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fractint-digest        Friday, January 2 1998        Volume 01 : Number 056




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

Date: Thu, 1 Jan 1998 20:53:57 -0600
From: "Tim Wegner" <[e-mail]>
Subject: Re: (fractint) Fractint pausing problem

Morgan asked:

> As far as Fractint _pausing_ during mode switches; are you sure that it
> does? I frequently find that once the monitor has finished switching modes,
> Fractint has already been drawing as if there had been no delay at all.

texsafe=save causes the entire graphics screen to be saved and
restored to a text file. This could result in a pause at high
resolutions when switching between graphics and text modes.

My monitor pauses significantly during video switches without any
help from Fractint. By the time the monitor is through blinking, the
default 320x200 mandelbrot is done <g!>

Tim

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

Date: Thu, 01 Jan 1998 19:20:16 -0800
From: Wizzle <[e-mail]>
Subject: Re: (fractint) Happy New Year!

Les....

I got this set of pars and formulas just fine.....thought you might want to
know....

Angela

At 09:16 PM 1/1/98 -0500, you wrote:
>Dick Amerman wrote:
>
>>> I've been following your trials and tribulations and wonder what it's
>all about.  I don't think the problem is entirely at your end.  I get your
>pars
>and run them with no editing and no problem.<<
>
>Hi, I'm glad somebody's getting them OK <g>
>
>I realised the mess that CompuServe's quoted-printable encoding was causing
>when I downloaded the archive of messages from
><http://www.xmission.com/pub/lists/fractint/> in order to extract the
>posted par files from this list. To my horror, all of mine, plus those from
>other CompuServe users (Sylvie Gallet & Lee Skinner included) were all
>messed up! Postings from just about everyone else were fine.
>I guess your server/software, like CompuServe, decodes Quoted-Printable
>Emails and so strips out the spurious garbage before you read it.
>
>Thanks for the feedback.
>
>Here's a couple of pars for you:
>
>9707A11.GIF        { ; "The Chase"
>                     ;                                      t=  0:08:39.70
>                     ; t=calc time [h:mm:ss.] using a PII-266 at 1600x1200
>                     ; (c)1997 by Les St Clair <[e-mail]>
>  reset=1960 type=formula formulafile=fractint.frm
>  formulaname=acc_man_mod function=cabs/exp passes=1
>  center-mag=-1.60782/-0.00607963/2.224486 params=0.6/0/0.111/0
>  float=y maxiter=300 inside=zmag decomp=256 periodicity=0
>  colors=CC9<7>7CG6DH6DH6DI<15>AITBJTBJUCKUCKVDLVDLW<4>MSaNTbPVdRXe<5>aemc\
>  gocgo<13>pppqqqppq<53>00A00A11B<42>ffiggjiik<14>wwwxxxxwv<10>yrWyqUypSyo\
>  QynNymLzlI<4>yjDxiCxhBxg9xg8<3>wc4vc3vb2ua0t`0<11>eN0dM0cL0aJ0`J0_J0<12>\
>  ID2GC3GC3<5>CC8 cyclerange=0/255
>  }
>
>9708B02.GIF        { ; "Abstract Art"
>                     ;                                      t=  0:01:10.75
>                     ; t=calc time [h:mm:ss.] using a PII-266 at 1600x1200
>                     ; (c)1997 by Les St Clair <[e-mail]>
>  reset=1960 type=formula formulafile=fractint.frm
>  formulaname=lesfrm34 function=tan/tan/atanh passes=1
>  center-mag=-0.0433953/-0.0601106/0.8637208/1/44.999
>  params=1000/0/50/0/50/0 float=y decomp=256
>  colors=oIP<27>E57D56E56<30>`00000<46>000SNF<14>zpastthhh<8>rsstuuuvvwxxx\
>  yyyzz<14>UPISNFSNF<46>zpa<11>bK4<23>vUDwUDwTF<6>uLQuKRtKR<2>pJP
>  cyclerange=0/255
>  }
>
>FRM:acc_man_mod {; Modified Sylvie Gallet formula
>             ; Modified acceleration_man.frm (generalized by Les St Clair)
>             ; use fn1=cabs, fn2=abs for default behaviour
>             ; set p1=0 and p2=0 for default behaviour
>  z2 = r = 0:
>  l = r, z = z2
>  z1 = z*z + pixel +p1
>  vel1 = z1 - z
>  z2 = z1*z1 + pixel +p2
>  vel2 = z2 - z1
>  acc = vel2 - vel1
>  r = fn1(acc)
>  r < 4 && fn2(l - r) >= 0.001
>}
>
>FRM:Lesfrm34 { ; Modified Sylvie Gallet formula
>           ; Modified Gallet-5-08
>           ; Les St Clair 1997
>  z = pixel*pi , x = real(z), y = imag(z):
>   x1 = x - p1*fn1(y + 0.5*fn2(y+fn1(x)) + fn3(p2*x) + fn3*fn1(p3*y))
>   y1 = y - p1*fn1(x + 0.5*fn2(x+fn1(y)) + fn3(p2*y) + fn3*fn1(p3*x))
>   x = x1^pi , y = y1^pi
>   z = (x + flip(y))^pi
>    |z| <= 32
>}
>
>
>Cheers, Les
>
>
>
>
>
>
>-
>------------------------------------------------------------
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>
>

