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From: owner-fractint-digest@lists.xmission.com (fractint-digest)
To: fractint-digest@lists.xmission.com
Subject: fractint-digest V1 #107
Reply-To: fractint-digest
Sender: owner-fractint-digest@lists.xmission.com
Errors-To: owner-fractint-digest@lists.xmission.com
Precedence: bulk
fractint-digest Thursday, February 12 1998 Volume 01 : Number 107
----------------------------------------------------------------------
Date: Wed, 11 Feb 1998 10:13:43 +0100 (CET)
From: Jan Kozicki <janek@thenut.eti.pg.gda.pl>
Subject: (fractint) FEIGENBAUM's constant: HELP ME
Hello there
I've just joined this e-mailing discussion list (hope it will be
interesting here ;-)).
And I have a problem with Feigenbaum's constant.
As we know F=4.66902016090+ (if I have a good memory)
As it can be readed in Fractint's help (but firstly I've meet feigenbaum's
constant in a book "Chaos - making new science" by James Gleick) -
Feigenbaum has calculated his universal chaos constant using a HP-65
calculator, where each iteration took about three minutes (whew! - he is a
superhuman for me) - and he discovered his universal constant only
because ha had a lot of time to think about the numbers from his HP-65.
Now begins the trouble - I thought I understand WHAT is and HOW to
calculate EXACTLY feigenbaum's constant.
So I began:
I programmed my HP-28C caltulator (where each iteration took less than an
eyewink), to iterate the same z(n+1)=r*z(n)*(1-z(n)) bifurcations that
Feigenbaum studied. And so I located the values of r where function
bifurcates:
from one branch to two branches r1=2.59999999930
from two to four branches r2=3.38199999991
from four to eight branches r3=3.54121000000
And one important thing I dicscovered using mathcad and fractint:
The higher precision you use, the lower values you get (that can be proven
by zooming constaltlny into bifurcating region in fractint's bifurcation
fractals)
NOW: as I understand the idea there shuold be equation:
(r2-r1)/(r3-r2)=f=4.669...
let's check that .78200000061/.15921000009=4.9117...(etc) that differs
from f
then I began to explore mandelbrot
With very high precision I located the places where mandelbrot's main
circles were touching each other:
the biggest (not exactly circle on the real side) with the next one
r1=-.75
the next one to the next smaller one r2=-1.25
and to the next one r3=-1.36809893939
I expected that (r2-r1)/(r3-r2)=f, and what I get?
.5/.11809893939=4.2337...(etc) that differs too
THAT's TOO much for my poor brain HOW ONE SHOULD CALCULATE FEIGENBAUM's
CONSTANT?????
HELP MEEEEEEEEeeeeeeee......
# Jan Kozicki
# janek@thenut.eti.pg.gda.pl
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------------------------------
Date: Wed, 11 Feb 1998 15:21:14 -0600
From: "Justin A. Kolodziej" <4wg7kolodzie@vms.csd.mu.edu>
Subject: Re: (fractint) Fractint for Windows NT
Wizzle wrote:
>
> Dinel...
>
> Fractint won't work a darn under NT for me (which I have at w*rk so I
> actually have to w*rk as an alternative!!!!).
What do you mean? Does it not even start, or does it start but have
limited video modes? It worked under NT 3.51 (remember when I wasted
*more* bandwidth while my computer was down?!), though I didn't try
hi-res. I don't know if it works for me under 4.0, though I suspect
programs on a floppy would be denied permission to run for us. Most of
our NT 4 stations are Motorola PowerPCs, so it wouldn't run anyway!
- --
Justin A. Kolodziej
Why pay for an OS when you can get a clearly superior one for free?
Justin Kolodziej is 4wg7kolodzie@vms.csd.mu.edu
Marquette University is www.mu.edu
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------------------------------
Date: Wed, 11 Feb 1998 14:47:40 -0800
From: "Mike or Linda Allison" <gumbycat@ix.netcom.com>
Subject: (fractint) Jon Noring's prints
This is a multi-part message in MIME format.
- ------=_NextPart_000_01BD36FC.00A03600
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
Hi, all!
I just had Jon Noring work his magic on my fractal "Perceptual Bliss." He
had a 4x5 positive transparency made, and a 15"x20" fujiflex print. They
are terrific! I've read on these mailing lists that the detail is
unbelievable, but I didn't realize just how unbelievable until I saw it for
myself!
If you haven't had one of your fractals transformed magically by Jon, stop
everything and start now!
