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From: owner-fractint-digest@lists.xmission.com (fractint-digest)
To: fractint-digest@lists.xmission.com
Subject: fractint-digest V1 #313
Reply-To: fractint-digest
Sender: owner-fractint-digest@lists.xmission.com
Errors-To: owner-fractint-digest@lists.xmission.com
Precedence: bulk
fractint-digest Sunday, October 11 1998 Volume 01 : Number 313
----------------------------------------------------------------------
Date: Sat, 10 Oct 1998 19:05:28 -0400
From: Sylvie Gallet <Sylvie_Gallet@compuserve.com>
Subject: (fractint) simplgif
Hi Tim,
>> This is a very important point. We completely redid both the GIF readi=
ng
>> and writing of Simplgif. I believe the one at my FTP site is the new
>> one. It is at
>>
>> ftp://ftp.phoenix.net/pub/USERS/twegner/simplgif.zip
>>
>> I really want to know if this version has any bugs. I haven't heard of=
>> any bad cases with the new simplgif.
I tried again with the Simplgif that is at your ftp site and found two
images that show the bug. Both were made of 4x4 1024x768 pieces and in
both cases, the first line of the resulting simplgif.gif is incorrect. =
Would you like me to put them on a CD ROM for you?
Cheers,
- Sylvie
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------------------------------
Date: Sat, 10 Oct 1998 17:59:02 -0500
From: "Peter Marsden" <marsdenp@ix.netcom.com>
Subject: (fractint) I'm missing some .frm's
This is a multi-part message in MIME format.
- ------=_NextPart_000_0009_01BDF477.A9F60480
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
I've been going through Les's monthly collections of pars & religiously =
updating my frm folder when necessary, but I have found that I am =
missing the following .frm's. Could anyone help me locate them, please ?
Year & Month .FRM Name=20
97_08 GALLET-8-04=20
98_01 3dstalks-julia=20
98_06 Ormandel12=20
98_07 T04-08=20
98_07 U02-14=20
98_08 colorit-3f=20
98_08 CARR1999=20
=20
Also, for some reason which I cannot understand, I cannot get the =
following fractals to plot, the correct .frm's are in my directory & the =
.par file entries do point to them. Has anyone else had this problem ?
Year & Month Image Name=20
98_08 Feather=20
97_09 TendrilP=20
=20
The work all the fractal producers is doing is absolutely splendid. =
Wish I had the time to join you.
Regards,
=20
Peter
=20
- ------=_NextPart_000_0009_01BDF477.A9F60480
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
<!DOCTYPE HTML PUBLIC "-//W3C//DTD W3 HTML//EN">
<HTML>
<HEAD>
<META content=3Dtext/html;charset=3Diso-8859-1 =
http-equiv=3DContent-Type>
<META content=3D'"MSHTML 4.71.1712.3"' name=3DGENERATOR>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV>
<P>I've been going through Les's monthly collections of pars & =
religiously=20
updating my frm folder when necessary, but I have found that I am =
missing the=20
following .frm's. Could anyone help me locate them, please ?</P>
<DIV align=3Dcenter>
<CENTER>
<TABLE border=3D2>
<TBODY>
<TR>
<TD>Year & Month</TD>
<TD>.FRM Name</TD></TR>
<TR>
<TD>97_08</TD>
<TD>GALLET-8-04</TD></TR>
<TR>
<TD>98_01</TD>
<TD>3dstalks-julia</TD></TR>
<TR>
<TD>98_06</TD>
<TD>Ormandel12</TD></TR>
<TR>
<TD>98_07</TD>
<TD>T04-08</TD></TR>
<TR>
<TD>98_07</TD>
<TD>U02-14</TD></TR>
<TR>
<TD>98_08</TD>
<TD>colorit-3f</TD></TR>
<TR>
<TD>98_08</TD>
<TD>CARR1999</TD></TR></TBODY></TABLE></CENTER></DIV>
<P>Also, for some reason which I cannot understand, I cannot get the =
following=20
fractals to plot, the correct .frm's are in my directory & the .par =
file=20
entries do point to them. Has anyone else had this problem ?</P>
<DIV align=3Dcenter>
<CENTER>
<TABLE border=3D2>
<TBODY>
<TR>
<TD>Year & Month</TD>
<TD>Image Name</TD></TR>
<TR>
<TD>98_08</TD>
<TD>Feather</TD></TR>
<TR>
<TD>97_09</TD>
<TD>TendrilP</TD></TR></TBODY></TABLE></CENTER></DIV>
<P>The work all the fractal producers is doing is absolutely splendid. =
Wish I=20
had the time to join you.</P>
<BLOCKQUOTE>
<P>Regards,</P>
<BLOCKQUOTE>
<BLOCKQUOTE>
=
<P>Peter</P></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></DIV></BODY></HTML>
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------------------------------
Date: Sat, 10 Oct 1998 19:23:27 -0400
From: "Peter Gavin" <pgavin@mindspring.com>
Subject: RE: (fractint) RE: [fractal-art] Immersive-visualization Solutions
//
// I must say I've never seen a file archiver that does have
// such a good ratio as
// RAR, but 10:1 surely isn't representative. It does little
// better that arj,
// zip, jar, and a lot better than zoo, lzh etc, but that's all.
