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fractint-digest       Thursday, August 27 1998       Volume 01 : Number 282




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

Date: Thu, 27 Aug 1998 07:41:30 -0400 (EDT)
From: [e-mail] (Kragen)
Subject: Re: (fractint) Spam?

On Wed, 26 Aug 1998, Ray Montgomery wrote:
>     Just read a posting from Damascena.  Maybe humorous, maybe not -
> but ended up as spam.  Am I wrong?

It would have been spam if Damascena had posted it in many places.  But
it was certainly unsolicited advertising, and off-topic.

BTW: search the web for "filk" if you liked those songs, because there
are thousands of others.  They were not written by the ad sponsors.

Kragen

- --
<[e-mail]>       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: Thu, 27 Aug 1998 07:58:54 EDT
From: [e-mail]
Subject: (fractint) another new page

  Here's another page I slapped together last night.  There's a total of 12
images which are some favorites of mine that I have posted in AOL, 2 of which
are 3D types that I couldn't post to the list as a parfile.  The page is very
similiar to the one I made recently, and will be touched up in the near
future, however...all the images can be viewed and downloaded as of now.
Enjoy~
     http://members.aol.com/jweaver285/page1.htm

Jim

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Date: Thu, 27 Aug 1998 16:05:27 +0200
From: "Dean-Christian Strik" <[e-mail]>
Subject: (fractint) Speaking of spam...

Some of us (see below), for some reason got a 'message' which was REAL SPAM.

Does anyone have a clue where it comes from?

Christian

>>>>
To: Angela Wilczynski <[e-mail]>,
        Anibal Valiente <[e-mail]>,
        Barry Bluestein <[e-mail]>,
        Bob Margolis <[e-mail]>, "Damien M. Jones" <[e-mail]>,
        Dean-Christian Strik <[e-mail]>,
        Derek Hasted <[e-mail]>,
        Elaina Tillinghast <[e-mail]>, Eva Jacsch <[e-mail]>,
        Frederik Slijkerman <[e-mail]>,
        Hans Bomers <[e-mail]>, James Weaver <[e-mail]>,
        Kathy Drake <[e-mail]>, Kathy Roth <[e-mail]>,
        Ken Childress <[e-mail]>,
        "Luc-AndrΘ Rey" <[e-mail]>,
        "Morgan L. Owens" <[e-mail]>,
        Sylvie Gallet <[e-mail]>,
        "W. Decker" <[e-mail]>, William Decker <[e-mail]>





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

Date: Thu, 27 Aug 1998 10:10:33 -0400 (EDT)
From: [e-mail] (Kragen)
Subject: Re: (fractint) Speaking of spam...

On Thu, 27 Aug 1998, Dean-Christian Strik wrote:
> Some of us (see below), for some reason got a 'message' which was REAL SPAM.
>
> Does anyone have a clue where it comes from?

No, but I think that if you forward me the full headers, I might have a
better idea.  It's not your run-of-the-mill spamware.

Kragen

- --
<[e-mail]>       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: Thu, 27 Aug 1998 10:30:31 -0400
From: Sylvie Gallet <[e-mail]>
Subject: (fractint) Speaking of spam...

Christian,

>> Some of us (see below), for some reason got a 'message' which was
>> REAL SPAM.
>>
>> Does anyone have a clue where it comes from?

  I haven't got spam for at least 4 days, probably because Compuserve's
filter works fine!

        - Sylvie

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

Date: Thu, 27 Aug 1998 11:54:15 -0500
From: "Damien M. Jones" <[e-mail]>
Subject: (fractint) Re: [fractal-art] Speaking of spam...

Christian,

 - Some of us (see below), for some reason got a 'message' which was REAL
 - SPAM. Does anyone have a clue where it comes from?

Yes, one of the regular posters to alt.binaries.pictures.fractals sent out
a "humor" message, but neglected to use blind carbon copies for the
addresses, thus making all the addresses the message sent to visible.  One
of the recipients then replied to the entire list of people with the bogus
chain-email message.

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

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

Date: Fri, 28 Aug 1998 01:03:43 +0200
From: "Dean-Christian Strik" <[e-mail]>
Subject: Re: (fractint) Speaking of spam...

Sylvie wrote:

>I haven't got spam for at least 4 days, probably because Compuserve's
>filter works fine!


I'm considering pobox (www.pobox.com) (Kragen has that). I believe it's $15 a
year. It gives you at least 3 [e-mail], redirecting to your real
e-mail address; $3/year for additional addresses. One month free trial. It
offers similar filtering. Of course there are also free redirection services
(like bigfoot), but I don't know if they support junkmail filtering.

Christian

PS. Why is your mail always via Blind.Copy.Receiver?