Just in case this is considered "off topic," here's the penalty par (below
and attached).
lethal-weapon-x { ; t= 0:02:47.41
; gumbycat@ix.netcom.com
; (c) 1998 by Linda Allison
reset=1960 type=formula formulafile=fractint.frm
formulaname=051597-002-m1-m2 function=atan/cotan
center-mag=0.014434/-0.00754877/0.8057795/1.286/-16.932/-1.156
params=25/10 float=y maxiter=2500 inside=bof60 decomp=256
viewwindows=1/1/yes/0/0
colors=166<7>022022110111113<19>Y`f_bi`bjabjbck<9>DKMAIJ8HH6FF6FF5EE<6>5\
CC5BB5BB4AA4A9<8>267266256246<4>124114030004<29>1Tr<10>fhwjjxllz<13>9XZ6\
VW6TU<5>3DE2BB2AA<2>145123123<4>124124125136<16>0BJ0BK0CL0CL0CM0DN<7>0GT\
0HU0IW<11>0Mo0Nq2Or<2>3Pr3Pr4Qs5Rs<20>2NP2NO1MM1LL<6>1CC1BB1AA199188188<\
4>177
}
frm:051597-002-m1-m2 {; Linda Allison May 15,1997
; modified by Sylvie Gallet
; modified again by Linda Allison
; 1st parameter: real(p1) = bailout
; 2nd parameter: imag(p1) = number of sides
z = 0
c = 0.2 * log(pixel^imag(p1)) :
z2 = fn1(z) + c , sqz2 = fn2(z2)
z = c * (1-sqz2)/(1+sqz2)
|z| <= p1
}
Linda
(gumbycat@ix.netcom.com) NO SPAM!
http://www.geocities.com/~gumbycat (last update: 02-07-98)
http://www.fortunecity.com//tattooine/stephenson/5/abpf.html (last update:
02-07-98)
http://www.toptown.com/innercircle/gumbycat/index.html (NEW! 02-01-98)
- ------=_NextPart_000_01BD36FC.00A03600
Content-Type: application/octet-stream; name="Penalty.par"
Content-Transfer-Encoding: quoted-printable
Content-Description: Penalty.par (PAR File)
Content-Disposition: attachment; filename="Penalty.par"
lethal-weapon-x { ; t=3D 0:02:47.41
; gumbycat@ix.netcom.com
; (c) 1998 by Linda Allison
reset=3D1960 type=3Dformula formulafile=3Dfractint.frm
formulaname=3D051597-002-m1-m2 function=3Datan/cotan
center-mag=3D0.014434/-0.00754877/0.8057795/1.286/-16.932/-1.156
params=3D25/10 float=3Dy maxiter=3D2500 inside=3Dbof60 decomp=3D256
viewwindows=3D1/1/yes/0/0
=
colors=3D166<7>022022110111113<19>Y`f_bi`bjabjbck<9>DKMAIJ8HH6FF6FF5EE<6>=
5\
=
CC5BB5BB4AA4A9<8>267266256246<4>124114030004<29>1Tr<10>fhwjjxllz<13>9XZ6\=
=
VW6TU<5>3DE2BB2AA<2>145123123<4>124124125136<16>0BJ0BK0CL0CL0CM0DN<7>0GT\=
=
0HU0IW<11>0Mo0Nq2Or<2>3Pr3Pr4Qs5Rs<20>2NP2NO1MM1LL<6>1CC1BB1AA199188188<\=
4>177
}
frm:051597-002-m1-m2 {; Linda Allison May 15,1997
; modified by Sylvie Gallet
; modified again by Linda Allison
; 1st parameter: real(p1) =3D bailout
; 2nd parameter: imag(p1) =3D number of sides
z =3D 0
c =3D 0.2 * log(pixel^imag(p1)) :
z2 =3D fn1(z) + c , sqz2 =3D fn2(z2)
z =3D c * (1-sqz2)/(1+sqz2)
|z| <=3D p1
}
- ------=_NextPart_000_01BD36FC.00A03600--
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------------------------------
Date: Wed, 11 Feb 98 15:32:30 PST
From: "Jim Prickett" <jprickett@satcom.net>
Subject: (fractint) Fractint .MAP tools: XMAP.ZIP
Since the copy of XMAP.ZIP on my webpage was corrupted I've uploaded a
new copy. Please try again if you got a file that wouldn't UNZIP.
MMAP - To make new '.map' files for Fractint. This is *NOT* MAKEMAP
XMAP - To modify an existing '.map' file. It does almost everything.
Full C source code is included with the DOS executables. Please let me
know if you compile the source code for Linux.
http://www.geocities.com/SiliconValley/Way/9943/
Jim Prickett
jprickett@satcom.net
Do you know about the new E-mail SPAM bills
in Congress ? Go to http://www.cauce.org/
and find out!
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------------------------------
Date: Wed, 11 Feb 1998 16:17:49 -0800 (PST)
From: FIRSTNAME LASTNAME <whookam88@yahoo.com>
Subject: Re: (fractint) Jon Noring's prints
- ---Mike or Linda Allison <gumbycat@ix.netcom.com> wrote:
>
> Hi, all!