// IF you're not compressing weakly-compressable binaries (exes
// and such). RAR
// can then even enlarge the file. It is annoying that this
// cannot(?) be turned
// off.
You're right, it isn't representative, but with RAR's Multimedia setting, it
works about twice as well as normal (i.e. avg. 4:1 vs. 2:1). RAR probably
enlarges the file because it has a very large header, but I'm not sure.
// Also, RAR doesn't have as many options as ARJ has. But ok,
// who *uses* all ARJ
// options? Although the more advanced, the nicer :-)
//
// The DOS version of RAR is also user-friendly. It of course
// works in command
// line mode, but also in a text-based full-screen interface.
// NOTE: the command
// line version of RAR delivered with WinRAR does *not* support
// the dos screen
// interface.
//
// Also, RAR is terribly slow with it's solid archive
// implementation. I have RAR
// files of over a 100 MBs, which take one or two eternities to
// be read, both by
// the dos and windows versions. The dos version further
// rereads the archive
// completely when you enter an archive's subdir from the
// screen interface. This
// could take up to 15mins! The windows version stores the
// archive info a bit
// better in memory; the archive is not to be completely reread
// after browsing
// through intra-archival directories. And here we are only
// browsing through the
// archive, not even doing anything useful like extracting or so.
// And there's a thing you should NEVER do with rar files:
// delete a file from the
// archive. This takes an eternity cause rar has a ridiculous
// method of keeping
// the archive real solid.
When RAR creates a solid archive, it treates all the files as a single file,
rather than restarting the compression (i.e. recreating the dictionary,
etc.) for each file. I compressed the set of PNG files (which already have
good compression ratios) for that animation, and got *2:1* compression on
them, even though their already compressed!
//
// Then, well, it *has* to be a coincidence (I hope!), but
// after burning a cd
// containing a rar, the rar archives again and again have crc
// errors. We (me and
// two fellow list-members) have this all the time with rar
// archives, and never
// with zips, arjs, etc.
//
I'm not sure about this, you may want to email the author.
// >> Not only that, but an archive created
// >> with the most efficient compression can't be converted
// into a dos EXE (only
//
// >> Win32 & os2).
//
// Yeah.. with the win/os2 versions! The real dos version of
// rar DOES support dos
// SFXs!
//
Well, I haven't used the real dos version, but I may have to. With the
version included with WinRAR, you can't create an SFX out of a RAR created
using a 1024K dictionary, unfortunately. All the files give you CRC errors
when decompressed.
// >> So, either you need to get the RAR program for dos (and
// >> extract it the way you would any other archive), or
// download the 2 megabyte
// >> zip file that I'm going to be posting shortly. (In
// comparison, the RAR
// >> archive is about 600k.)
//
// I really wonder what pre-set compression rate you used for
// (win)zip. The
// difference in zip/rar is too much for zip to be at max compression.
Max compression. I got about 4 times that with RAR using multimedia
compression.
//
// I also have a rar-related question: what is RAR' url??? My
// rar documentations
// mentions some hazy url http://www.thepoint.net/~jkracht
// Couple of weeks ago I
// checked, but i do not believe this url to be still active.
//
I think www.rar.com is right..
// Dean
//
//
//
//
// --------------------------------------------------------------
// Thanks for using Fractint, The Fractals and Fractint Discussion List
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//
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------------------------------
Date: Sat, 10 Oct 1998 20:34:00 EDT
From: SKarl52884@aol.com
Subject: Re: (fractint) I'm missing some .frm's
In a message dated 10/10/98 7:08:13 PM Eastern Daylight Time,
marsdenp@ix.netcom.com writes:
<< I've been going through Les's monthly collections of pars & religiously
updating my frm folder when necessary, but I have found that I am missing the
following .frm's. Could anyone help me locate them, please ?
Year & Month .FRM Name
97_08 GALLET-8-04 >>
I knew I had this one!