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

Date: Thu, 27 Aug 1998 16:34:17 -0700
From: Ray Montgomery <[e-mail]>
Subject: (fractint) Re: DeCelle address

    Hi, Bob,

    Thanks for the posting.  It prompted me to go back and try again and was
successful.  It must have been a problem with my browser.  Normally, to
find such a problem, I would just look in a mirror to find the cause but
this time I double and triple checked.
    The end of it is that it was a worthwhile visit because I was very
impressed with the images.
    Thanks again.  Wish I was smart enough to understand the contents of the
book you were writing about.  A hundred or so years ago I took an aptitude
test and my rating in the math department went off the page - downward.
Words, on the other hand, went off the page - upward.  So, I guess
everything balances out.  (In its own peculiar way.)

            Regards            Ray


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

Date: Thu, 27 Aug 1998 19:38:54 -0400
From: Sylvie Gallet <[e-mail]>
Subject: (fractint) Re: Speaking of spam...

Damien,

>> Yes, one of the regular posters to alt.binaries.pictures.fractals
>> sent out a "humor" message, but neglected to use blind carbon copies
>> for the addresses, thus making all the addresses the message sent to
>> visible.

  Though my address is in the list, I haven't seen this message.  What wa=
s
it about?

  Cheers,

        - Sylvie

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

Date: Thu, 27 Aug 1998 19:56:05 -0400
From: Sylvie Gallet <[e-mail]>
Subject: Re: (fractint) Speaking of spam...

Christian,

>> PS. Why is your mail always via Blind.Copy.Receiver?

  I don't know!

        - Sylvie

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

Date: Fri, 28 Aug 1998 11:57:51 +1200
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Re: [fractal-art] Speaking of spam...

At 11:54 27/08/98 -0500, you wrote:
>Christian,
>
> - Some of us (see below), for some reason got a 'message' which was REAL
> - SPAM. Does anyone have a clue where it comes from?
>
>Yes, one of the regular posters to alt.binaries.pictures.fractals sent out
>a "humor" message, but neglected to use blind carbon copies for the
>addresses, thus making all the addresses the message sent to visible.  One
>of the recipients then replied to the entire list of people with the bogus
>chain-email message.
>
My standard reaction to this kind of chain-email message is to inform the
Federal Trade Commission and the United States Postal Inspection Service
(and if claims of an inflated income are involved, the Inland Revenue
Service).

Morgan L. "Havoc" Owens


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

Date: Thu, 27 Aug 1998 20:05:03 -0700
From: Mark Christenson <[e-mail]>
Subject: Re: (fractint) Formula inclusion

At 05:10 PM 8/26/98 +1200, Morgan L. Owens wrote:

(regarding function calls / subroutines )

>The main disadvantage would basically be that it would make the language
>more complex (especially since adding more extensive flow control support
>would not be too far down the line then) and difficult to learn. But it
>might be argued (mightn't it?) that the formula language's "flat" structure
>is starting to become a drawback?

Definitely!  In addition to making code easier to re-use, subroutines would
also make code easier to read.  Folks could easily plug different coloring
methods into their formulae, and, if more user controlled variables (or a way
for the "x" screen to be made aware of embedded coloring methods) were
made available, even change them "on the fly."  It would also address
the needs of people with a primary interest, be it the basic mathematics,
or the coloring method, or whatever.

I wouldn't be averse to the #include construct.


Bud


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

Date: Thu, 27 Aug 1998 21:24:36 -0700
From: "Angela Wilczynski" <[e-mail]>
Subject: Re: (fractint) AGP video cards & 1600x1200

Sylvie...

I have the Millennium II (8 megs).....I'm fairly sure it has AGP....and
1600 x 1200 works just fine.

'Angela

Sylvie Gallet wrote:
>
> Hi All,
>
>   I'm about to get a new system with either the ATI AGP Xpert Work (8 megs)
> or the Millennium II AGP (8 megs): has anyone been able to use Fractint at
> 1600x1200 with one of these cards?
>
>   Cheers,
>
>         - Sylvie
>
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------------------------------

Date: Thu, 27 Aug 1998 21:32:21 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: (fractint) New coloring schemes

Just a heads up--the next 3 messages from me are 3 different coloring
schemes.  They're all based on the same idea--watching the orbit for its
closest approach to 2 curves.  The 3 cases are:  2 circles, 2 lines, and 1
circle/1 line.  The narratives will all read the same, but they really are
slightly different.  And, if you don't care about any of this, you now
know that you can skip those posts are go on living a happy life!

- -------------------------------------------------------------------------------
Kerry Mitchell
[e-mail]
- -------------------------------------------------------------------------------


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Date: Thu, 27 Aug 1998 21:33:23 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: (fractint) "2 circles" coloring scheme

comment { ; narrative copyright Kerry Mitchell 26aug98

2 Circles Coloring Method

Several coloring schemes have been put together that color according
to the orbit's nearest approach to a specified point or curve.  This
method extends that idea by coloring according to the orbit's nearest
simultaneous approach to 2 specified circles.