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

Date: Thu, 01 Jan 1998 19:22:04 -0800
From: Wizzle <[e-mail]>
Subject: (fractint) Binary Decompression

Paul Writes....

I still can't send email to the Fractint list, so would you do me
a favor and send this for me?   The subject could be
Re: Binary Decomposition

Thanks!  Paul Carlson
- -------------------------------------------------------------
I haven't seen everthing that's been posted about this and I'm
certainly no guru, but this might help:

trydecomp { ; Paul W. Carlson
    ; Bailout occurs when the absolute value of w exceeds real(p1).
    ; The spacing of the "field lines" is highly sensitive to
    ; this value.  Here absolute value means sqrt(|w|).
    ; A value of 10 will reproduce the pictures for the Mset and
    ; Julia sets in the book _The Beauty of Fractals_.
    w = 0
    c = pixel
    color = 0
    iter = 0
    bailout = 0:
    ;
    w = w * w + c
    IF (sqrt(|w|) > p1)
    bailout = 1
    IF (imag(w) > 0)
        color = 1;
    ELSE
        color = 2;
    ENDIF
    ENDIF
    iter = iter + 1
    z = color - iter
    bailout == 0
}

decomp_mset        { ; Paul Carlson
             ; Reproduces the image on page 74 in
             ; _The Beauty of Fractals_.
  reset=1960 type=formula formulafile=dcomp.frm formulaname=trydecomp
  center-mag=-0.714727/-1.7e-006/0.8130071 params=10/0 float=y
  maxiter=256 inside=0 outside=summ colors=000zzz000<252>000
  }




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

Date: Thu, 1 Jan 1998 20:36:16 -0800
From: "Jay Hill" <[e-mail]>
Subject: (fractint) Re Field lines, monitors and CompuServe mess...

Hi guys,

I am coming up out of DOS to see the email. I've been
making field lines. More on that later Damien. My web page
shows the BINARY decomposition. I agree getting the
exact line needs more bits.  All bits, IMHO, can be gotten
in one simple equation involving log(z).

About the monitor delay. I have a new NEC MultiSync XV 17+
and only get delays at modes above 1024x768.

Sorry for the off-topic here but I'm using MS Internet explorer
email reader on an cable modem (very fast) and I have not
seen the mess-up you all are referring to.  I assume that if
it is real, the remainder of this post should show it. Does
any one see anything wrong with this post? I leave Les' here
for you to see. It came in fine. So I conclude it is not
CompuServe!  Or did MS finally get it right, it can read
garbage?

