^n), oz=z,
    z=1+z+an
    |z-oz|>.00001
    }

frm:rsp_may005 {
    z=w=c=pixel, n=p1,
    :
    w=w*w+c, z=(w-floor(w))*n
    |w|<p2
    }

frm:rsp_may007 {
    z=w=pixel, c=pixel, n=p1
    :
    z=z*z+c, w=(w-floor(w))*n
    |z|<p2  || |w|>n
    }

frm:rsp_may008 {
    z=w=pixel, c=pixel, n=p1,
    :
    z=z*z+c, w=(z/n-floor(z/n))*n
    |z|<p2  || |w|>n
    }

frm:rsp_may011(xaxis){
    n=a=b=c=d=e=f=g=f0=f1=0
    u=pixel, z=0, cc=pixel
    :
    n=n+1
    u=u*u+cc, a0=real(u), a1=imag(u),
    v=u*u+cc, b0=real(v), b1=imag(v),
    w=v*v+cc, c0=real(w), c1=imag(w),
    a=b0-a0, b=b1-a1, c=c0-a0, d=c1-a1
    e=a*(a0+b0) + b*(a1+b1),
    f=c*(a0+c0) + d*(a1+c1),
    g=2*(a*(c1-b1)-b*(c0-b0)),
    f0=(d*e-b*g)/f, f1=(a*g-c*e)/f,
    r2=sqrt((a0-f0)*(a0-f0)+(a1-f1)*(a1-f1)),
    z=ceil(cabs(v-u)+cabs(w-v)), count=n
    (|z|>=|r2*p1|)  || (count>257)
    }

rsp_may012{
    n=a=b=c=d=e=f=g=f0=f1=0
    u=pixel, z=0,
    cc=p2
    :
    n=n+1
    u=u*u+cc, a0=real(u), a1=imag(u),
    v=u*u+cc, b0=real(v), b1=imag(v),
    w=v*v+cc, c0=real(w), c1=imag(w),
    a=b0-a0, b=b1-a1, c=c0-a0, d=c1-a1
    e=a*(a0+b0) + b*(a1+b1),
    f=c*(a0+c0) + d*(a1+c1),
    g=2*(a*(c1-b1)-b*(c0-b0))
    f0=(d*e-b*g)/f, f1=(a*g-c*e)/f
    r2=sqrt((a0-f0)*(a0-f0)+(a1-f1)*(a1-f1)),
    z=ceil(cabs(v-u)+cabs(w-v)), count=n
    (|z|>=|r2*p1|)  || (count>257)
    }


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Date: Thu, 20 May 1999 12:07:42 -0600
From: Phil McRevis <[e-mail]>
Subject: Re: (fractint) quickie pars

In article <[e-mail]>,
    [e-mail]  writes:

> We haven't All...but its damn close isn't it?

<shrug>  I haven't even taken time to download UF because I'm working
on extending fractint by getting rid of the "medium" memory model and
adding a porting interface that makes it easier to port fractint to
some other system like a Mac or BeOS.  Lots of people who were in a
position to contribute something to fractint were put off by all the
restrictions of working in a 640K overlaid medium-memory model.  The
code itself goes through many contortions and backflips just to fit
into this 8088 style model of programming.  The next evolution of
fractint will leave 8088/80286 machines behind but will provide a
significantly easier environment for casual programmers to add new
features.
- --
<http://www.xmission.com/~legalize/>    Legalize Adulthood!
    ``Ain't it funny that they all fire the pistol,
      at the wrong end of the race?''--PDBT
[e-mail]    <http://www.eden.com/~thewho>

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Date: Thu, 20 May 1999 15:17:34 -0500
From: "Allison, Joshua" <[e-mail]>
Subject: (fractint) Fractint on NT

Has anyone had any experience with fractint on NT?

Joshua

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Date: Thu, 20 May 1999 14:42:41 -0600
From: Phil McRevis <[e-mail]>
Subject: Re: (fractint) Fractint on NT

In article <[e-mail]>,
    "Allison, Joshua" <[e-mail]>  writes:

> Has anyone had any experience with fractint on NT?

