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fractint-digest       Monday, December 29 1997       Volume 01 : Number 047




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

Date: Sun, 28 Dec 1997 15:51:24 -0800
From: Wizzle <[e-mail]>
Subject: (fractint) Jay's variation

P. S.

I do think Jay managed to find a "sexist" variation on my
image....<<<<snikker>>>>> Nice ....um....phrallic choice of colors.  I'm
gonna have to go find a fem counterpart....I didn't know phractals could be
so stimulating.

Angela

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Date: Sun, 28 Dec 1997 19:27:01 -0800
From: Peter Jakubowicz <[e-mail]>
Subject: Re: (fractint) 3D_Balls_Mset

At 09:36 AM 12/28/97 -0500, you wrote:
>  Here's another formula and par from Paul Carlson.  I hope
>it gets through:   - Lee Skinner

Thanks, it did, it's way cool. Did you both work on these? Or are you just
posting for Mr Carlson. BTW, how does one reach Mr Carlson. If I am not
mistaken, he is the man who recently released a program to merge GIFs into
PNGs that I have find very neat. Peter


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Date: Sun, 28 Dec 1997 16:23:56 -0800
From: "Jay Hill" <[e-mail]>
Subject: Another warning. was Re: (fractint) DEEPER Program

Jason Hine <[e-mail]> wrote:
> Jay scorned:
> >
> >Not happy with DEEPZOOM I wrote several years ago?
> >So you wrote DEEPER?  :-)   Well fine!
> >
>
> Actually, Jay, DEEPER *is* DEEPZOOM with  an extra
> semicolon... ;^)
> But really, I'm not sure I've seen DEEPZOOM - can I can I
> can I?
>
> And thanks! for the info on aborting a batch file... I'm
> sure it'll come in handy!
> laters, Jason

Handy, indeed, if we only could...............please read.  :-)

Hello Fractintiers and DeepZoomers,

For your enjoyment and WARNING - a little history.........

DEEPZOOM(tm) was introduced to the world back in '93.  It has since
been stored in a vault at Spanky, but now that it has been rendered
harmless, it is lately available at my page (you will understand):
http://www.geocities.com/CapeCanaveral/Lab/3825/Software.htm

Someone in Alaska had bragged of zooming to 44 digits using BASIC.
Another complained of a deep zooming program that set you back
$90 (a lot in those days).  $90, and 44 digits!  I could not stand it, so
that very evening I wrote DEEPZOOM. The next day I released it upon
the world.  Oh, if only I had known....

Arthur Clarke had warned us.

A lively discussion followed as 13 versions were announced.  I
quote here a few postings from that time in the distant past which
included repeated warnings and even an example 70 digit zoom. In
those days of 486/66 machines, there was little hope for any who
caught Zoom Fever.  Machines and eyes were locked up for days
as the little white dot slowly crossed the screen.

The fever was speading.  Those who could not get it, wanted it.  I tried
to control the technology, only releasing executables and hints of how
it was coded.  But it was unstoppable!  It was only a matter of time...

Finally, extended math was added to Fractint, dooming my DeepZoom
and all (about 270) who had a copy of DeepZoom. DeepZoom's grasp was
replaced by an even tighter grip, Fractint's, which even the fastest Pentiums
have not broken.   And now, with Deeper.exe, our fate is sealed.  We
are caught in the trap where not even a twitch of the finger is required
as the lock is now automatically maintained through ever deeper zooms.
It only takes the pressing of a single key to release us, but not one of us
can make the slightest move.  The body becomes totally frozen as
the eyes search the depths for the tinniest midget....

Oh, if only I had known....