Jay

- ----------
> From: Les St Clair <[e-mail]>
> To: INTERNET:[e-mail]
> Subject: Re: (fractint) Happy New Year!
> Date: Thursday, January 01, 1998 6:16 PM
>
> Dick Amerman wrote:
>
> >> I've been following your trials and tribulations and wonder what it's
> all about.  I don't think the problem is entirely at your end.  I get your
> pars
> and run them with no editing and no problem.<<
>
> Hi, I'm glad somebody's getting them OK <g>
>
> I realised the mess that CompuServe's quoted-printable encoding was causing
> when I downloaded the archive of messages from
> <http://www.xmission.com/pub/lists/fractint/> in order to extract the
> posted par files from this list. To my horror, all of mine, plus those from
> other CompuServe users (Sylvie Gallet & Lee Skinner included) were all
> messed up! Postings from just about everyone else were fine.
> I guess your server/software, like CompuServe, decodes Quoted-Printable
> Emails and so strips out the spurious garbage before you read it.
>
> Thanks for the feedback.
>
> Here's a couple of pars for you:
>
> 9707A11.GIF        { ; "The Chase"
>                      ;                                      t=  0:08:39.70
>                      ; t=calc time [h:mm:ss.] using a PII-266 at 1600x1200
>                      ; (c)1997 by Les St Clair <[e-mail]>
>   reset=1960 type=formula formulafile=fractint.frm
>   formulaname=acc_man_mod function=cabs/exp passes=1
>   center-mag=-1.60782/-0.00607963/2.224486 params=0.6/0/0.111/0
>   float=y maxiter=300 inside=zmag decomp=256 periodicity=0
>   colors=CC9<7>7CG6DH6DH6DI<15>AITBJTBJUCKUCKVDLVDLW<4>MSaNTbPVdRXe<5>aemc\
>   gocgo<13>pppqqqppq<53>00A00A11B<42>ffiggjiik<14>wwwxxxxwv<10>yrWyqUypSyo\
>   QynNymLzlI<4>yjDxiCxhBxg9xg8<3>wc4vc3vb2ua0t`0<11>eN0dM0cL0aJ0`J0_J0<12>\
>   ID2GC3GC3<5>CC8 cyclerange=0/255
>   }
>
> 9708B02.GIF        { ; "Abstract Art"
>                      ;                                      t=  0:01:10.75
>                      ; t=calc time [h:mm:ss.] using a PII-266 at 1600x1200
>                      ; (c)1997 by Les St Clair <[e-mail]>
>   reset=1960 type=formula formulafile=fractint.frm
>   formulaname=lesfrm34 function=tan/tan/atanh passes=1
>   center-mag=-0.0433953/-0.0601106/0.8637208/1/44.999
>   params=1000/0/50/0/50/0 float=y decomp=256
>   colors=oIP<27>E57D56E56<30>`00000<46>000SNF<14>zpastthhh<8>rsstuuuvvwxxx\
>   yyyzz<14>UPISNFSNF<46>zpa<11>bK4<23>vUDwUDwTF<6>uLQuKRtKR<2>pJP
>   cyclerange=0/255
>   }
>
> FRM:acc_man_mod {; Modified Sylvie Gallet formula
>              ; Modified acceleration_man.frm (generalized by Les St Clair)
>              ; use fn1=cabs, fn2=abs for default behaviour
>              ; set p1=0 and p2=0 for default behaviour
>   z2 = r = 0:
>   l = r, z = z2
>   z1 = z*z + pixel +p1
>   vel1 = z1 - z
>   z2 = z1*z1 + pixel +p2
>   vel2 = z2 - z1
>   acc = vel2 - vel1
>   r = fn1(acc)
>   r < 4 && fn2(l - r) >= 0.001
> }
>
> FRM:Lesfrm34 { ; Modified Sylvie Gallet formula
>            ; Modified Gallet-5-08
>            ; Les St Clair 1997
>   z = pixel*pi , x = real(z), y = imag(z):
>    x1 = x - p1*fn1(y + 0.5*fn2(y+fn1(x)) + fn3(p2*x) + fn3*fn1(p3*y))
>    y1 = y - p1*fn1(x + 0.5*fn2(x+fn1(y)) + fn3(p2*y) + fn3*fn1(p3*x))
>    x = x1^pi , y = y1^pi
>    z = (x + flip(y))^pi
>     |z| <= 32
> }
>
>
> Cheers, Les
>
>
>
>
>
>
> -
> ------------------------------------------------------------
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------------------------------