>
> I just had Jon Noring work his magic on my fractal "Perceptual
Bliss." He
> had a 4x5 positive transparency made, and a 15"x20" fujiflex print.
They
> are terrific! I've read on these mailing lists that the detail is
> unbelievable, but I didn't realize just how unbelievable until I saw
it for
> myself!
>
> If you haven't had one of your fractals transformed magically by
Jon, stop
> everything and start now!
>
> Just in case this is considered "off topic," here's the penalty par
(below
> and attached).
>
> lethal-weapon-x { ; t= 0:02:47.41
> ; gumbycat@ix.netcom.com
> ; (c) 1998 by Linda Allison
> reset=1960 type=formula formulafile=fractint.frm
> formulaname=051597-002-m1-m2 function=atan/cotan
> center-mag=0.014434/-0.00754877/0.8057795/1.286/-16.932/-1.156
> params=25/10 float=y maxiter=2500 inside=bof60 decomp=256
> viewwindows=1/1/yes/0/0
>
colors=166<7>022022110111113<19>Y`f_bi`bjabjbck<9>DKMAIJ8HH6FF6FF5EE<6>5\
>
CC5BB5BB4AA4A9<8>267266256246<4>124114030004<29>1Tr<10>fhwjjxllz<13>9XZ6\
>
VW6TU<5>3DE2BB2AA<2>145123123<4>124124125136<16>0BJ0BK0CL0CL0CM0DN<7>0GT\
>
0HU0IW<11>0Mo0Nq2Or<2>3Pr3Pr4Qs5Rs<20>2NP2NO1MM1LL<6>1CC1BB1AA199188188<\
> 4>177
> }
>
> frm:051597-002-m1-m2 {; Linda Allison May 15,1997
> ; modified by Sylvie Gallet
> ; modified again by Linda Allison
> ; 1st parameter: real(p1) = bailout
> ; 2nd parameter: imag(p1) = number of sides
> z = 0
> c = 0.2 * log(pixel^imag(p1)) :
> z2 = fn1(z) + c , sqz2 = fn2(z2)
> z = c * (1-sqz2)/(1+sqz2)
> |z| <= p1
> }
>
>
> Linda
> (gumbycat@ix.netcom.com) NO SPAM!
> http://www.geocities.com/~gumbycat (last update: 02-07-98)
> http://www.fortunecity.com//tattooine/stephenson/5/abpf.html (last
update:
> 02-07-98)
> http://www.toptown.com/innercircle/gumbycat/index.html (NEW! 02-01-98)
>
>
> ATTACHMENT part 2 application/octet-stream name=Penalty.par
I cut and pasted it but my copy of FRACTINT 19.60 said
it couldn't understand the color arguments i.e. color=166... ect. My
copy of the FRACTINT.exe is dated 05/07/97 10:29PM, file size =
1,215KB. Also It comes up less than full screen no matter what video
mode I try. What settings do you use? I use SF7
1024x768x256 works with most SUPERVGA.
Let me say I am not a programmer, I don't even like batch files, so I
really am not into coding stuff. I just wanna know if I can use a
setting to get it to understand the color arguments. PLEASE let me
know ASAP.
BTW I'm one of the users of FRACTINT who is into it for the "purty
colors". Not the math. In case that helps in formulating your
response.
James R. McKenzie
_________________________________________________________
DO YOU YAHOO!?
Get your free @yahoo.com address at http://mail.yahoo.com
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------------------------------
Date: Wed, 11 Feb 1998 22:14:57 -0500
From: Gedeon Peteri <gedeon@InfoAve.Net>
Subject: Re: (fractint) Jon Noring's prints
FIRSTNAME LASTNAME wrote:
> I cut and pasted it but my copy of FRACTINT 19.60 said
> it couldn't understand the color arguments i.e. color=166... ect. My
> copy of the FRACTINT.exe is dated 05/07/97 10:29PM, file size =
> 1,215KB. Also It comes up less than full screen no matter what video
> mode I try. What settings do you use? I use SF7
> 1024x768x256 works with most SUPERVGA.
The copy of Linda's par you attached to your letter shows that the color
lines are double spaced. This is an error which occurs sometimes during
transmission of par files. Simply edit out the double spacing - carefully so
you don't delete anything else - and Fractint will recognize the colors. As
for the "less than full screen" view - it is part of Linda's par. It
specifies a square image. That is what the line "viewwindows=1/1/yes/0/0"
means. After you have viewed Linda's image, you can reset your full screen
view by the <delete> key and selecting it from among those offered.