Jay "Not tonight honey, I'm with the guys planning another ZOOM" Hill
- --
main(){int f,g,h=0;float a,b,c,d,e;for(;h<3920;putchar("!/-,;<:lnb/bh`r\
/ylqbAmmhI/S/x`K\013"[++h>3840&&g<25?31-g:g>79?31:f]^1))if((f=(256*(c=(d
=(g=1+h%80)/31.-2)*d+(e=.047*(h/80-24))*e)-96)*c+32*d<3?24:16+32*d+16*c<
1?30:0)==0)for(a=d,b=c=0;(b=2*b*c+e)*b+(c=a)*a<=4&&++f<26;a=d-b*b+c*c);}

================= HISTORY =================
>From ast.saic.com!jupiter!hilljr Fri Oct 22 10:58:21 1993
Article: 2126 of sci.fractals
Newsgroups: sci.fractals,bit.listserv.frac-l
Path: ast.saic.com!jupiter!hilljr
From: [e-mail] (Jay R. Hill)
Subject: Re: Have we seen it all?
Message-ID: <[e-mail]>
Followup-To: sci.fractals
Lines: 47
Sender: [e-mail]
Organization: SAIC
References: <[e-mail]> <29mbqa$[e-mail]>
<[e-mail]>
Date: Wed, 20 Oct 1993 00:02:37 GMT

In article <[e-mail]>,
[e-mail] (Jay R. Hill) writes:
|> In article <29mbqa$[e-mail]>,
  [e-mail] (Jeff Epler) writes:
|> |> [e-mail] (Jay R. Hill) writes quoting from Robert Munafo
  on FRACT-L:
|> |>
|> |> >>Distance-Estimator method, and setting it to view the area of
|> |> >>the complex plane centered at
|> |>
|> |> >  -1.769 110 375 463 767 386 0  +  0.009 020 388 228 023 439 7i
|> |>
|> |> >>with an edge length (height and width) of 6.4e-17 .  Make sure
|> |> >>the number of iterations is at least 10,000.
|> |>
|> |> Anybody get this to go with Xfractint?  I'm using it on a Linux 386
|> |> machine, and it always rudely dumps me back to the shell prompt after
|> |> I enter those center coords and a magnification of 1.5625e16.  (I've
|> |> had other problems with xfractint, my binary may just have problems.)
|>
|> To get this view you need 80 bit floats such as that provided by INTEL.
|> I rolled my own code in C++ (also you can use Turbo Pascal) using
|> long double.  If you are stuck with double, you only get 54 bits mantissa
|> or 10^-16 resolution.
[...]

OK, listen up all you lerkers and quiet observers of the chaos and orbiting
articles on sci.fractals.  Are we just going to sit and complain about not
enough bits?  --  No!  You want more bits - for free?  YES!  Just send me
email and I'll send you version 0.01 MSDOS executable of a 70 digit zoomer
I wrote last night.  It comes with only one guarantee: it will take up even
more of you 486/66 CPU time than ever before ;-)   It runs at about 300
iterations of z := z^2 + c per second, requires SVGA and patience.  Send
me email and I'll hit you with 2 uuencoded files of total 79K.  It is a
zip file (pkzip1.1).  You get to choose the picture size from 1x1   :-)
up to 1024x768.  I adjust SVGA mode, jumping from 320x200 to 320x400 to
460x480 to 800x600 to 1024x768 as needed.

Now remember, it is one day old and free, so be kind.


Jay
- --
{ [e-mail] } begin writeln(3*ln(640320)/sqrt(163):17:15) end.
void main(){double sqrt(), y=1/sqrt(2.), a=.5, m=1,z; int n=0;
for(;m*=2,z=sqrt(1-y*y),y=(1-z)/(1+z),a=a*(1+y)*(1+y)-m*y,n<4;n++);
printf("%17.15lf\n",1/a);}


>From ast.saic.com!jupiter!hilljr Mon Dec 13 13:39:23 1993
Article: 2483 of sci.fractals
Newsgroups: sci.fractals,bit.listserv.frac-l
Path: ast.saic.com!jupiter!hilljr
From: [e-mail] (Jay R. Hill)
Subject: A warning to DEEPZOOMers
Message-ID: <[e-mail]>
Followup-To: sci.fractals
Sender: [e-mail]
Organization: SAIC
Date: Mon, 13 Dec 1993 19:44:00 GMT

       A warning to DEEPZOOM users.

Few can forecast the effects of technology on our futures as well
as Arthur C. Clarke.  Since he has written of at least one who
zoomed too deep once too often, we might want to be careful.  In
his 1990 novel _The Ghost from the Grand Banks_, he describes one
Edith Craig at the Torrington Clinic for psychological disorders,
who is mentally locked in a 40 digit deep zoom into the Mandelbrot
Set.