Date: Thu, 1 Jan 1998 23:52:08 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Humor Hint

>                     ; Email: [e-mail]

Is that hostname for real? If not, people're gonna have a hard time giving
feedback about the PAR!

(BTW it is 11:38. If this thing bounces but goes through at 12:01, we'll
know for sure about the list having some kind of offpeak time restriction.)

- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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

Date: Wed, 31 Dec 1997 00:28:26 -0500
From: "Blake Hyde" <[e-mail]>
Subject: Re: (fractint) My Web Pages (again)

I don't think that's enough links, Paul. I mean, what's 500 or so? <notes
that he might actually have the complete text up in about 5,000 years>


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

Date: Fri, 2 Jan 1998 00:24:45 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) The weirdest bird off the planet

[snip]

Thanks for the formula.

[12:10...see if this fails to bounce but the first one bounces]

Anyone else notice how a lot of very weird (and very LONG) formulas with
strange new abilities are coming out now that 19.6 has the If-Then clause?




- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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

Date: Wed, 31 Dec 1997 01:03:01 -0500
From: "Blake Hyde" <[e-mail]>
Subject: Sorry... Was: {Re: (fractint) My Web Pages (again)}

:I don't think that's enough links, Paul. I mean, what's 500 or so? <notes
:that he might actually have the complete text up in about 5,000 years>


Reading this, I noticed that it came across all wrong... it sounds "mean."
it was supposed to be humor. *mutters about needing sleep*


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

Date: Fri, 2 Jan 1998 01:28:18 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Multiple part files

Windows NT? shit. I only have 95, and I'll have a big NT advertising sign
shoved up my butt and twisted before I'll upgrade to NT with its miserable
DOS support.



- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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

Date: Fri, 2 Jan 1998 01:34:51 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) My new homepage!

><DIV><FONT color=3D#000000 size=3D2>    Please come an d =
>lok at my=20
>new webpages dedicated to my fractals, its still under construction so =
>please=20
>forgive the speed (fairly slow).  I will speed it up by and=20
>by.</FONT></DIV>
><DIV><FONT color=3D#000000 size=3D2>    Please let me =
>know what you=20
>all think.</FONT></DIV>

Guy posts in HTML(:P), asking us to see his fractal page, and then
neglects to supply the URL. Ladies and gentlemen, we have a newbie!


- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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

Date: Fri, 02 Jan 1998 01:40:54 -0500
From: Gedeon Peteri <[e-mail]>
Subject: Re: (fractint) Happy New Year!

Les, here is another report on your pars.  I received all of them completely
without "spurious garbage."  However, in all of them some lines, and in Happy
New Year! all lines were double spaced. I certainly don't mind editing your
pars, however. I generated all of them. Great images!  HNY!, both the image and
the formula, are amazing!  Gedeon.




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

Date: Fri, 2 Jan 1998 06:39:40 -0000
From: "Bagpuss" <[e-mail]>
Subject: Re: (fractint) My new homepage!

>
>Guy posts in HTML(:P), asking us to see his fractal page, and then
>neglects to supply the URL. Ladies and gentlemen, we have a newbie!
>
>
That post was a draft, which got sent by accident.
I apologise for the HTML, I just assume that everyone can read it, I have no
problems with HTML mail, obviously Im wrong.  I sent another message about 5
minutes later with the URL.  In case you didnt get it its:-
                    http://homepages.iol.ie/~bagpuss/

Again I apologise for the mixup.  As for newbie, im fairly new to fractals,
but i have been using Email since before there was a World Wide Web, back in
the bad old days when VMS/CMS was the norm, and UNIX was heavensent!