Here's :::::
Gallet-8-04 { ; Sylvie Gallet, sylvie_gallet@compuserve.com, Mar 1997
; Requires periodicity = 0
; p1 = exponent
; p2 > 1
z = zn = pixel , ex = p1 - 1
IF (p2 || imag(p2))
k = p2
ELSE
k = 1
ENDIF
:
znex = zn^ex , num = znex*zn - 1 , mnum = |num|
den = p1*znex , zn = zn - num/den
IF ( mnum > |z^p1-1|)
z = zn * k
ENDIF
mnum >= 0.001
}
=================
Steve
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------------------------------
Date: Sat, 10 Oct 1998 20:52:22 EDT
From: SKarl52884@aol.com
Subject: Re: (fractint) Web site and software update
In a message dated 10/10/98 3:45:12 PM Eastern Daylight Time,
rbarnett@telenet.net writes:
<< Ron Barnett
Hidden Dimension
http://www.hiddendimension.com
>>
From your site [ which is very kewl! ]
<<Anti-alaising using the Photoshop
bicubic interpolation algorithm has been applied to some of the images>>
Would you mind explaining the bi-cubic...just enough to let me know where it
is... Or just point me to the button?
[I use PSP5]
Thank you,
Steve
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------------------------------
Date: Sat, 10 Oct 1998 19:52:07 -0500
From: "Peter Marsden" <marsdenp@ix.netcom.com>
Subject: Re: (fractint) I'm missing some .frm's
Thanks, Steve.
Peter
- -----Original Message-----
>
> Year & Month .FRM Name
> 97_08 GALLET-8-04 >>
>I knew I had this one!
- --------------------------------------------------------------
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------------------------------
Date: Sat, 10 Oct 1998 22:14:41 -0400
From: Ron Barnett <rbarnett@telenet.net>
Subject: RE: (fractint) Web site and software update
Steve,
I am using Photoshop 4.0, but 5.0 should be the same. Select "preferences"
on the file menu, and then "general". There should be an drop down box for
"interpolation". Select bicubic. Whenever you reduce the size of an image,
Photoshop will apply bicubic interpolation ("anti-alaising") to the image.
I usually do a 2.5 - 3 fold reduction to get good anti-alaising. I can't
tell you right off hand what the mathematical details are, I just know its
one of the most accurate methods for image reduction.
- -----Original Message-----
From: SKarl52884@aol.com [SMTP:SKarl52884@aol.com]
Sent: Saturday, October 10, 1998 8:52 PM
To: fractint@lists.xmission.com
Subject: Re: (fractint) Web site and software update
In a message dated 10/10/98 3:45:12 PM Eastern Daylight Time,
rbarnett@telenet.net writes:
<< Ron Barnett
Hidden Dimension
http://www.hiddendimension.com
>>
>From your site [ which is very kewl! ]
<<Anti-alaising using the Photoshop
bicubic interpolation algorithm has been applied to some of the images>>
Would you mind explaining the bi-cubic...just enough to let me know where
it
is... Or just point me to the button?
[I use PSP5]
Thank you,
Steve
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------------------------------
Date: Sun, 11 Oct 1998 03:06:11 +0100
From: "Les St Clair" <les_stclair@crosstrees.prestel.co.uk>
Subject: Re: (fractint) I'm missing some .frm's
Hi Peter,
Here are the missing formulas.
I'll upload the corrected frac_ml.frm collection next month.
Thanks for spotting these omissions!
Gallet-8-04 { ; Sylvie Gallet, sylvie_gallet@compuserve.com, Mar 1997
; Requires periodicity = 0
; p1 = exponent
; p2 > 1
z = zn = pixel , ex = p1 - 1
IF (p2 || imag(p2))
k = p2
ELSE
k = 1
ENDIF
:
znex = zn^ex , num = znex*zn - 1 , mnum = |num|
den = p1*znex , zn = zn - num/den
IF ( mnum > |z^p1-1|)
z = zn * k
ENDIF
mnum >= 0.001
}
3DStalks_Julia (ORIGIN) {; Copyright (c) Paul W. Carlson, 1997
;****************************************************
; Always use floating point math and outside=summ.
;
; Parameters:
; p1 = the value of complex constant c in the equation
; real(p2) = a factor controlling the width of the stalks
; (this is actually 1/2 the width of the "trap")
; imag(p2) = bailout value for |w|
; real(p3) = number of color ranges
; imag(p3) = number of colors in each color range
;
; Note that the equation variable is w, not z. Always
; initialize z to zero.