A circle in the x-y plane can be specified by (x - xcenter)^2 +
(y - ycenter)^2 = radius^2, where (xcenter, ycenter) is the coordinate
of the center of the circle, and radius is the circle's radius.  For
complex numbers z = x+i*y, (and center = xcenter+i*ycenter)

f(z) = |z - center| - radius^2 (using Fractint's || convention)

is a real-valued function that gives the relationship of z to the
circle.  If f(z) < 0, then z is inside the circle.  A positive
value of f(z) means that z is outside of the circle, and f=0 means
that z is on the circle.

Using 2 circles then results in 2 functions, fx(z) and fy(z).  One
circle corresponds to fx, and the other to fy.  At each iteration,
a new complex variable, w, can be defined as, w = fx(z)+i*fy(z).
To check for the closest simultaneous approach of the orbit to both
circles, it is sufficient to check for the smallest |w|.  This w is
saved, and at the end of the iteration, "decomp=256" is used to color
the pixel according to the polar angle of w.

In its most general form, this method requires 6 real parameters:
2 each for the x- and y-coordinates of the centers of the circles,
and 2 for the radii of the 2 circles.  For Mandelbrot implementation,
this requires hardcoding the bailout value, which has been set to
10^12.  For Julia implementations, the bailout is also hardcoded, but
another 2 parameters are needed to specify the Julia parameter, c.
The "general_jul" formula is written with a hardcoded value of c, to
allow for the greatest flexibility in choosing circles.

A great deal of choice can still be allowed by only using 4 parameters
to choose the circles, thereby freeing the other 2 for picking c.
The "cenx=ceny_jul" method uses concentric circles (both having the
same center).  The radii of the circles are independently chosen.
A variation of this is the "cenx=-ceny_jul" formula, wherein the
centers of the circles are placed symmetrically with respect to the
origin of the complex plane.  Another variation uses the same radii
for both circles, but different centers.  In "offset_rx=ry_jul",
this is accomplished by choosing a point on the plane.  One circle
is place a little outward of this point, and the other is a little
inward of the chosen point.  The amount of shift along the radial
line is 1 of the parameters.

Because of the wide variety of parameter settings, it's not possible
to say what happens with the image as the circles are moved.  However,
you'll get very different results if the circles don't intersect from
when they do.  If they do intersect, you'll tend to see points in the
image where all the colors come together (this corresponds to where
the orbit found the intersection point).  Varied ribbon-like effects
can be seen when the circles are very close to each other--either
concentric with slightly different radii, or offset by a small amount.

}

general_man { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "2 general circles" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm
  formulaname=general_man passes=1 center-mag=-0.7/0/0.6\
  /1/-90 params=-2/0/-2/0/1.95/2.05 float=y maxiter=256
  inside=0 decomp=256 colors=zwj<2>zyvzzzxxz<13>SSzPPzOO\
  w<14>000<15>zo0<14>zywzzzxxz<13>RRzPPzOOv<11>55B337223\
  110<13>tj0xm0zo1<13>zxtzyxyyz<12>VVzTTzRRzPPyNNu<12>33\
  6112220<14>yn0zo2<14>zyyyyz<13>SSzQQzOOx<14>111000<15>\
  zo0<10>zvf cyclerange=0/255 periodicity=0
  }

general_jul { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "2 general circles" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm
  formulaname=general_jul passes=1 center-mag=0/0/0.6666667
  params=-2/0/0/2/1.414/1.414 float=y maxiter=256 inside=0
  decomp=256 periodicity=0 colors=540<27>xm0zo0zo1<29>zyxz\
  zzyyz<29>RRzPPzPPy<30>000<30>yn0zo0zo2<29>zyyzzzyyz<29>Q\
  QzPPzOOx<29>111000110330 cyclerange=0/255
  }

concentric { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "2 concentric circles" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm
  periodicity=0 formulaname=cenx=ceny_jul passes=1 center\
  -mag=0/0/0.8 params=0/1/0/0/0.98/1.02 float=y maxiter=256
  inside=0 decomp=256 colors=cX0<21>yn0zo0zo0zo1<61>zzzzzz\
  yyz<60>QQzPPzPPzPPy<61>000000110<37>bW0 cyclerange=0/255
  }