        Stephen


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

Date: Fri, 2 Jan 1998 01:47:05 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) A Wizzle-ish New Year

Football? WTF do footballs have to do with New Year's?


- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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

Date: Thu, 01 Jan 1998 23:06:28 -0800
From: Wizzle <[e-mail]>
Subject: Re: (fractint) My new homepage!

Stephen....

Your original email came thru to me looking like an email....but I have
gotten some that looked like html code now and again.....I always wondered
what was happening and now I have a glimmer ........what email program do
you use that makes code like that??

Didn't you ask about pointers for color maps???  I think I forgot to
answer.....the way I got started was by reading Linda Allison's
lessons.....they are posted at my website.  My first color maps were really
pathetic so I used hers for a while until I could relate a map....and what
I wanted to achieve....with the fractal image.  But I'm still
learning....and I usually spend time looking at the color maps that are
generated by folks here.....I've gotten lots of great ideas....especially
from Paul Carlson.

Angela

At 06:39 AM 1/2/98 -0000, you wrote:
>
>
>>
>>Guy posts in HTML(:P), asking us to see his fractal page, and then
>>neglects to supply the URL. Ladies and gentlemen, we have a newbie!
>>
>>
>That post was a draft, which got sent by accident.
>I apologise for the HTML, I just assume that everyone can read it, I have no
>problems with HTML mail, obviously Im wrong.  I sent another message about 5
>minutes later with the URL.  In case you didnt get it its:-
>                    http://homepages.iol.ie/~bagpuss/
>
>Again I apologise for the mixup.  As for newbie, im fairly new to fractals,
>but i have been using Email since before there was a World Wide Web, back in
>the bad old days when VMS/CMS was the norm, and UNIX was heavensent!
>
>
>        Stephen
>
>
>-
>------------------------------------------------------------
>Thanks for using Fractint, The Fractals and Fractint Discussion List
>Post Message:   [e-mail]
>Get Commands:   [e-mail] "help"
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>Unsubscribe:    [e-mail] "unsubscribe fractint"
>
>

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

Date: Fri, 2 Jan 1998 01:57:16 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) New Year's Wish List

>stuck with NT at w*rk)

W*rk? I've never heard of w*rk in my life. What is it? It sounds like it's
a place, from the context...

:-)

- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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

Date: Fri, 2 Jan 1998 02:03:34 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Binary decomp...256 decomp...*continuous

>So I tried it with Julia sets.  And what I discovered is that it works as
>long as the imaginary component of C is zero.  Then it works spectacularly
>well.  But as soon as the imaginary component becomes non-zero (as it does
>for most points in the M-set!) then it stops working and you start seeing
>all kinds of weird hyperbolic-like errors.  Interesting, but not right!
>
>If you have successfully made this work, even in custom code, I'd love to
>see it.


Not even attempted yet. ProtoMatter hasn't reached that stage. The first
real "smoke test", a plain LSM Mandelbrot, isn't even in store for a few
weeks yet!


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Date: Fri, 02 Jan 1998 01:35:08 -0600
From: "Paul N. Lee" <[e-mail]>
Subject: Re: Sorry... Was: {Re: (fractint) My Web Pages (again)}

Blake Hyde wrote:
>
> : I don't think that's enough links, Paul.  I mean,
> : what's 500 or so?  <notes that he might actually
> : have the complete text up in about 5,000 years>
>
> Reading this, I noticed that it came across all wrong...
> it sounds "mean."  it was supposed to be humor.
> *mutters about needing sleep*
>

Your lucky you sent this second message.  I was about to send you the
other four volumes of Fractal Related Links.  ;-}

P.N.L.