Some people have reported success; others have reported problems.
Expect fractint to evolve soon (not the next release, but maybe the
release after that) into a native Win32 client where these problems
of DOS compatability disappear.
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      at the wrong end of the race?''--PDBT
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Date: Thu, 20 May 1999 18:34:36 EDT
From: [e-mail]
Subject: Re: (fractint) quickie pars

I know the new version of fractint is in the oven...and i'm sure UF has put a
lot of pressure on its (fractint's) development.  To be honest I think
fractint is excellent.  All of fractints' bells and whistles still turn me
on.  I don't make money or consider my self an artist or a mathematician just
a frequent weekend fragler...all

best regards,
Rui


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Date: Thu, 20 May 1999 16:56:21 -0600
From: Phil McRevis <[e-mail]>
Subject: Re: (fractint) quickie pars

In article <[e-mail]>,
    [e-mail]  writes:

> ...and i'm sure UF has put a
> lot of pressure on its (fractint's) development.

<again I shrug :>  My impetus for extending fractint doesn't have
anything to do with "pressure" from UF.  I have written my own fractal
software in the past, mostly to test out little tricks for isolated
images -- see <http://www.xmission.com/~legalize/fractals/> where I
wrote my own software to compute the hue and texture colorings of M.  I
had considered doing an UF-like thing whereby I wrote my own fractal
imaging app from the ground-up.  However, every time I considered doing
that it always stuck in my craw that I'd be reinventing everything
fractint already had.  In the end, I decided it would be better for me
and the fractal community at large if I extended fractint rather than
reinvent the wheel.

My investigations into fractint source code quickly revealed that I
wouldn't be able to add any of my whizz-bang ideas to fractint until
a stake was driven into the heart of the medium memory model first.
I was hoping someone else would do this, but noone waved their hands
and said "I'll do this!".  Sure, everyone wants to do a Win32 "port"
but noone wants to deal with the realities of such a port: medium
memory model must go.  This is a rather unglamorous, extensive and
tedious programming task that doesn't have the ego-salve of glory that
most people seem to want.  So rather than contribute back to the
fractint community, they lurk on the sidelines or reinvent the wheel
to build a shrine to their own ego.

Does anyone here truly have any idea how huge fractint is?  In source
code its about 137,700 lines of source code comprising about 500K of
storage.  When printed out double sided it amounts to a 6 inch thick
printout -- not including the help file sources.  Its a minor miracle
of software engineering that it still runs on an 8088 with 640K of
memory.

This is, of course, my opinion and not any "official" statement on
behalf of fractint developers.  If you were offended by what I said,
then I must have said something important. :-)
- --
<http://www.xmission.com/~legalize/>    Legalize Adulthood!
    ``Ain't it funny that they all fire the pistol,
      at the wrong end of the race?''--PDBT
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Date: Thu, 20 May 1999 19:52:35 EDT
From: [e-mail]
Subject: Re: (fractint) quickie pars

In a message dated 5/20/99 6:59:02 PM Eastern Daylight Time,
[e-mail] writes:

> If you were offended by what I said,
>  then I must have said something important. :-)

I wasn't offended, nor did I mean to offend.  In anyway am I minimizing the
grand accomplishment that fractint is and will continue to be.

Regards,
Rui


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Date: Thu, 20 May 1999 20:51:13 -0500
From: "David J. Dollevoet" <[e-mail]>
Subject: (fractint) Pars

This is a multi-part message in MIME format.
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Here are some julia(fn||fn) and lambda(fn||fn) pars.  Some use a bailout
value much lower than the default value of 64.

- --------------2D855D714AD3C03C7347996E
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML>
<FONT FACE="Times New Roman,Times">Here are some julia(fn||fn) and lambda(fn||fn)
pars.  Some use a bailout value much lower than the default value
of 64.</FONT></HTML>

- --------------2D855D714AD3C03C7347996E--

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- --------------2BE859CBD5174A596C5B1627--


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Date: Thu, 20 May 1999 22:27:46 -0500
From: Bob Margolis <[e-mail]>
Subject: (fractint) Some Useful Fractal Links

http://archives.math.utk.edu/topics/fractals.html

Submitted by Bob Margolis.

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Date: Fri, 21 May 1999 11:35:10 +0200
From: "Randall Britten" <[e-mail]>
Subject: RE: (fractint) Fractal Noise

I was reading Martin Gardner's book "Fractal Music, Hypercards and More" and
the chapter on Fractal Music describes 1/f signals in layman's terms quite
nicely.

Having an intuitive understanding of how one can create a 1/f signal, and
where they occur naturally is also worthwhile, so I will try and explain
what I learnt.