Gedeon
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------------------------------
Date: Wed, 11 Feb 1998 21:52:21 -0600
From: Bob Margolis <rttyman@wwa.com>
Subject: Re: (fractint) Fractint Wish List
Paul Derbyshire wrote:
>
> Palette editor commands: make 'n' negate the range between the selected
> colors; make commands ($, %, ^?) negate red only, green only, or blue only
> in the range; make commands to flip a range (reverse the order of the
> colors) or to flip the red values in a range, or green, or blue (&, *, (?)
> and make all of these plus !, @, # work with 't'n to do every nth color in
> the range...
>
Excellent ideas, Paul, to which I annex mine:
Whereas "d" is used to duplicate the inactive color register's value to
the active color register, I would like to be able to duplicate a range
of colors so that I don't have to keep tapping "d" for each color I wish
to duplicate and thereby speed up the dupication process. Possibly I
would be able to run the mouse over the range of colors I wish to
duplicate and copy that range in another area, similar to cut, copy and
paste in word processing software.
The other idea is one I posted here months ago. That was to be warned if
the filename of a palette that is being saved to disk drive is the same
as one already on the disk drive. I would be given the option of
overwriting the previous file or changing the filename of the new
palette.
Bob Margolis
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------------------------------
Date: Wed, 11 Feb 1998 22:00:52 -0600
From: "Justin A. Kolodziej" <4wg7kolodzie@vms.csd.mu.edu>
Subject: Re: (fractint) Palette editing
Wizzle wrote:
>
> I loathe slider controls!!! Hate...despise....spit!!!!!!! Dislike even.
>
> I have spent much more time fiddling with those blankety blank sliders than
> with any palette. <<curse....gag>> Can you tell I don't like them??? And I
> have YET to produce a single fractal from the slider approach that comes
> close to the stuff I get with fractint or fractal orbits which both have
> the palette which provides such superb control. Who cares about easy if you
> get yicky images? Find me a slider that can give you a single band of color
> precisely where you want it and i MIGHT stop throwing up.
>
I guess you've never used Chaos: The Software then. OK, here goes a
brief description of what the sliders on that program do:
You have a palette of only 16 colors. You can select each color
individually and change the red, green, and blue values independently of
each other and independently of the other colors in the palette using
the slider controls. Or do you _like_ using the + and - keys to change
the value and the r, g, and b keys to change which values you are
adjusting? Seems a bit masochistic to me. Then again, Chaos: The
Software was the fractal program I grew up on from the time you could
still buy a 286 until I discovered WinFract 17.? a couple of years back
on a shareware compilation CD.
> >I want slider controls for the RGB values. THat would make things much
> >easier. I don't care if another window pops up or not (although it
> >would be real easy to do in X). Does anyone remember "Chaos: the
> >Software" by Autodesk? That had a nice editor (though only 16 colors!)
> >with slider bars. I'd like to see something like that, whether in the
> >same window or in a seperate one.
> >
- --
Justin A. Kolodziej
Why pay for an OS when you can get a clearly superior one for free?
Justin Kolodziej is 4wg7kolodzie@vms.csd.mu.edu
Marquette University is www.mu.edu
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------------------------------
Date: Wed, 11 Feb 1998 01:50:19 -0800 (PST)
From: FIRSTNAME LASTNAME <whookam88@yahoo.com>
Subject: Re: (fractint) orgform
OK folks, here it is. I meant to send the ORGFORM.ZIP file to "ONE
PERSON". I put that persons names in the box marked "To:", Yahoo Mail
Sent it to the whole list amyway. I am sorry if I blew out your mail
accounts/attachments/lives/universes/quantum existances, it was not
done on purpose. I am subscribe to this list using this account
because the list confliucted with my standard email account i.e. I
couldn't recieve anything at all. I am still attempting to get used
to this type of e-mail account I plead guilty to making a mistake and
nothing more.
Nuff sed?
_________________________________________________________
DO YOU YAHOO!?
Get your free @yahoo.com address at http://mail.yahoo.com
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------------------------------
Date: Wed, 11 Feb 1998 22:16:33 -0600
From: Janet Preslar <preslar@memphisonline.com>
Subject: (fractint) Video cards
I apologize for not paying attention when this topic was discussed before. But
now that I have the opportunity to upgrade my computer I need some advice. I am
looking at several configurations which include the following video cards:
3D Labs Permedia 2 AGP
Riva 128 3D
Diamond Viper V330 3D
Diamond Viper AGP
Number Nine 334 AGP
STB nVidia AGP
Does anyone have experience (good or bad) with any of these?
Any advice would be appreciated. You can respond to me privately if you wish.
Thanks, Janet
mailto:preslar@memphisonline.com
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------------------------------
Date: Thu, 12 Feb 1998 01:28:00 -0500
From: alex dukay <dukay@interlog.com>
Subject: Re: (fractint) orgform
LASTNAME FIRSTNAME
>Nuff sed?