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Date: Wed, 31 Dec 1997 02:50:09 -0500
From: "Blake Hyde" <[e-mail]>
Subject: Re: Sorry... Was: {Re: (fractint) My Web Pages (again)}

:other four volumes of Fractal Related Links.  ;-}

Where did you find this anyway?
And do all fractal ppl stay up late?


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Date: Fri, 2 Jan 1998 03:20:07 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) another 24-bit coloring idea

>I don't want the decomp angle, it is incorrect!  It does not use atan2.
>It looks like I want imag(log(z)).

It's an approximation isn't it, closer as the bailout increases.

>Well it should not work.  The description is wrong or confusing, I'll
>check for which tonight.  IMHO, what you do is iterate until you bailout.
>Then color = white if imag(z)>0 else color = black.  Or the other way
>around... :^).  Should be simple using the deep dark secrets in this post,
>but I won't tell!   :-)

*ahem* Wrong or confusing? Since when am I confusing? :-)
You seem to be thinking of binary decomp. I'm thinking of the process of
decomp, binary, then 4-fold, up to Fractint's limit of 256-fold, carried
to the limit.


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Date: Fri, 2 Jan 1998 03:24:52 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Algorithm Reply

>Actually... it was a typo.  Sorry!  :)

Yeah, spammers can't harvest lists and we Fractint Men could stand to meet
more intelligent young women ;) Then we wouldn't need to amuse ourselves
with gynecological fractals, as we could have fun with the real thing. :-)
(Too bad I live in Ottawa, and none of the intelligent young women on this
list seem to hail from anyplace closer than New York... not that I'd
expect to encounter anyone else from this little shithole of a city
anyways, except Mike, who a) is not female and b) heard about this list from
me--or was it the other way around?)


Typo huh? Get a halfway decent mail program, then you don't have to type
it every time you send a msg, only once. :-)


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Date: Fri, 2 Jan 1998 03:47:02 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) My Web Pages (again)

Mine's in my .sig :-)


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Date: Fri, 2 Jan 1998 04:28:00 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Fractint pausing problem

Did you get a new monitor? Some monitors are faster and quieter at syncing
different modes than others. (Modes with different numbers of pixels down,
require the monitor sync to change. Text is usually displayed at 640x480.
You may be fractalling at 1024x768 or something. So the scanlines changes
and the monitor changes frequency every time you switch modes.)


Note: ProtoMatter will remain in graphics mode throughout execution, so
this problem won't exist with it.


Have you tried using the old monitor with the new machine?


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Date: Fri, 2 Jan 1998 04:29:00 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Champagne Swirl

>and the Quad formula

HEY! I've been working on a new formula named Quad. The name's taken. Pick
a new one please. :-)


I love quad... ehehehehehe!


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Date: Fri, 2 Jan 1998 04:29:52 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) text editor

Define "nasty peculiarities" :-)


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Date: Fri, 2 Jan 1998 04:31:09 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Bitmap randomizer

>Does anyone know of a freeware bitmap randomizer for Win95? Thanks!--Alice

One word: Panorama32.

(I don't HAVE the URL. Someone follow up and post it please.)


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Date: Fri, 2 Jan 1998 04:46:59 -0500
From: "Jason Hine" <[e-mail]>
Subject: Re: Sorry... Was: {Re: (fractint) My Web Pages (again)}

Blake queried:
>And do all fractal ppl stay up late?

No, some of us get up early instead! :)
Jason


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Date: Fri, 2 Jan 1998 05:32:49 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Formula Question

>Is it a geometry thing? Or Trig? *sigh*

No, no, it's not geometry or trig... it's far, far, worse.

It's calculus.


<listens to various modems hanging up and NO CARRIERs popping on people's
terminals, one heart attack, two burst cerebral aneurysms, and five
nervous breakdowns>

Okay, those of you still listening: The best formulas for iteration have
multiple critical points; places where the deriuvative (consult your
entry-level calculus text) goes to zero. The rest have one, but never ever
ever zero.