;****************************************************
w = pixel
c = p1
z = 0
bailout = 0
iter = 0
range_num = 0
;****************************************************
; In the accompanying par file, mnkyface.par,
; we have 2 color ranges with 98 colors in each range
; for a total of 196 colors. The first range starts at
; color 1. Pixels will use color 0 when |w| < bailout.
; Other values can be used here as long as the product
; of num_ranges times colors_in_range is less than 255.
; Color 0 is reserved for the background color and color
; 255 can be used for the inside color.
;****************************************************
num_ranges = real(p3)
colors_in_range = imag(p3)
;****************************************************
; Real(p2) controls the width of the stalks.
; These values will usually be in the range 0.001 to 0.5
;****************************************************
stalk_width = real(p2)
index_factor = (colors_in_range - 1) / stalk_width:
;****************************************************
; The equation being iterated. Almost any equation
; that can be expressed in terms of a complex variable
; and a complex constant will work with this method.
; This line in the formula is the only one that needs
; to be changed for other equations.
; This example uses the "magnet2j" equation.
;****************************************************
w=((w^3+3*w*(c-1)+(c-1)*(c-2))/(3*w*w+3*w*(c-2)+(c-1)*(c-2)+1))^2
;****************************************************
; Find which axis the orbit point is closest to.
;****************************************************
IF (abs(real(w)) <= abs(imag(w)))
min_dist_to_axis = abs(real(w))
ELSE
min_dist_to_axis = abs(imag(w))
ENDIF
;****************************************************
; If the orbit point is within stalk_width of an axis,
; set z to the index into the colormap and set the bailout flag.
; Also, prevent bailout on the first two iterations.
;****************************************************
IF (min_dist_to_axis < stalk_width && iter > 1)
z = index_factor * min_dist_to_axis + range_num * colors_in_range + 1
bailout = 1
ENDIF
;****************************************************
; Cycle through the range numbers (0 thru num_ranges - 1)
; With two color ranges, even iterations use color
; range 0, odd iterations use color range 1.
;****************************************************
range_num = range_num + 1
IF (range_num == num_ranges)
range_num = 0
ENDIF
;****************************************************
; Since we are using outside=summ, we have to subtract
; the number of iterations from z.
;****************************************************
iter = iter + 1
z = z - iter
;****************************************************
; Finally, we test for bailout
;****************************************************
bailout == 0 && |w| < imag(p2)
}
Ormandel12(YAXIS) {; Copr. 1995 by Jack A. Orman
z=c=pixel, t=pixel:
t=t+pixel
neg=(fn1(z)/fn2(z))^p1 * (z<t)
pos=(fn1(z)/fn2(z))^p1 * (z>=t)
z=neg + pos + c
|z|<t
}
T04-08{; = 2zT03-T02
t=p1,bailout=4,z=pixel:
x=real(z),y=imag(z)
xx=x*x,yy=y*y
Tx=sin(8*xx*(xx-1)+1)
Ty=sin(8*yy*(yy-1)+1)
x=x-t*Ty,y=y+t*Tx
z=x+flip(y)
|z|<=bailout
}
U02-14(XYAxis){; = 2zU01-U00
bailout=real(p2)/10000,z=pixel:
f=4*z*z-1
fd=8*z
oz=z
w=z-f/fd
fw=4*w*w-1
z=w-fw/fd
bailout<=sqrt(|(|z|)-(|oz|)|)
}
Colorit-3f { ; (c) Jay Hill, 1998
; p1= light angle (cos a, sin a)
; use these, float=y inside=0 outside=real
periodicity=0
iter=0, zc = 0, c = pixel, dz=1
; 23 is the color of the period 1 component.
z=23*(|(2*sinh(asinh(sqrt(-6.75)*c)/3))|<=1.0)
done=-(z>0) ; done if we know z is not 0
if(p1==0)
p1=1
endif
: ; initialization.
iter = iter+1 ; gotta count the iterations
dz=3*sqr(zc)*dz+1 ; derivative, dz/dc, a slope
for shading
zc=zc*sqr(zc) + c ; standard MSet cubic
iteration z=z^3+c
if(|zc| >= 1024) ; Bailout
z = z-8+((sin(2*pi*iter/256)*Real(p1*dz/zc))>0) + iter
done=-1 ; Set flag to force an exit.
endif
done >= 0 ; Continue if the flag >=0.