As far as I'm concerned your apology is accepted by me...You should however
get a spell checker...Why don't you use your real name?
Alex Dukay
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------------------------------
Date: Wed, 11 Feb 1998 23:36:41 -0700 (MST)
From: Kerry Mitchell <lkmitch@primenet.com>
Subject: (fractint) Explanation, formulas & pars--root coloring (long)
comment { ; narrative copyright Kerry Mitchell 11feb98
Root
Complex numbers, of which the real numbers are a subset, all have
two square roots. That is, for a given complex number a, there
are two numbers, b1 and b2, such that b1*b1 (or b2*b2) = a. It
so happens that b2 = -b1, since -1 * -1 = 1. One of these numbers
(typically the one returned by the function sqrt(a)) is termed
the principal square root of a. For example, if a=9, then the
square roots are 3 and -3. 3 is the principal square root.
For the Mandelbrot and Julia sets, this concept is implemented by
expanding the standard iteration loop. Instead of:
z_new = z_old * z_old + c, use
w = z_old * z_old
z_new = w + c.
The question is then, is z_old the principal root of w? This can
be determined by assuming that sqrt(w) returns the principal root.
Then, z_old is compared with sqrt(w) and -sqrt(w), to see which
root of w z_old was.
For the root (_man and _jul) formulas, this is performed on the
last iteration. The yes/no answer is converted to a binary coloring
of the image. The rootcount formulas make this determination for
every iteration, incrementing a counter each time z_old was the
principal root. At the end, the counter is normalized by the total
number of iterations, then scaled into an angle for coloring using
the decomposition method.
}
rootcount-sample { ; copyright Kerry Mitchell 09feb98
reset=1960 type=formula formulafile=fractint.frm
formulaname=rootcount_jul passes=1 center-mag=-0.200\
555/0.472607/10 params=-0.01742899818791213/0.662179\
6505893933/1e+030/0/0/5 float=y maxiter=2000 inside=0
decomp=256 periodicity=0 colors=006108<4>30F40G40H50\
I50I61J<8>A2QB2QB2RC2RC2S<5>F4VG4WG4WH4W<12>N8aO9bO9\
bPAbPAc<20>ZKj_Kk_Lk`Mk<13>gUpgVphWphXpiXq<33>zyzzzz\
zyz<31>jZqiYqiXqhXphWpgVp<25>WGhVFgVFgUEfUEf<18>K6_K\
6ZJ6ZJ6YI5Y<3>G4WG4WF4VF3U<14>71M71L61K61J50I<3>30F3\
0E20C20B<2>006000 cyclerange=0/255
}
root-sample { ; copyright Kerry Mitchell 09feb98
reset=1960 type=formula formulafile=fractint.frm
formulaname=root_jul passes=1 center-mag=-0.200555/0\
.472607/10 params=-0.01742899818791213/0.66217965058\
93933/3/0 float=y maxiter=2000 inside=0 decomp=256
periodicity=0 colors=000CGS<4>9Ne<7>eFQbJPZNOOWNCdM7\
fN1iP<3>5Vc<9>NnZPqYRqY<6>kqS<4>mux<3>zaY<13>T3pQ0rQ\
4r<13>Wyw<2>GJ1<6>x2N<2>pBmtRWxfE<9>SD1<12>ecO<5>KSU\
zzzCOW8MY<14>4pJ<11>EHC<4>si5<10>bka<4>0jv<2>TEY<4>c\
oOfwLfuN<13>hUp<4>Fjo<13>8T67R29T4<7>ShOVjRZeS<5>x7_\
<7>ime<8>Wge cyclerange=0/255
}
frm:root_jul { ; Kerry Mitchell 11feb98
; p1 = Julia parameter
; real(p2) = bailout (try 1e30)
; imag(p2) = unused
; use decomp=something (only 2 colors are used)
zc=pixel, c=p1, iter=1, maxr=real(p2):
iter=iter+1, z2=sqr(zc), znew=z2+c
if ((|znew|>maxr)||(iter==maxit))
w=sqrt(z2), r1=|zc-w|, r2=|zc+w|
z=2*(r1<r2)-1
iter=-1
else
zc=znew
end if
iter>0
;
; colors Julia set by whether or not previous iterate
; is the principal root of the current z^2.
;
}
frm:root_man { ; Kerry Mitchell 11feb98
; real(p1) = bailout (try 1e30)
; imag(p1) = unused
; use decomp=something (only 2 colors are used)
zc=0, c=pixel, iter=1, maxr=real(p1):
iter=iter+1, z2=sqr(zc), znew=z2+c
if ((|znew|>maxr)||(iter==maxit))
w=sqrt(z2), r1=|zc-w|, r2=|zc+w|
z=2*(r1<r2)-1
iter=-1
else
zc=znew
end if
iter>0
;
; colors Mandelbrot set by whether or not previous
; iterate is the principal root of the current z^2.