Take the regular M-set formula. It is z^2+c. The derivative is 2z, which
is zero when z is zero (twice nothing's still nothing). Thus, it has one,
so there are fascinating julia sets more than likely (and indeed there
are) and an M-set. The Julia sets are obtained by fixing a value for 'c',
different for each Julia set, and varying z to get an image:

z=pixel, c=p1:
z=sqr(z)+c,
lastsqr<p2


The M-set is had by setting z=0, the critical point, and varying c:

z=0, c=pixel:
z=sqr(z)+c,
lastsqr<p2

Now look at the formula z^3-3*c*z+c. The derivative is 3z^2-3*c, or z^2=c,
or z=+/- sqrt(c). Thus there are two critical points. Each gives an M-set:

c=pixel, z=sqrt(c):
z=sqr(z)*z-3*c*z+c,
lastsqr<p2

c=pixel, z=-sqrt(c):
z=sqr(z)*z-3*c*z+c,
lastsqr<p2

And Julia sets like so:

c=p1, z=pixel:
z=sqr(z)*z-3*c*z+c,
lastsqr<p2


Also, to avoid a solid black screen, make sure the thing will tend to
infinity for some z!
Polynomials of at least 2nd degree work. Any Newton formula or twist upon
same will work. Any rational where the degree of the numerator exceeds
that of the denominator, or a term that increases with z is added to the
quotient, will work. Trig works because the sin and cos functions go to
infinity for large imaginary values, even though the familiar sine wave is
bounded. That bounded wave is only what goes on on the real axis and isn't
the whole picture.
Logs go to infinity, but too slowly. The derivative should exceed the unit
circle for z bigger than some bound. This means the modulus of f'(z)
should be greater than 1 for z with a modulus exceeding a certain bound.

Note that some formulas e.g. Newton don't adhere to these rules much! They
generate stuff because they still have many attractors. But since all are
finite, things are trickier. You must spot the finite attractors and make
an orbit trap aroun them:

PlainNewton {
  z=pixel:
  z2=sqr(z)
  z=z-(z*z2-1/(3*z2)),
  |z-1|>p2
}

This is the Newton iteration for z^3-1, with an orbit trap around 1. The
last line before the lone close brace is the orbit trap.

For a Newton fractal, an orbit trap of a different type works:

  z2=sqr(z)
  diff=(z*z2-1/(3*z2))
  z=z-diff,
  |diff|>p2

This catches all three attractors. Because the difference between the old
and new z is "diff", if diff gets close to 0 and stays there, z has hit a
point attractor. This thus traps orbits around all three attractors.

If you are unsure of the locations of attractors, or they vary based on c
or are too complicated to bother with (like two of the three in the Newton
iteration above), just trap for a z that stays put:

  oldzed=z
  z=...etc.etc.etc.
  |oldzed-z|>p2

(Note: All of these use p2 as a bailout. If p2 is left the default 0
expect blank looks from your computer! Literally. Instead set a small
value, like 0.001, and use float=y.)

By keeping older zeds:

olderzed=oldzed
oldzed=z
...
|z-olderzed|>p2

you can trap for both fixed point and 2-cycle attractors, whilst making
false alarms with 2-cycles less likely.

Note that for orbit traps around finite attractors, often periodicity=0 is
needed to get a picture at all, or else to get rid of bogus black squares.

You can trap for longer cycles without doing any work at all by
capitalizing on Fractint's periodicity checking. This time leave
periodicity ON! All you have to do is have no orbit traps at all (except
maybe at infinity), count iterations (iter=0, ..., iter=iter+1,...), and
then on termination have your thing set z to iter on the last iteration,
or 0 if iter==maxiter. Generate using outside=iter, inside=zmag, and
you'll get any infintie basin colored by iteration, any finite basins
colored by iteration, and points that never were trapped by periodicity
cheking colored color zero.


When you're making formulas, calculus is your friend.


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 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
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End of fractint-digest V1 #56
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