opposing { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "2 opposing circles" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm
  formulaname=cenx=-ceny_jul passes=1 center-mag=0/0/0.8
  params=-0.779702280199264/0.1503397589375293/0/1/1/1
  float=y maxiter=256 inside=0 decomp=256 periodicity=0
  cyclerange=0/255 colors=000<15>zo0<14>zyvzzzxxz<13>SSzP\
  PzOOw<14>000<15>zo0<14>zywzzzxxz<13>RRzPPzOOv<11>55B337\
  223110<13>tj0xm0zo1<13>zxtzyxyyz<12>VVzTTzRRzPPyNNu<12>\
  336112220<14>yn0zo2<14>zyyyyz<13>SSzQQzOOx<14>111
  }

offset { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "2 offset circles" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm
  periodicity=0 formulaname=offset_rx=ry_jul center-mag=0\
  /0/0.6666667 params=0.39/0.44/1/0/1/0.1 float=y maxiter=256
  inside=0 decomp=256 colors=xm0zo0<30>zyxzzzyyz<29>RRzPPzP\
  Py<30>000<30>yn0zo0zo2<29>zyyzzzyyz<29>QQzPPzOOx<29>11100\
  0110<28>vk0 cyclerange=0/255 passes=1
  }

frm:general_man { ; Kerry Mitchell 26aug98
    ;
    ; "2 general circles" coloring method for Mandelbrot
    ; c = pixel = Mandelbrot parameter
        ; p1 = x-circle center
        ; p2 = y-circle center
        ; real(p3) = x-circle radius
        ; imag(p3) = y-circle radius
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        c=pixel, zc=0, bailout=1e12, iter=1, rmin=1e12
        cenx=p1, radx=real(p3), rad2x=radx*radx
        ceny=p2, rady=imag(p3), rad2y=rady*rady:
        iter=iter+1, zc=sqr(zc)+c
        tempx=|zc-cenx|-rad2x
        tempy=|zc-ceny|-rad2y
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }

frm:general_jul { ; Kerry Mitchell 26aug98
    ;
    ; "2 general circles" coloring method for Julia sets
    ; c = Julia parameter, hardcoded
        ; p1 = x-circle center
        ; p2 = y-circle center
        ; real(p3) = x-circle radius
        ; imag(p3) = y-circle radius
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=(0.39,0.44), bailout=1e12, iter=1, rmin=1e12
        cenx=p1, radx=real(p3), rad2x=radx*radx
        ceny=p2, rady=imag(p3), rad2y=rady*rady:
        iter=iter+1, zc=sqr(zc)+c
        tempx=|zc-cenx|-rad2x
        tempy=|zc-ceny|-rad2y
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }

frm:cenx=ceny_jul { ; Kerry Mitchell 26aug98
    ;
    ; "2 concentric circles" coloring method for Julia sets
    ; p1 = c = Julia parameter
    ; p2 = (both) circle center
        ; real(p3) = x-circle radius
        ; imag(p3) = y-circle radius
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=p1, bailout=1e12, iter=1, rmin=1e12
        cenx=p2, radx=real(p3), rad2x=radx*radx
        ceny=cenx, rady=imag(p3), rad2y=rady*rady:
        iter=iter+1, zc=sqr(zc)+c
        tempx=|zc-cenx|-rad2x
        tempy=|zc-ceny|-rad2y
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }

frm:cenx=-ceny_jul { ; Kerry Mitchell 26aug98
    ;
    ; "2 opposing circles" coloring method for Julia sets
    ; p1 = c = Julia parameter
        ; p2 = x-circle center
        ; -p2 = y-circle center
        ; real(p3) = x-circle radius
        ; imag(p3) = y-circle radius
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=p1, bailout=1e12, iter=1, rmin=1e12
        cenx=p2, radx=real(p3), rad2x=radx*radx
        ceny=-cenx, rady=imag(p3), rad2y=rady*rady:
        iter=iter+1, zc=sqr(zc)+c
        tempx=|zc-cenx|-rad2x
        tempy=|zc-ceny|-rad2y
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }

frm:offset_rx=ry_jul { ; Kerry Mitchell 26aug98
    ;
    ; "2 offset circles" coloring method for Julia sets
    ; p1 = c = Julia parameter
    ; p2 = approximate circle center
    ; real(p3) = (both) circle radius
    ; imag(p3) = center offsets--added to p2 for
    ;   centerx, subtracted from p2 for centery
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=p1, bailout=1e12, iter=1, rmin=1e12
        cenx=p2*(1+imag(p3)), radx=real(p3), rad2x=radx*radx
        ceny=p2*(1-imag(p3)), rad2y=rad2x:
        iter=iter+1, zc=sqr(zc)+c
        tempx=|zc-cenx|-rad2x
        tempy=|zc-ceny|-rad2y
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }



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Date: Thu, 27 Aug 1998 21:33:57 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: (fractint) "2 lines" coloring method

comment { ; narrative copyright Kerry Mitchell 26aug98

2 Lines Coloring Method

Several coloring schemes have been put together that color according
to the orbit's nearest approach to a specified point or curve.  This
method extends that idea by coloring according to the orbit's nearest
simultaneous approach to 2 specified lines.