}
Carr1999 (XAXIS) {; Modified Sylvie Gallet frm. [101324,3444],1996
z= c =pixel+1/log(pixel),
c1=1.5*z , c2=2.25*z , c3=3.375*z , c4=5.0625*z,
l1=real(p1) , l2=imag(p1) , l3=real(p2) , l4=imag(p2),
bailout=16, iter=0 , pp2 = pixel/imag(p2):
t1=(iter==l1) , t2=(iter==l2) , t3=(iter==l3) , t4=(iter==l4),
t=1-(t1||t2||t3||t4) , z=z*t , c=c*t + c1*t1 + c2*t2 + c3*t3 + c4*t4 + pp2
z=z*z+c,
iter=iter+1
(|real(z)|) <= bailout
}
cheers, Les
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------------------------------
Date: Sun, 11 Oct 1998 03:12:51 +0100
From: "Les St Clair" <les_stclair@crosstrees.prestel.co.uk>
Subject: Re: (fractint) I'm missing some .frm's
Hi Peter,
>> for some reason which I cannot understand, I cannot get the following
fractals to plot, the correct .frm's are in my directory & the .par file entries
do point to them. Has anyone else had this problem ?<<
"feather" (97_08, not 98_08) and "tendrilP" both work fine for me.
- - Les
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------------------------------
Date: Sun, 11 Oct 1998 03:48:02 -0500
From: "Paul N. Lee" <Paul.N.Lee@Worldnet.att.net>
Subject: Re: (fractint) Web site and software update
SKarl52884@aol.com wrote:
>
> << Ron Barnett
> Hidden Dimension
> http://www.hiddendimension.com
> >>
> From your site [ which is very kewl! ]
> <<Anti-alaising using the Photoshop bicubic interpolation
> algorithm has been applied to some of the images>>
>
> Would you mind explaining the bi-cubic... just enough to let
> me know where it is... Or just point me to the button?
> [I use PSP5]
>
To use a similar "bi-cubic" in JASC's Paint Shop Pro 5.0, you need to
use the menu selection of IMAGE | RESIZE... Then within the pop-up
window there is a drop-down list for Resize Type, one of the options is
for "Bicubic resample" (another is Bilinear).
Bilinear and Bicubic Resampling Methods
The Bicubic Resampling method of resizing minimizes the raggedness
normally associated with expanding an image by using a process called
interpolation. As applied here, interpolation smoothes out rough spots
by estimating how the "missing" pixels should appear, and then filling
them with the appropriate color. It produces better results than the
Pixel Resize method with photo-realistic images and with images that are
irregular or complex. Use the Bilinear Resampling method for shrinking
these images and Bicubic for enlarging them.
Bilinear and Bicubic resampling are available for grey scale images and
24-bit images.
If the image does not fit these categories, and you would like to use
one of these methods, do the following:
1. Increase the imageÆs color depth.
2. Resize the image.
3. Reduce the imageÆs color depth and return it
to the original depth.
Further information on "increasing" and "reducing" will be found in
PSP's Help file.
- -------------------------------------------------
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Date: Sun, 11 Oct 1998 12:30:04 -0000
From: "Dean-Christian Strik" <dean2@bigfoot.com>
Subject: Re: (fractint) RE: [fractal-art] Immersive-visualization Solutions
Peter wrote:
>You're right, it isn't representative, but with RAR's Multimedia setting, it
>works about twice as well as normal (i.e. avg. 4:1 vs. 2:1). RAR probably
>enlarges the file because it has a very large header, but I'm not sure.
Hmm. I think it's time to check out WINRar soon... I'll try multimedia compression. May be
useful - I'm always running out of disk space.
> // I also have a rar-related question: what is RAR' url??? My
> // rar documentations
> // mentions some hazy url http://www.thepoint.net/~jkracht
> // Couple of weeks ago I
> // checked, but i do not believe this url to be still active.
> //
>
>I think www.rar.com is right..
No. It would seem so right. I in fact tried this url first; and when it didn't work, i
browsed through the documentation, where i found the thepoint url.
I just checked out www.winrar.com www.rar.org www.winrar.org www.rar.net and
www.winrar.net
but none of these actually work.
Dean
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Date: Sun, 11 Oct 1998 06:46:21 EDT
From: SKarl52884@aol.com
Subject: Re: (fractint) Web site and software update
In a message dated 10/11/98 4:49:44 AM Eastern Daylight Time,
Paul.N.Lee@Worldnet.att.net writes:
<< << Ron Barnett
> Hidden Dimension
> http://www.hiddendimension.com
> >>
> From your site [ which is very kewl! ]
> <<Anti-alaising using the Photoshop bicubic interpolation
> algorithm has been applied to some of the images>>
>
> Would you mind explaining the bi-cubic... just enough to let
> me know where it is... Or just point me to the button?