;
}
frm:rootcount_man { ; Kerry Mitchell 11feb98
; real(p1) = bailout (try 1e30)
; imag(p1) = unused
; real(p2) = inner coloring speed (0 for outside only)
; imag(p2) = outer coloring speed (0 for inside only)
; use decomp=256
zc=0, c=pixel, iter=1, maxr=real(p1), count=0
inspeed=real(p2)*pi*255/128
outspeed=imag(p2)*pi*255/128:
iter=iter+1, z2=sqr(zc), w=sqrt(z2),
r1=|zc-w|, r2=|zc+w|, zc=z2+c
if (r1<r2)
count=count+1
end if
if (iter==maxit)
angle=inspeed*count/(iter-1)
z=cos(angle)+flip(sin(angle))
iter=-1
end if
if (|zc|>maxr)
angle=outspeed*count/(iter-1)
z=cos(angle)+flip(sin(angle))
iter=-1
end if
iter>0
;
; Colors Mandelbrot set by how often previous iterate
; is the principal root of the current z^2. The
; count of principal root times is divided by the
; total number of iterations, and scaled into an
; angle for decomposition coloring. Either inside
; or outside can be switched off by setting the
; appropriate coloring speed parameter to 0.
;
}
frm:rootcount_jul { ; Kerry Mitchell 11feb98
; p1 = Julia parameter
; real(p2) = bailout (try 1e30)
; imag(p2) = unused
; real(p3) = inner coloring speed (0 for outside only)
; imag(p3) = outer coloring speed (0 for inside only)
; use decomp=256
zc=pixel, c=p1, iter=1, maxr=real(p2), count=0
inspeed=real(p3)*pi*255/128
outspeed=imag(p3)*pi*255/128:
iter=iter+1, z2=sqr(zc), w=sqrt(z2),
r1=|zc-w|, r2=|zc+w|, zc=z2+c
if (r1<r2)
count=count+1
end if
if (iter==maxit)
angle=inspeed*count/(iter-1)
z=cos(angle)+flip(sin(angle))
iter=-1
end if
if (|zc|>maxr)
angle=outspeed*count/(iter-1)
z=cos(angle)+flip(sin(angle))
iter=-1
end if
iter>0
;
; Colors Julia set by how often previous iterate
; is the principal root of the current z^2. The
; count of principal root times is divided by the
; total number of iterations, and scaled into an
; angle for decomposition coloring. Either inside
; or outside can be switched off by setting the
; appropriate coloring speed parameter to 0.
;
}
- -------------------------------------------------------------------------------
Kerry Mitchell
lkmitch@primenet.com
- -------------------------------------------------------------------------------
- -
- ------------------------------------------------------------
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------------------------------
Date: Wed, 11 Feb 1998 23:37:29 -0700 (MST)
From: Kerry Mitchell <lkmitch@primenet.com>
Subject: (fractint) Explanation, formulas and pars--triangle method (long)
comment { ; narrative copyright Kerry Mitchell 11feb98
Triangle
The triangle method is based on a simple characteristic of complex
numbers: the magnitude of the sum of two complex numbers, |a+b|,
is strictly limited to a range determined by a and b:
|a+b| >= ||a| - |b||, and
|a+b| <= |a| + |b|,
where |z| is the square root of the sum of the squares of the
components, not the sum of the squares, as in Fractint. The
extremes of this inequality are easily seen with a few examples.
If a=1 and b=2, then:
|a| = 1, |b| = 2;
||a| - |b|| = |1-2| = |-1| = 1;
|a| + |b| = 1+2 = 3;
|a+b| = |3| = 3;
1 <= 3 <= 3.
The upper bound occurs when both addends have the same polar angle.
The geometric interpretation of this is that the complex numbers add
up, and the length of the sum is simply the sum of the individual
lengths.
The lower bound occurs when the polar angles of the complex numbers
differ by 180 degrees; the two numbers are diametrically opposed.
Then, the length of the sum is the difference of the lengths. For
example, if a=3i and b=-5i, then:
|a| = 3, |b| = 5;
||a| - |b|| = |3-5| = |-2| = 2;
|a| + |b| = 3 + 5 = 8;
|a+b| = |-2i| = 2;
2 <= 2 <= 8.
In general, the length of the sum is somewhere inbetween, and can be
thought of in terms of a triangle, which is how the inequality gets
its name. If |a| is the length of one side of a triangle, and |b|
is the length of the second side, then |a+b| is the length of the
third side, and lies somewhere within the range shown above.
Back to fractals. The two numbers of interest are z^2 and c. Given
z (the previous iterate) and c (the Mandelbrot or Julia parameter),
the range for the magnitude of the new iterate can then be determined.