To start with, 1/f signals are contrasted with "white noise" and "brown
noise"

White noise is the typical hissing you hear if your radio receiving on a
frequency that no one is transmitting on.
To generate a white noise signal with dice would simply be a matter of
having say 3 dice, and throwing all three and totalling their scores at each
throw.  The possible range would be from 3 to 18, but 3's and 18's would be
rare compared to 10's and 11's, in fact on average the throw would be 10.5.
The popularity of the various scores is a "bell curve"/ normally
distributed.
The sequence is a white noise signal, and example would be 8, 12, 15, 4, 17,
11, etc.
(The sequence can be shifted to be 'symmetrical' about 0 by subtracting 10.5
from each value.)

Brown (for Brownian) noise is obtained by renumbering one dice as
follows -2.5, -1.5, -0.5,  0.5, 1.5, 2.5
Now, start on 0.  To get the next value in the sequence throw the dice and
add it to the previous value.
This is like a "random walk", and the motion of microscopic particles in
solutions is "brownian".

Now, white noise is always totally random, and the signal never "correlates"
with itself.   I.e. take a splice of the signal and compare it with all
other parts of the signal and there is always no correlation, no matter
which splice you start with and which other part you compare it to.  This is
a "power function" which is 1 for a phase shift of 0 (i.e. the signal only
compares to itself exactly), and 0 everywhere else.  Gardner says this is a
1/f^0 signal.  A brown signal is a 1/f^2 signal (I have no idea why), so
midway between them is 1/f noise.

Now, my point was to show how to use dice to generate a 1/f signal, since
knowing that its power function is 1/f doesn't really help intuitively (at
first anyway).

My approach is as follows: similar to the way the dice was numbered for
brown noise, number each of three dice -2.5, -1.5, -0.5,  0.5, 1.5, 2.5
Start with 0.
For each subsequent value of the sequence, throw and total all three dice,
but divide by three and add to the previous value.

It is similar to brown noise.  In both brown and 1/f, the next value depends
on the previous value + some random value.
But in a brown signal, this random value is "uniformly distributed", whereas
in a 1/f signal this random value is "normally distributed" (i.e. bell
curve).

Where do 1/f signals arise naturally?
Almost everywhere in nature, and in real life: the levels of a river, the
price of a stock market share, the density of the traffic etc.

The general rule is anything that that behaves almost randomly, but depends
on its previous state.  The next sample will vary from the previous sample
by some normally distributed random value.  The chances of a smaller
variation from the previous value are higher than the chances of a larger
variation.

Melodic music is 1/f in that the next note differs from the previous note
usually by a small number of tones, but sometimes by a larger difference.
Also the note durations are like a 1/f signal.  Martin argues that we enjoy
melodic music because it is like our everyday experience in life which is
full of 1/f signals.

(Note, the process I have described for generating a 1/f signal is different
from Gardner's simpler version which he states only generates an
approximately 1/f signal.  Also, the white signal process I described could
have been "normalised with the others" by subtracting 10.5 and dividing by
3).

Hope that helps.

- -------------------------
Randall Britten






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Date: Fri, 21 May 1999 13:39:23 +0200
From: Guy Marson <[e-mail]>
Subject: Re: (fractint) Some Useful Fractal Links

At 22:27 20.05.1999 -0500, you wrote:
>http://archives.math.utk.edu/topics/fractals.html
>
>Submitted by Bob Margolis.
>

Thanks Bob, very useful!!!


Guy




Guy Marson
45b, rue de Bettembourg
L-5810 Hesperange
(Luxembourg, Europe)


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Date: Fri, 21 May 1999 09:42:51 -0300
From: "Fliguer, Miguel" <[e-mail]>
Subject: RE: (fractint) Fractint on NT

I got Fractint 19.6 working at SF5 (640x480x256)
on a Vectra VE (Pentium II 300 MHz) under NT 4.0 WS
The video hardware is on the motherboard and
reports itself as Integrated SiS 6205.

SF5 is the best I could get (some people on this list
were amazed I could use a VESA mode under NT)

Good luck
Miguel Fliguer - Buenos Aires, Argentina
Franktal Gallery
http://members.xoom.com/fliguer/franktal.html

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Date: Fri, 21 May 1999 10:29:16 -0400
From: Barry N Merenoff <[e-mail]>
Subject: (fractint) Re: 1/f Noise

Two questions:

In music with a "strong beat," is the frequency of the rhythm an exceptio=
n
to the 1/f scaling?

I don't understand how the algorithm presented for 1/f noise could work.
Can you point me to a proof, or if it's an approximation, can you tell me=

the exact version? (I am not intimidated by math, and I am somewhat
familiar with Fourier Series, Taylor Series, and operators. So don't be
afraid to get technical.)

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End of fractint-digest V1 #390
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