> [I use PSP5]
>
To use a similar "bi-cubic" in JASC's Paint Shop Pro 5.0, you need to
use the menu selection of IMAGE | RESIZE... Then within the pop-up
window there is a drop-down list for Resize Type, one of the options is
for "Bicubic resample" (another is Bilinear). >>
Ron and Paul...Thank you!
Regards,
Steve
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Date: Mon, 12 Oct 1998 00:05:18 +1300
From: "Morgan L. Owens" <packrat@nznet.gen.nz>
Subject: Re: (fractint) Web site and software update
At 03:48 11/10/98 -0500, Paul wrote:
>
>Bilinear and Bicubic Resampling Methods
>
>The Bicubic Resampling method of resizing minimizes the raggedness
>normally associated with expanding an image by using a process called
>interpolation. As applied here, interpolation smoothes out rough spots
>by estimating how the "missing" pixels should appear, and then filling
>them with the appropriate color. It produces better results than the
>Pixel Resize method with photo-realistic images and with images that are
>irregular or complex. Use the Bilinear Resampling method for shrinking
>these images and Bicubic for enlarging them.
>
Pixel resize, bilinear, and bicubic interpolations actually form a series
of related interpolation methods. All involve fitting curves to points.
A fourth, "biquadratic", which is virtually never used, also belongs to
this family, and fits in between bilinear and bicubic. The family continues
with "biquartic", "biquintic", etc.
Every second interpolation method (starting with "biconstant" or pixel
resize, and biquadratic) has the problem of sharp edges appearing between
blocks of pixels that give away its enlarged nature. This is why
biquadratic interpolation isn't used.
All use the values of a certain-sized neighbourhood of pixels in the
original image to guess what the interpolated pixels in the enlarged image
should be. The difference is in the size of the neighbourhood.
With one pixel, the method takes the colour of that pixel and copies it
throughout its neighbourhood. This is constant, or "pixel resize"
interpolation.
*--
*-- *--
With two pixels, we can draw imagine drawing a straight line between them
and colouring it with a smooth gradient from one pixel's colour to the
other. So one quarter of the way from a red pixel to a blue pixel would be
"three-quarters red, one-quarter blue"; and half way we'd find a
medium-dark magenta. This is linear interpolation.
*
/ \
/ \
* *
With three pixels, we have enough information to draw a quadratic curve
from the first pixel through the second to the third. The section between
the first and second pixels is then coloured to fit this curve. If the
third pixel is higher than the second:
*
/
*
/
*- the interpolated pixels are generally closer in colour to the first
pixel, and only toward the end do they drift up to match the second. If, on
the other hand, the third pixel is _lower_ than the second:
-*-
/ \
* * The interpolated pixels between the first and second pixels will
tend to be more like the second pixel in colour.
Cubic interpolation is next. This takes _four_ pixels to define a cubic
curve. The section that actually gets filled in is the part between the
second and third pixels. This means that not only is the shape of the curve
affected by where it's going, but where it has come from as well. This
avoids the sharp edges that appear in constant and quadratic interpolation.
-*-
/ \
-*- *
/
*
Now that we have a way of interpolating colours between two pixels in a
line, we need to extend it to two dimensions. How does one go from cubic
interpolation to bicubic? In this situation we end up with little
rectangles that need to be coloured in, instead of little line segments.
* * * Do all the vertical edges with cubic interpolation, and
| | | then fill in the spaces between horizontally using cubic interpolation
* * * again.
| | |
* * *
Pure drivel, but there might something in it.
Morgan
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Date: Sun, 11 Oct 1998 10:04:43 -0500
From: "Peter Marsden" <marsdenp@ix.netcom.com>
Subject: Re: (fractint) I'm missing some .frm's
Thanks to Les, Bill & Steve for replying. This will enable me to finish my
fractal plotting. For those who are interested, you can put all the images
from 97_08 to 98_09 on one CD-R with about 20MB to spare (assuming 800x600
images).
Peter
- -----Original Message-----
From: Les St Clair <les_stclair@crosstrees.prestel.co.uk>
To: fractint@lists.xmission.com <fractint@lists.xmission.com>
Date: Saturday, October 10, 1998 9:17 PM
Subject: Re: (fractint) I'm missing some .frm's
>Hi Peter,
>
>>> for some reason which I cannot understand, I cannot get the following
>fractals to plot, the correct .frm's are in my directory & the .par file
entries
>do point to them. Has anyone else had this problem ?<<
>
>"feather" (97_08, not 98_08) and "tendrilP" both work fine for me.