A line in the x-y plane can be specified by the standard form: a*x +
b*y + c = 0, where the slope of the line = -a/b (when b=0, the line is
vertical).  For complex numbers z = x+i*y, then function

f(z) = a*real(z) + b*imag(z) + c

is a real-valued function that gives the relationship of z to the
line.  If f(z) < 0, then z is on one side of the line, and if f(z) > 0,
z is on the other side.  If f=0, then z is on the line.

Using 2 lines then results in 2 functions, fx(z) and fy(z).  One line
corresponds to fx, and the other to fy.  At each iteration, a new complex
variable, w, can be defined as, w = fx(z)+i*fy(z).  To check for the
closest simultaneous approach of the orbit to both lines, it is
sufficient to check for the smallest |w|.  This w is saved, and at the
end of the iteration, "decomp=256" is used to color the pixel according
to the polar angle of w.

In its most general form, this method requires 6 real parameters:
3 (a, b, c) for each line.  For Mandelbrot implementation, this requires
hardcoding the bailout value, which has been set to 10^12.  For Julia
implementations, the bailout is also hardcoded, but another 2 parameters
are needed to specify the Julia parameter, c.  The "general_jul" formula
is written with a hardcoded value of c, to allow for the greatest
flexibility in choosing lines.

A great deal of choice can still be allowed by only using 4 parameters
to choose the lines, thereby freeing the other 2 for picking c.
The "parallel_jul" method uses parallel lines.  A variation of this is
the "orthogonal_jul" formula, wherein the lines meet at right angles.
Another variation uses the opposite slopes for the 2 lines.  For example,
if one line forms a 30 degree angle with the real axis, then the other
line would make a -30 degree angle.

Because of the wide variety of parameter settings, it's not possible
to say what happens with the image as the lines are moved.  However,
you'll get very different results if the lines don't intersect from
when they do.  If they do intersect, you'll tend to see points in the
image where all the colors come together (this corresponds to where
the orbit found the intersection point).  Varied ribbon-like effects
can be seen when the lines are very close to each other--either
parallel with a small gap between them, or with slightly different slopes.

}

general_man { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "2 general lines" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm periodicity=0
  formulaname=general_man passes=1 center-mag=-0.73/0/0.74/1/-90
  params=1/0/0.75/0/1/0 float=y maxiter=256 inside=0 decomp=256
  colors=000<30>x0mz0oz1o<29>zxyzzzyzy<29>RzRPzPPyP<30>000<30>\
  y0nz0oz2o<29>zyyzzzyzy<29>QzQPzPOxO<29>111 cyclerange=0/255
  }

general_jul { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "2 general lines" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm periodicity=0
  formulaname=general_jul passes=1 center-mag=0/0/0.75/1/-12.5
  params=1/0/2/0/1/1.5 float=y maxiter=2000 inside=0 decomp=256
  colors=DVD<14>111000101<29>x0mz0oz1o<29>zxyzzzyzy<29>RzRPzPP\
  yP<30>000<30>y0nz0oz2o<29>zyyzzzyzy<29>QzQPzPOxO<13>DXD
  }

parallel { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "2 parallel lines" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm decomp=256
  periodicity=0 formulaname=parallel_jul passes=1 center-mag\
  =0/0/0.8/1/-7.5 params=0.39/0.44/2.64/-1/0.1/-0.1 float=y
  maxiter=256 inside=0 colors=c0X<10>y0nz0oz2o<29>zyyzzzyzy\
  <29>QzQPzPOxO<29>111000101<29>x0mz0oz1o<29>zxyzzzyzy<29>R\
  zRPzPPyP<30>000<18>a0V cyclerange=0/255
  }

orthogonal { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "2 orthogonal lines" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm
  formulaname=orthogonal_jul passes=1 center-mag=0/0/0.8
  params=-0.779702280199264/0.1503397589375293/1/2/1/2 float=y
  maxiter=256 inside=0 decomp=256 periodicity=0 colors=HeH<20>\
  000<30>y0nz0oz2o<29>zyyzzzyzy<29>QzQPzPOxO<29>111000101<29\
  >x0mz0oz1o<29>zxyzzzyzy<29>RzRPzPPyP<8>IgI cyclerange=0/255
  }

opposite { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "2 lines with opposite angles" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm cyclerange=0/255
  formulaname=oppangle_jul passes=1 center-mag=0/0/0.6666667
  params=-0.0573720519293145/0.6691939992424446/3/1/0/0 float=y
  maxiter=2000 inside=0 decomp=256 periodicity=0 colors=`z`<18>\
  QzQPzPPzPPyP<61>000000101<60>y0nz0oz0oz1o<61>zzzzzzyzy<40>aza
  }