Hmmmm.  There are now about 70 who have gotten my DEEPZOOM program.
In the novel Clarke notes that "there are no less than sixty-three
examples of Mandelmania now in the data banks."

Warmly,
Jay "Not tonight honey, just another factor of ten, just..." Hill
- --
{ [e-mail] } begin writeln(3*ln(640320)/sqrt(163):17:15) end.
void main(){double sqrt(), y=1/sqrt(2.), a=.5, m=1,z; int n=0;
for(;m*=2,z=sqrt(1-y*y),y=(1-z)/(1+z),a=a*(1+y)*(1+y)-m*y,n<4;n++);
printf("%17.15lf\n",1/a);}


>From mvb.saic.com!ast.saic.com!jupiter!hilljr Fri Dec 17 17:28:59 1993
Article: 2528 of sci.fractals
Newsgroups: sci.fractals,bit.listserv.frac-l
Path: mvb.saic.com!ast.saic.com!jupiter!hilljr
From: [e-mail] (Jay R. Hill)
Subject: Re: A warning to DEEPZOOMers
Message-ID: <[e-mail]>
Followup-To: sci.fractals
Keywords: Mandelbrot, chaos
Lines: 86
Sender: [e-mail]
Organization: SAIC
References:  <[e-mail]>
Date: Thu, 16 Dec 1993 00:53:13 GMT

In article <[e-mail]>,
   [e-mail] (Jay R. Hill) writes:
|>        A warning to DEEPZOOM users.
|>
|> Few can forecast the effects of technology on our futures as well
|> as Arthur C. Clarke.  Since he has written of at least one who
|> zoomed too deep once too often, we might want to be careful.  In
|> his 1990 novel _The Ghost from the Grand Banks_, he describes one
|> Edith Craig at the Torrington Clinic for psychological disorders,
|> who is mentally locked in a 40 digit deep zoom into the Mandelbrot
|> Set.
|>
|> Hmmmm.  There are now about 70 who have gotten my DEEPZOOM program.
|> In the novel Clarke notes that "there are no less than sixty-three
|> examples of Mandelmania now in the data banks."
|>
|> Warmly,
|> Jay "Not tonight honey, just another factor of ten, just..." Hill

In an email I was asked:
> A naive question at a late date: what's Mandelmania?

In the novel, MSet pictures were everywhere by the turn of the
century.  Some people just couldn't handle the infinite detail
and beauty.  They had to see it all, experience it all.  Some
let it get to the point of an incurable Mandelmania.  No cure.
Well, about 80% make an 'adjustment' back to normality by use
of medications and for some, as Clarke indicated, implants - duuh.


The real line portion of the Mandelbrot Set provides an exhibit
of several types of iteration behavior.  Outside of the interval
(-2..0.25) iteration diverges.  An example of a Misiurewicz point
is -2.  Then inside the buds and cardioids the iterations become
periodic.  On the edge of a bud or cardioid iteration convergence
is very slow since the Lyapunov exponent is 0.  Other points are
chaotic with Lyapunov exponents greater than 0.  But the Lyapunov
exponent is defined in the limit of infinitely many iterations.
Without carrying the calculation to infinity, can we determine if
an arbitrary point is chaotic?  I doubt it.  Aha!  An excuse to ZOOM!

The Lyapunov exponent for c=-1.8 is approximately 0.4046 which
certainly looks chaotic.  I wondered what the MSet looks like if I
repeatedly zoom in on such a chaotic point.  So I used DEEPZOOM to
do just that.  With -1.8 in the center, each increase in magnification
shows the point -1.8 missing midgets repeatedly, with small ones
near -1.8 always moving just out of reach.  Finally, at 10^68
magnification I moved the focus over a pixel or so to a midget
right next to -1.8.  The final view at 10^70 magnification is shown
in 18000000.gif which I just posted to alt.binaries.pictures.fractals.
The gif took more than two days to compute on my 486/33.  The deepzoom
parameters were

maxiter = 3200076
x =
- -1.79999999999999999999999999999999999999999999999999999999999999999941756
y  =  962e-72
dx = 1280e-72
dy =  960e-72

My warning post (see above) got a few interesting replies.  Alas, it
looks like it's too late.  One reply was, in part, "...seeing as how my
brain is already warped and locked into a permanent ZOOM state...".