>
>- Les
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Date: Sun, 11 Oct 1998 09:43:12 -0700
From: kathy roth <kroth@well.com>
Subject: (fractint) gravijul triangle
Damien Jones wrote:
> The triangle-inequality Julia formulas I posted last night
> are not quite correct. They will produce images which are
interesting,
but
> are slightly incorrect. The two formulas below are the correct
versions;
I
> have named them differently so that if you have already used last
night's
> formulas, you will still be able to reproduce them.
>
Thanks for posting those. I made these last month-
not at all sure what it was "supposed" to be doing
but pretty sure it wasn't this, but I liked them anyway.
Also, they nearly but don't quite have y-axis
symmetry.
tri3 { ; kathy roth triangle jellyfish
reset=1960 type=formula formulafile=jul-tr~1.frm
formulaname=jul1-Triangle function=log/tan/sqr
center-mag=0.0294433/0.00645471/2.899684/1/-90
params=100000/1/100/4/4/4 float=y
outside=real invert=1/0/0
colors=000BBM<14>WWz<7>J9J<15>zWz<7>J0\
9<15>z0W<7>J90<15>zW0<7>JJ0<15>zz0\
<7>99J<15>WWz<7>0J9<15>0zW<7>0JJ<14>0xx\
0zz2tt<6>JE9<15>yjU<7>BJF<15>_zn<6>LO3<8>px9<6>FGI
}
tri4 { ; kathy roth 8-98
reset=1960 type=formula formulafile=jul-tr~1.frm
formulaname=jul1-Triangle function=log/tan/sqr
center-mag=9.46552/5.90557/2.321759/1/-17.5
params=100000/1/100/4/4/4 float=y outside=atan invert=1/0/0
colors=000BBM<14>WWz<7>J9J<15>zW\
z<7>J09<15>z0W<7>J90<15>zW0<7>JJ0<15>zz0\
<7>99J<15>WWz<7>0J9<15>0zW<7>0JJ<14>0xx\
0zz2tt<6>JE9<15>yjU<7>BJF<15>_zn<6>LO3<8>px9<6>FGI
}
tri5 { ; kathy roth 8-98
reset=1960 type=formula formulafile=jul-tr~1.frm
formulaname=jul1-Triangle function=log/tan/sqr
center-mag=16.353/-0.0326252/0.3562583/1/-90
params=100000/1/100/4/4/4 float=y
outside=atan invert=1/0/0
colors=000BBM<14>WWz<7>J9J<15>zWz<7>J0\
9<15>z0W<7>J90<15>zW0<7>JJ0<15>zz0\
<7>99J<15>WWz<7>0J9<15>0zW<7>0JJ<14>0xx\
0zz2tt<6>JE9<15>yjU<7>BJF<15>_zn<6>LO3<8>px9<6>FGI
}
tri1 { ; kathy roth 8-98
reset=1960 type=formula formulafile=jul-tr~1.frm
formulaname=jul1-Triangle function=log/recip/sqr
center-mag=2.07004/0.00592987/0.9579595/1.0253/-89.119/-1.737
params=100000/1/100/4/4/4 float=y outside=atan
colors=000000CCP<13>WWz<7>J9J<15>zWz<7>J0\
9<15>z0W<7>J90<15>zW0<7>JJ0<15>\
zz0<7>99J<15>WWz<7>0J9<15>0zW<7>0JJ<14>0xx\
0zz2tt<6>JE9<15>yjU<7>BJF<15>_\
zn<6>LO3<8>px9<6>FGI
}
tri2 { ; kathy roth 8-98
reset=1960 type=formula formulafile=jul-tr~1.frm
formulaname=jul1-Triangle function=log/recip/sqr
center-mag=1.49584/0.0518169/0.7929758/1.0253/-89.119/-1.737
params=100000/1/100/4/4/4 float=y outside=atan
colors=000BBM<14>WWz<7>J9J<15>zWz<7>J0\
9<15>z0W<7>J90<15>zW0<7>JJ0<15>zz0\
<7>99J<15>WWz<7>0J9<15>0zW<7>0JJ<14>0xx\
0zz2tt<6>JE9<15>yjU<7>BJF<15>_zn<6>LO3<8>px9<6>FGI
}
frm:jul1-Triangle{; variant of Damien Jones dmj-Mand-Triangle
;kathy roth 9-98
;p1 does not work
; original idea and formula from L. Kerry Mitchell
;gravijul by Mark Christenson
; modified for total continuity by dmj, 9-8-97
IF (real(p3) == 0) ; Invalid value for color scale.
p3 = 75 + flip(imag(p3)) ; Substitute a default value.