frm:general_man {
    ;
        ; "2 general lines" coloring method for Mandelbrot
    ; c = pixel = Mandelbrot parameter
        ; real(p1) = x-line a
        ; imag(p1) = x-line b
        ; real(p2) = x-line c
        ; imag(p2) = y-line a
        ; real(p3) = y-line b
        ; imag(p3) = y-line c
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        c=pixel, zc=0, bailout=1e12, iter=1, rmin=1e12
        ax=real(p1), bx=imag(p1), cx=real(p2)
        ay=imag(p2), by=real(p3), cy=imag(p3):
        iter=iter+1, zc=sqr(zc)+c
        x=real(zc), y=imag(zc)
        tempx=ax*x+bx*y+cx
        tempy=ay*x+by*y+cy
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }

frm:general_jul {
    ;
        ; "2 general lines" coloring method for Julia sets
        ; c = Julia parameter, hardcoded
        ; real(p1) = x-line a
        ; imag(p1) = x-line b
        ; real(p2) = x-line c
        ; imag(p2) = y-line a
        ; real(p3) = y-line b
        ; imag(p3) = y-line c
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=(.26,.0014), bailout=1e12, iter=1, rmin=1e12
        ax=real(p1), bx=imag(p1), cx=real(p2)
        ay=imag(p2), by=real(p3), cy=imag(p3):
        iter=iter+1, zc=sqr(zc)+c
        x=real(zc), y=imag(zc)
        tempx=ax*x+bx*y+cx
        tempy=ay*x+by*y+cy
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }

frm:parallel_jul {
    ;
        ; "2 parallel lines" coloring method for Julia sets
        ; p1 = c = Julia parameter
        ; real(p2) = x-line a = y-line a
        ; imag(p2) = x-line b = y-line b
        ; real(p3) = x-line c
        ; imag(p3) = y-line c
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=p1, bailout=1e12, iter=1, rmin=1e12
        ax=real(p2), bx=imag(p2), cx=real(p3)
        ay=ax, by=bx, cy=imag(p3):
        iter=iter+1, zc=sqr(zc)+c
        x=real(zc), y=imag(zc)
        tempx=ax*x+bx*y+cx
        tempy=ay*x+by*y+cy
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }

frm:orthogonal_jul {
    ;
        ; "2 orthogonal lines" coloring method for Julia sets
        ; p1 = c = Julia parameter
        ; real(p2) = x-line a = negative of y-line b
        ; imag(p2) = x-line b = negative of y-line a
        ; real(p3) = x-line c
        ; imag(p3) = y-line c
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=p1, bailout=1e12, iter=1, rmin=1e12
        ax=real(p2), bx=imag(p2), cx=real(p3)
        ay=bx, by=-ax, cy=imag(p3):
        iter=iter+1, zc=sqr(zc)+c
        x=real(zc), y=imag(zc)
        tempx=ax*x+bx*y+cx
        tempy=ay*x+by*y+cy
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }

frm:oppangle_jul {
    ;
        ; "2 opposing lines" coloring method for Julia sets
        ; p1 = c = Julia parameter
        ; real(p2) = x-line a = y-line a
        ; imag(p2) = x-line b = negative of y-line b
        ; real(p3) = x-line c
        ; imag(p3) = y-line c
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=p1, bailout=1e12, iter=1, rmin=1e12
        ax=real(p2), bx=imag(p2), cx=real(p3)
        ay=ax, by=-bx, cy=imag(p3):
        iter=iter+1, zc=sqr(zc)+c
        x=real(zc), y=imag(zc)
        tempx=ax*x+bx*y+cx
        tempy=ay*x+by*y+cy
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }



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

Date: Thu, 27 Aug 1998 21:34:47 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: (fractint) "circle & line" coloring method

comment { ; narrative copyright Kerry Mitchell 26aug98

Circle & Line Coloring Method

Several coloring schemes have been put together that color according
to the orbit's nearest approach to a specified point or curve.  This
method extends that idea by coloring according to the orbit's nearest
simultaneous approach to a circle and a line.

A circle in the x-y plane can be specified by (x - xcenter)^2 +
(y - ycenter)^2 = radius^2, where (xcenter, ycenter) is the coordinate
of the center of the circle, and radius is the circle's radius.  For
complex numbers z = x+i*y, (and center = xcenter+i*ycenter)

f(z) = |z - center| - radius^2 (using Fractint's || convention)

is a real-valued function that gives the relationship of z to the
circle.  If f(z) < 0, then z is inside the circle.  A positive
value of f(z) means that z is outside of the circle, and f=0 means
that z is on the circle.