And this. "You can add me to the 'mentally locked up Mandelbrot Zoomers
Set'.  I have recently downloaded DEEPZOOM, and have started playing
with it.  It's great.  This program is just another great reason to
leave my computer on all night."

The current version, 0.10, has an improved color scheme using 108
rainbow colors before repeating.  Also, I have added a sleep mode
which aids TSR screen grabbers.  In four days, DEEPZOOM will be two
months old and is still FREE.  ;-)  Maybe by then (Real Soon Now) I
will add gif-ability.  Then automatic generation of a gif sequence
which can be used for an mpeg ought to really jam my machine.  If we
magnify by a factor of two, there are obvious reuse of calculations
from the last view.  There should be information reuse even if the
magnification jump is 15%.  Any ideas?

Warmly,
Jay "Not tonight honey, I'm stuck at magnification 10^70" Hill
- --
{ [e-mail] } begin writeln(3*ln(640320)/sqrt(163):17:15) end.
void main(){double sqrt(), y=1/sqrt(2.), a=.5, m=1,z; int n=0;
for(;m*=2,z=sqrt(1-y*y),y=(1-z)/(1+z),a=a*(1+y)*(1+y)-m*y,n<4;n++);
printf("%17.15lf\n",1/a);}




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

Date: Sun, 28 Dec 1997 19:40:09 -0500
From: Lee Skinner <[e-mail]>
Subject: (fractint) Paul's 4th frm & par

Wizzle wrote:

> I was looking at Paul Carlson's homepage and got to wondering if we had=

>the formula he used......
>
> Clifford Pickover's quartic variation of Ushikis's "Phoenix" Julia set
> equations: Z =3D Z*Z - .5Z + C, X =3D Z*Z - .5Y + C, Y =3D Z, Z =3D X

That equation is not part of Fractint, but I just translated it into
a Fractint formula, along with a par file to try it out.  Here it is:

3D_Phoenix_Spirals {; Copyright (c) Paul W. Carlson, 1997
    ;****************************************************
    ; Always use floating point math and outside=3Dsumm.
    ;
    ; Parameters:
    ;   p1       =3D coordinates of the Julia set
    ;   real(p2) =3D number of color ranges
    ;   imag(p2) =3D number of colors in each color range
    ;
    ; Note that the equation variable is w, not z.  Always
    ; initialize z to zero.
    ;****************************************************
    prev_w =3D y =3D pixel
    c =3D p1
    z =3D 0
    bailout =3D 0
    iter =3D 0
    range_num =3D 0
    ;****************************************************
    ; In the accompanying par file, phxspirs.par,
    ; we have 2 color ranges with 125 colors in each range
    ; for a total of 250 colors. The first range starts at
    ; color 1.  Pixels will use color 255 when w < 1.0.
    ; Other values can be used here as long as the product
    ; of num_ranges times colors_in_range is less than 255.
    ;****************************************************
    num_ranges =3D real(p2)
    colors_in_range =3D imag(p2):
    ;****************************************************
    ; The equations being iterated.
    ;****************************************************
    w =3D prev_w * prev_w - 0.5 * prev_w + c
    b =3D w * w - 0.5 * y + c
    y =3D w
    w =3D b
    ;****************************************************
    ; If w exceeds a value of 1.0, set z to the index
    ; into the colormap and set the bailout flag.
    ;****************************************************
    IF (w > 1)
    ;***************************************************
    ; Compute the angle between the last 2 orbit points
    ;***************************************************
    delta_i =3D imag(w) - imag(prev_w)
    delta_r =3D real(w) - real(prev_w)
    angle =3D abs(atan(delta_i / delta_r))
    IF (delta_r < 0)
        angle =3D pi - angle
    ENDIF
    bailout =3D 1
    range_index =3D 2 * colors_in_range * angle / pi
    z =3D range_index + range_num * colors_in_range + 1
    ENDIF
    ;***************************************************
    ; Update previous value of w
    ;***************************************************
    prev_w =3D w
    ;****************************************************
    ; 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 =3D range_num + 1
    IF (range_num =3D=3D num_ranges)
        range_num =3D 0
    ENDIF
    ;****************************************************
    ; Since we are using outside=3Dsumm, we have to subtract
    ; the number of iterations from z.
    ;****************************************************
    iter =3D iter + 1
    z =3D z - iter
    ;****************************************************
    ; Finally, we test for bailout
    ;****************************************************
    bailout =3D=3D 0
}