With this range, the magnitude of the new iterate can be rescaled to
a fraction between 0 and 1 inclusive:
min = ||z_old^2| - |c||, max = |z_old^2| + |c|,
z_new = z_old * z_old + c
fraction = (|z_new| - min) / (max - min).
This fraction is then scaled into an angle for coloring with the
decomposition method.
In the triang formulas (_man and _jul variations), this operation
is performed on the last iterate. The triangcount formulas compute
the fraction at every iteration, and color the image based on the
average fraction (over all iterations).
}
triangle-sample { ; copyright Kerry Mitchell 09feb98
reset=1960 type=formula formulafile=fractint.frm
formulaname=triang_jul center-mag=0/0/0.85 params=-0\
.735038819963/0.14041387858/4/0/7/0 float=y maxiter=256
inside=0 decomp=256 periodicity=0 colors=000<41>0x00z\
00y0<39>020000001<42>00x00z00y<39>002000100<40>z00<40\
>200 cyclerange=0/255 passes=1
}
triangcount-sample { ; copyright Kerry Mitchell 09feb98
reset=1960 type=formula formulafile=fractint.frm
formulaname=triangcount_jul passes=1 center-mag=-0.2\
19856/0.463628/3 params=-0.0573720519293145/0.669193\
9992424446/1e012/0/0/3 float=y maxiter=2000 inside=0
decomp=256 periodicity=0 colors=000<41>0x00z00y0<39>\
020000001<42>00x00z00y<39>002000100<40>z00<40>200
cyclerange=0/255
}
frm:triang_man { ; Kerry Mitchell 11feb98
; real(p1) = bailout (try 1e12)
; imag(p1) = unused
; real(p2) = inner coloring speed (0 for outer only)
; imag(p2) = outer coloring speed (0 for inner only)
; use decomp=256
zc=pixel, c=pixel, rc=cabs(c), iter=1
r2zc=|zc|, maxr=real(p1)
inspeed=real(p2)*pi*255/128
outspeed=imag(p2)*pi*255/128:
iter=iter+1, z2=sqr(zc)+c, rz2=cabs(z2),
fac=abs(r2zc-rc), q=(rz2-fac)/(r2zc+rc-fac)
zc=z2, r2zc=|zc|
if (iter==maxit)
angle=inspeed*q
z=cos(angle)+flip(sin(angle))
iter=-1
endif
if (r2zc>maxr)
angle=outspeed*q
z=cos(angle)+flip(sin(angle))
iter=-1
endif
iter>0
;
; Colors Mandelbrot set by magnitude of last iterate
; within a range determined by the triangle inequality.
; Take location in range and scale into an angle for
; decomp coloring. Decouple inside from outside by
; setting appropriate coloring speed to 0.
;
}
frm:triang_jul { ; Kerry Mitchell 11feb98
; p1 = Julia parameter
; real(p2) = bailout (try 1e12)
; imag(p2) = unused
; real(p3) = inner coloring speed (0 for outer only)
; imag(p3) = outer coloring speed (0 for inner only)
; use decomp=256
zc=pixel, c=p1, rc=cabs(c), iter=1
r2zc=|zc|, maxr=real(p2)
inspeed=real(p3)*pi*255/128
outspeed=imag(p3)*pi*255/128:
iter=iter+1, z2=sqr(zc)+c, rz2=cabs(z2),
fac=abs(r2zc-rc), q=(rz2-fac)/(r2zc+rc-fac)
zc=z2, r2zc=|zc|
if (iter==maxit)
angle=inspeed*q
z=cos(angle)+flip(sin(angle))
iter=-1
endif
if (r2zc>maxr)
angle=outspeed*q
z=cos(angle)+flip(sin(angle))
iter=-1
endif
iter>0
;
; Colors Julia set by magnitude of last iterate
; within a range determined by the triangle inequality.
; Take location in range and scale into an angle for
; decomp coloring. Decouple inside from outside by
; setting appropriate coloring speed to 0.
;
}
frm:triangcount_man { ; Kerry Mitchell 11feb98
; real(p1) = bailout (try 1e12)
; imag(p1) = unused
; real(p2) = inner coloring speed (0 for outer only)
; imag(p2) = outer coloring speed (0 for inner only)
; use decomp=256
zc=pixel, c=pixel, rc=cabs(c), iter=1
r2zc=|zc|, maxr=real(p1), count=0
inspeed=real(p2)*pi*255/128
outspeed=imag(p2)*pi*255/128:
iter=iter+1, z2=sqr(zc)+c, rz2=cabs(z2),
fac=abs(r2zc-rc), q=(rz2-fac)/(r2zc+rc-fac)
count=count+q, zc=z2, r2zc=|zc|
if (iter==maxit)
angle=inspeed*count/(iter-1)
z=cos(angle)+flip(sin(angle))
iter=-1
endif
if (r2zc>maxr)
angle=outspeed*count/(iter-1)
z=cos(angle)+flip(sin(angle))
iter=-1
endif
iter>0
;
; Colors Mandelbrot set by average value of magnitude
; within a range determined by the triangle inequality.