A line in the x-y plane can be specified by the standard form: a*x +
b*y + c = 0, where the slope of the line = -a/b (when b=0, the line is
vertical).  For complex numbers z = x+i*y, then function

f(z) = a*real(z) + b*imag(z) + c

is a real-valued function that gives the relationship of z to the
line.  If f(z) < 0, then z is on one side of the line, and if f(z) > 0,
z is on the other side.  If f=0, then z is on the line.

Using both a circle and a line then results in 2 functions, fx(z) and
fy(z).  The circle corresponds to fx, and the line to fy.  At each
iteration, a new complex variable, w, can be defined as, w = fx(z) +
i*fy(z).  To check for the closest simultaneous approach of the orbit
to both curves, it is sufficient to check for the smallest |w|.  This
w is saved, and at the end of the iteration, "decomp=256" is used to
color the pixel according to the polar angle of w.

In its most general form, this method requires 6 real parameters:
2 for the x- and y-coordinates of the center of the circles and 1 for
its radius, and 3 (a, b, c) for the line.  For Mandelbrot implementation,
this requires hardcoding the bailout value, which has been set to
10^12.  For Julia implementations, the bailout is also hardcoded, but
another 2 parameters are needed to specify the Julia parameter, c.
The "general_jul" formula is written with a hardcoded value of c, to
allow for the greatest flexibility in choosing the circle and line.

A great deal of choice can still be allowed by only using 4 parameters
to choose the curves, thereby freeing the other 2 for picking c.
The "center_jul" formula uses a diametric line through the center of
the circle.  The radius of the circle and the slope of the line are
independently chosen.  A variation of this is the "tangent_jul"
formula, wherein the line is tangent to the circle.  The point of
tangency is at a specified angle on the circle.  Another variation is
the "offset_jul" formula.  This is similar to the tangent formula, but
the line is offset from the circle by the amount of the radius.

Because of the wide variety of parameter settings, it's not possible
to say what happens with the image as the curves are moved.  However,
you'll get very different results if they don't intersect from when
they do.  If they do intersect, you'll tend to see points in the
image where all the colors come together (this corresponds to where
the orbit found the intersection point).

}

general_man-1 { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "general circle & line" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm
  formulaname=general_man passes=1 center-mag=-0.3/0/0.7
  params=1/1/2/0/1/1 float=y maxiter=256 inside=0
  decomp=256 colors=000<61>y99zAAzAAzBB<61>zzzzzzzyz<60>\
  i1ih0hh0hg0g<61>000 cyclerange=0/255 periodicity=0
  }

general_man-2 { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "general circle & line" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm
  periodicity=0 formulaname=general_man center-mag=-0.6\
  66667/0/0.7/1/-90 params=-1/0/0.25/0/1/0 float=y
  maxiter=256 inside=0 decomp=256 colors=000<30>y99zAAz\
  CC<30>zzz<30>i1ih0hf0f<28>303101100<29>x99zAAzBB<30\
  >zzz<30>i2ih0hg0g<30>000 cyclerange=0/255 passes=1
  }

general_jul { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "general circle & line" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm
  formulaname=general_jul passes=1 center-mag=0/0/0.75/1/5
  periodicity=0 params=-2/0/3/1/0/4 float=y maxiter=256
  inside=0 decomp=256 colors=f0f<28>202000000<30>y99zAAzCC\
  <30>zzz<30>i1ih0hf0f<28>303101100<29>x99zAAzBB<30>zzz<30>\
  i2ih0hg0g cyclerange=0/255
  }

center { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "circle & diameter line" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm
  formulaname=center_jul passes=1 center-mag=0/0/0.813\
  /1/-7.5 params=0.39/0.44/0.39/0.44/0.45/53.9125 float=y
  maxiter=256 inside=0 decomp=256 periodicity=0 cyclerange=0/255
  colors=000<61>y99zAAzAAzBB<61>zzzzzzzyz<60>i1ih0hh0hg0g<61>000
  }

tangent { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "circle & tangent line" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm
  periodicity=0 formulaname=tangent_jul passes=1 center-\
  mag=0/0/1/1/90 params=0.26/0/0/0/0.2/45 float=y maxiter=1000
  inside=0 decomp=256 colors=U0U<9>202200<14>y99<15>zyyzxz<13>\
  j5ji1if0f<14>101300<14>zAA<15>zzz<15>h0h<14>303000000<15>zAA\
  <15>zzz<14>i3ih0he0e<11>808505303100<13>t99x99zBB<13>zuuzxxz\
  yz<13>j6ji2ig0g<3>X0X cyclerange=0/255
  }