phxspirs           { ; Copyright (c) Paul W. Carlson, 1997
  reset=3D1920 type=3Dformula formulafile=3Dphnxspir.frm
  formulaname=3D3d_phoenix_spirals passes=3Dt
  corners=3D0.52418/0.54062/0.01183/0.02416
  params=3D0.563/0/2/125 float=3Dy maxiter=3D322 inside=3D255
  outside=3Dsumm colors=3D000zVz<123>G0GVzz<123>0GG000<3>000
  }

Also, none of the URLs below are my homepage, as such.  I can't
write to any of them - they are all maintained by others.  I hope
to set up a page of my own in the near future.  The fractal.mta.ca
site has no text, but it has by far the most fractals (about
300 1024x768 resolution images) and is the only site that has my
latest stuff.

Regards,
Paul Carlson
- ------------------------------------------------------------------
                email   [e-mail]

WWW Fractal Galleries   http://sprott.physics.wisc.edu/carlson.htm
                        http://fractal.mta.ca/fractals/carlson/
                        http://www.cnam.fr/fractals/carlson.html
- ------------------------------------------------------------------

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

Date: Sun, 28 Dec 1997 19:50:34 -0500
From: Lee Skinner <[e-mail]>
Subject: (fractint) 3D_Balls_Mset

Peter,

>>Thanks, it did, it's way cool. Did you both work on these? Or are you
just posting for Mr Carlson. BTW, how does one reach Mr Carlson. If I am
not mistaken, he is the man who recently released a program to merge GIFs=

into PNGs that I have find very neat. <<

Paul did it solo.  He was having trouble posting to the list, so he asked=

me to do it for him.  Apparently he can read the list.  His e-mail addres=
s
apprears at the end of the messages I've posted for him.  Yes, he is the
one who wrote GIFS2PNG.EXE.  - Lee

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

Date: Sun, 28 Dec 1997 21:02:39 -0500
From: "Jason Hine" <[e-mail]>
Subject: Re: Another warning. was Re: (fractint) DEEPER Program

Jay belaboured:
>It only takes the pressing of a single key to release us,
but not one of us
>can make the slightest move.  The body becomes totally
frozen as
>the eyes search the depths for the tinniest midget....
>
>Oh, if only I had known....

>Jay "Not tonight honey, I'm with the guys planning another
ZOOM" Hill
>--

No! Nooooo!  All we need are faster computers, and,... and
synchronous orbits, and,...
hardware fractal engines, and THEN we'll be ok, right?...
RIGHT???  AUUUGH!!!!!
As PHiSH once intoned, 'You'll never get out of this
maze'... they obviously hadn't heard of fractals!  Zooming
my life away,
Jason


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

Date: Sun, 28 Dec 1997 18:34:49 -0800
From: Wizzle <[e-mail]>
Subject: Re: (fractint) Paul's 4th frm & par

Thanks Paul...but...Yipes!!!!

I'm only a beginner...where do I put what????? I have no idea what to do
with ifs....

So far I've stuffed the pars I find here into a web1.par file and the
accompanying .frm into a separate file in my \fractint
directory.....help!!!!!!

I can't tell what is what in the information you gave but am VERY anxious
to be able to play with this set of thingys