ENDIF
IF (imag(p3) == 0) ; Invalid value for bailout.
p3 = (0,128) + real(p3) ; Substitute a default value.
ENDIF
sum = 0 ; Running total.
done = 1 ; Iteration counter.
ac = cabs(pixel) ; Absolute value of pixel (precalc).
il2 = 1/log(2.0) ; Inverse log 2 (precalc).
lp = log(log(imag(p3))) ; log(log bailout) (precalc).
f = -1 ; No fractional iteration yet.
z = pixel, c =p1:
az2 = |z| ; Save absolute value of first term.
w=fn1(z)
z=fn3(1/fn2(w*w)) ;gravijul variant
lowbound = abs(az2 - ac) ; Calculate lower bound for sum.
sum = sum + (cabs(z) - lowbound) / (az2+ac - lowbound)
; Ratio between bounds.
done = done + 1 ; Done one more iteration.
IF (az2 > imag(p3)) ; Point exceeds bailout.
IF (f < 0) ; First time; let it go again.
f = il2*lp - il2*log(log(cabs(z))) + 2; Fractional iteration.
oldsum = sum / done ; Save the average ratio so far.
ELSE ; Second time past bailout.
sum = sum / done ; Average ratio.
f = oldsum + (sum-oldsum) * (f-1) ; Interpolate sum.
z = f * real(p3) ; Apply color scale.
z = z - 255*trunc(z/real(255)) ; Wrap at 255.
z = z - done - 5 ; Return value.
done = -1 ; Set flag to force an exit.
ENDIF
ENDIF
done >= 0 ; Continue if the flag is clear.
}
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Date: Sun, 11 Oct 1998 20:00:25 +0100
From: "Kim Bach Petersen" <kimb@post8.tele.dk>
Subject: (fractint) High iteration zooms
I just did some high iteration zooms into the mandelbrot set
and here's the PAR's for those who find it worth the wait...
The impatient ones can see the pictures in smalish 400x300 format at my
website:
http://home8.inet.tele.dk/kimb/
You might want to bypass my danish introductory page and go directly to the
pictures:
http://home8.inet.tele.dk/kimb/fractal.htm
Enjoy, Kim :-)
- -----8<----
kbp1 { ; > 302 iterations 20:45 @ 800x600
; Mandelbrot by Kim Bach Petersen 1998
reset=1960 type=mandel
center-mag=-0.75017936855172060/-0.01161074644406282/663682.8
params=0/0 float=y maxiter=20000
colors=000000<29>00k00m01m<29>0ky0mz1mz<30>zzz<46>2zz0zz0yz<45>02z00z00y\
<59>002000000
}
kbp2 { ; > 5270 iterations 57:40 @ 800x600
; Mandelbrot by Kim Bach Petersen 1998
reset=1960 type=mandel
center-mag=-0.75017938225569000/-0.01161072996831062/4880021
params=0/0 float=y maxiter=100000
colors=000000<29>00k00m01m<29>0ky0mz1mz<30>zzz<46>2zz0zz0yz<45>02z00z00y\
<59>002000000
}
kbp3 { ; > 6758 iterations 55:47 @ 800x600
; Mandelbrot by Kim Bach Petersen 1998
reset=1960 type=mandel
center-mag=-0.75017954823748270/-0.01161053697134931/1.64732e+009
params=0/0 float=y maxiter=100000
colors=000000<29>00k00m01m<29>0ky0mz1mz<30>zzz<46>2zz0zz0yz<45>02z00z00y\
<59>002000000
}
kbp4 { ; > 13236 iterations 1:21:37 @ 800x600
; Mandelbrot by Kim Bach Petersen 1998
reset=1960 type=mandel
center-mag=-0.75017954826745840/-0.01161053694982410/7.162162e+010
params=0/0 float=y maxiter=100000
colors=000000<29>00k00m01m<29>0ky0mz1mz<30>zzz<46>2zz0zz0yz<45>02z00z00y\
<59>002000000
}
kbp5 { ; > 19454 iterations 2:12:10 @ 800x600
; Mandelbrot by Kim Bach Petersen 1998
reset=1960 type=mandel
center-mag=-0.75017954826734170/-0.01161053695008511/7.067146e+011
params=0/0 float=y maxiter=100000
colors=000000<29>00k00m01m<29>0ky0mz1mz<30>zzz<46>2zz0zz0yz<45>02z00z00y\
<59>002000000
}
- ------8<------
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