offset { ; copyright Kerry Mitchell 26aug98
  ;
  ; sample for "circle & offset line" coloring method
  ;
  reset=1960 type=formula formulafile=fractint.frm
  formulaname=offset_jul passes=1 center-mag=0/0/0.8
  params=-0.778/0.201/-2/0/1/90 float=y maxiter=256
  inside=0 decomp=256 periodicity=0 colors=303000000<15>\
  zAA<15>zzz<14>i3ih0he0e<11>808505303100<13>t99x99zBB\
  <13>zuuzxxzyz<13>j6ji2ig0g<14>202200<14>y99<15>zyyzxz\
  <13>j5ji1if0f<14>101300<14>zAA<15>zzz<15>h0h<13>606
  }

frm:general_man {
    ;
        ; "general circle & line" coloring method for Mandelbrot
    ; c = pixel = Mandelbrot parameter
        ; p1 = x-circle center
        ; real(p2) = x-circle radius
        ; imag(p2) = y-line a
        ; real(p3) = y-line b
        ; imag(p3) = y-line c
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        c=pixel, zc=0, bailout=1e12, iter=1, rmin=1e12
        cenx=p1, radx=real(p2), rad2x=radx*radx
        ay=imag(p2), by=real(p3), cy=imag(p3):
        iter=iter+1, zc=sqr(zc)+c
        tempx=|zc-cenx|-rad2x
        tempy=ay*real(zc)+by*imag(zc)+cy
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }

frm:general_jul {
    ;
        ; "general circle & line" coloring method for Julia sets
        ; c = Julia parameter, hardcoded
        ; p1 = x-circle center
        ; real(p2) = x-circle radius
        ; imag(p2) = y-line a
        ; real(p3) = y-line b
        ; imag(p3) = y-line c
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=(0,1), bailout=1e12, iter=1, rmin=1e12
        cenx=p1, radx=real(p2), rad2x=radx*radx
        ay=imag(p2), by=real(p3), cy=imag(p3):
        iter=iter+1, zc=sqr(zc)+c
        tempx=|zc-cenx|-rad2x
        tempy=ay*real(zc)+by*imag(zc)+cy
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }

frm:center_jul {
    ;
        ; "circle & line thru center" coloring method for Julia sets
        ; p1 = c = Julia parameter
        ; p2 = x-circle center
        ; real(p3) = x-circle radius
        ; imag(p3) = y-line slope angle, degrees
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=p1, bailout=1e12, iter=1, rmin=1e12
        cenx=p2, radx=real(p3), rad2x=radx*radx
        theta=imag(p3)*pi/180, ct=cos(theta), st=sin(theta)
        ay=-st, by=ct, cy=-ct*imag(cenx)+st*real(cenx):
        iter=iter+1, zc=sqr(zc)+c
        tempx=|zc-cenx|-rad2x
        tempy=ay*real(zc)+by*imag(zc)+cy
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }

frm:tangent_jul {
    ;
        ; "circle & tangent line" coloring method for Julia sets
        ; p1 = c = Julia parameter
        ; p2 = x-circle center
        ; real(p3) = x-circle radius
        ; imag(p3) = angle of line from circle center to tangent
        ;    point of y-line, degrees
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=p1, bailout=1e12, iter=1, rmin=1e12
        cenx=p2, radx=real(p3), rad=radx, rad2x=|radx|
        theta=imag(p3)*pi/180, ct=cos(theta), st=sin(theta)
        xt=real(cenx)+rad*ct, yt=imag(cenx)+rad*st
        phi=theta+pi/2, cp=cos(phi), sp=sin(phi)
        ay=sp, by=-cp, cy=cp*yt-sp*xt:
        iter=iter+1, zc=sqr(zc)+c
        tempx=|zc-cenx|-rad2x
        tempy=ay*real(zc)+by*imag(zc)+cy
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }

frm:offset_jul {
    ;
        ; "circle & offset line" coloring method for Julia sets
        ; p1 = c = Julia parameter
        ; p2 = x-circle center
        ; real(p3) = x-circle radius
        ; imag(p3) = angle of line from circle center to tangent
        ;    point, degrees.  y-line is parallel to tangent line
        ;    and offset by amount of radius.
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=p1, bailout=1e12, iter=1, rmin=1e12
        cenx=p2, radx=real(p3), rad=2*radx, rad2x=|radx|
        theta=imag(p3)*pi/180, ct=cos(theta), st=sin(theta)
        xt=real(cenx)+rad*ct, yt=imag(cenx)+rad*st
        phi=theta+pi/2, cp=cos(phi), sp=sin(phi)
        ay=sp, by=-cp, cy=cp*yt-sp*xt:
        iter=iter+1, zc=sqr(zc)+c
        tempx=|zc-cenx|-rad2x
        tempy=ay*real(zc)+by*imag(zc)+cy
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }



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

End of fractint-digest V1 #282
******************************