; Scale average into an angle for decomp coloring.
; Decouple inside from outside by setting appropriate
; coloring speed to 0.
;
}
frm:triangcount_jul { ; Kerry Mitchell 11feb98
; p1 = Julia parameter
; real(p2) = bailout (try 1e12)
; imag(p2) = unused
; real(p3) = inner coloring speed (0 for outer only)
; imag(p3) = outer coloring speed (0 for inner only)
; use decomp=256
zc=pixel, c=p1, rc=cabs(c), iter=1
r2zc=|zc|, maxr=real(p2), count=0
inspeed=real(p3)*pi*255/128
outspeed=imag(p3)*pi*255/128:
iter=iter+1, z2=sqr(zc)+c, rz2=cabs(z2),
fac=abs(r2zc-rc), q=(rz2-fac)/(r2zc+rc-fac)
count=count+q, zc=z2, r2zc=|zc|
if (iter==maxit)
angle=inspeed*count/(iter-1)
z=cos(angle)+flip(sin(angle))
iter=-1
endif
if (r2zc>maxr)
angle=outspeed*count/(iter-1)
z=cos(angle)+flip(sin(angle))
iter=-1
endif
iter>0
;
; Colors Julia set by average value of magnitude
; within a range determined by the triangle inequality.
; Scale average into an angle for decomp coloring.
; Decouple inside from outside by setting appropriate
; coloring speed to 0.
;
}
- -------------------------------------------------------------------------------
Kerry Mitchell
lkmitch@primenet.com
- -------------------------------------------------------------------------------
- -
- ------------------------------------------------------------
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------------------------------
Date: Thu, 12 Feb 1998 03:34:58 -0800 (PST)
From: FIRSTNAME LASTNAME <whookam88@yahoo.com>
Subject: Re: (fractint) orgform
- ---alex dukay <dukay@interlog.com> wrote:
>
> LASTNAME FIRSTNAME
> >Nuff sed?
> As far as I'm concerned your apology is accepted by me...You should
however
> get a spell checker...Why don't you use your real name?
> Alex Dukay
I don't use my real name because incidents like what just happened,
this is also not my primary E-Mqail account. I've learned through 4.5
years of INTERNET experience that sometimes when you piss "some"
people off they don't feel sufficiently releived to just say "I
thought what you did really sucked big time" or "What the hell are you
doing and don't do it again". On occassion I have found some people
obssess on the issue and like to hurl barbs of social discontent (not
to mention bad manners) and even the occassion "MAIL BOMB" i.e.
loading ones mail box with the same inane little message several
hundred time, this with full malice intended. I do sign my name at
the bottom of most messages (James R. McKenzie) so I am not attempting
to be unknown here.
Also FIRSTNAME LASTNAME is my little comlaint about all these danmed
forms we all have fillout on the INTERNET in order to do anything at
all.
As for the spellcheck thing, YAHOO MAIL's is located in their system
and I have a 28.8 DUN connection, I tried about a week ago and it took
ten minutes to get a response at 1:30 am EST. Patience Ain't that
much of a virtue, even if it is I'm not "THAT" virtuous.
James R. McKenzie
And now to upload that full scale TIF format picture of Hadrian's Wall
to the list. 8->
Just kidding.
_________________________________________________________
DO YOU YAHOO!?
Get your free @yahoo.com address at http://mail.yahoo.com
- -
- ------------------------------------------------------------
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------------------------------
Date: Thu, 12 Feb 1998 15:00:17 EST
From: RBarn0001@aol.com
Subject: Re: (fractint) Palette editing
In a message dated 98-02-11 00:18:35 EST, you write:
<< 've gotten used to the palette editor and find it fairly friendly. Maybe
under Truecolor it would make sense for the colors to be in the more
standard RGB coding of 1 to 255, since many of us who run graphics programs
as well are used to seeing colors described that way. I found the palette
in Fractal Orbits a snap to use, but it's fairly similar to the Fractint
palette except for color nomenclature. It took me longer to figure out
what combination of RGB produced what approximate color in the gif-ish
approach fractint uses. >>
Wizzle, and anyone else with an interest:
I am planning in the near future to include a palette editor for Trumand.
Before I start work on it I would like to get some input. I know there is a
wish list already out there, but I would like to hear some pro's, con's and
priorities. In the absence of any input I will implement something like
Makemap as a popup control.
Ron Barnett
- -
- ------------------------------------------------------------
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------------------------------
End of fractint-digest V1 #107
******************************