Angela aka wizzle


At 07:40 PM 12/28/97 -0500, you wrote:
>Wizzle wrote:
>
>> I was looking at Paul Carlson's homepage and got to wondering if we had
>>the formula he used......
>>
>> Clifford Pickover's quartic variation of Ushikis's "Phoenix" Julia set
>> equations: Z = Z*Z - .5Z + C, X = Z*Z - .5Y + C, Y = Z, Z = X
>
>That equation is not part of Fractint, but I just translated it into
>a Fractint formula, along with a par file to try it out.  Here it is:
>
>3D_Phoenix_Spirals {; Copyright (c) Paul W. Carlson, 1997
>    ;****************************************************
>    ; Always use floating point math and outside=summ.
>    ;
>    ; Parameters:
>    ;   p1       = coordinates of the Julia set
>    ;   real(p2) = number of color ranges
>    ;   imag(p2) = number of colors in each color range
>    ;
>    ; Note that the equation variable is w, not z.  Always
>    ; initialize z to zero.
>    ;****************************************************
>    prev_w = y = pixel
>    c = p1
>    z = 0
>    bailout = 0
>    iter = 0
>    range_num = 0
>    ;****************************************************
>    ; In the accompanying par file, phxspirs.par,
>    ; we have 2 color ranges with 125 colors in each range
>    ; for a total of 250 colors. The first range starts at
>    ; color 1.  Pixels will use color 255 when w < 1.0.
>    ; Other values can be used here as long as the product
>    ; of num_ranges times colors_in_range is less than 255.
>    ;****************************************************
>    num_ranges = real(p2)
>    colors_in_range = imag(p2):
>    ;****************************************************
>    ; The equations being iterated.
>    ;****************************************************
>    w = prev_w * prev_w - 0.5 * prev_w + c
>    b = w * w - 0.5 * y + c
>    y = w
>    w = b
>    ;****************************************************
>    ; If w exceeds a value of 1.0, set z to the index
>    ; into the colormap and set the bailout flag.
>    ;****************************************************
>    IF (w > 1)
>    ;***************************************************
>    ; Compute the angle between the last 2 orbit points
>    ;***************************************************
>    delta_i = imag(w) - imag(prev_w)
>    delta_r = real(w) - real(prev_w)
>    angle = abs(atan(delta_i / delta_r))
>    IF (delta_r < 0)
>        angle = pi - angle
>    ENDIF
>    bailout = 1
>    range_index = 2 * colors_in_range * angle / pi
>    z = range_index + range_num * colors_in_range + 1
>    ENDIF
>    ;***************************************************
>    ; Update previous value of w
>    ;***************************************************
>    prev_w = w
>    ;****************************************************
>    ; 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
>}
>
>
>phxspirs           { ; Copyright (c) Paul W. Carlson, 1997
>  reset=1920 type=formula formulafile=phnxspir.frm
>  formulaname=3d_phoenix_spirals passes=t
>  corners=0.52418/0.54062/0.01183/0.02416
>  params=0.563/0/2/125 float=y maxiter=322 inside=255
>  outside=summ colors=000zVz<123>G0GVzz<123>0GG000<3>000
>  }
>
>Also, none of the URLs below are my homepage, as such.  I can't
>write to any of them - they are all maintained by others.  I hope
>to set up a page of my own in the near future.  The fractal.mta.ca
>site has no text, but it has by far the most fractals (about
>300 1024x768 resolution images) and is the only site that has my
>latest stuff.
>
>Regards,
>Paul Carlson
>------------------------------------------------------------------
>                email   [e-mail]
>
>WWW Fractal Galleries   http://sprott.physics.wisc.edu/carlson.htm
>                        http://fractal.mta.ca/fractals/carlson/
>                        http://www.cnam.fr/fractals/carlson.html
>------------------------------------------------------------------
>
>-
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Date: Sun, 28 Dec 1997 18:43:52 -0800
From: Wizzle <[e-mail]>
Subject: (fractint) Homepage Bargain

If anyone wants to set up a fractal homepage.....I highly recommend

www.simplenet.com

For a piddly $10 per month you get unlimited...that's right...space for a
homepage.  With fractal gifs taking up the space they do.... one can use
all the space available.

I have two other providers who dole out 5 and 2 megs.....<<<hurmpf>>> for
homepages.

The $10 is just for homepage space...no email or connect time.  But if you
already have a competitive way to connect.... this can be a bargain. I
think I have about 30 megs of junk at simplenet and they haven't made any
waves.  Note that the files there must be connected to the web...they can't
just be for storage. And for the most part the server is fast and stable.

Angela aka wizzle

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Date: Sun, 28 Dec 1997 22:03:57 -0500
From: Lee Skinner <[e-mail]>
Subject: (fractint) Paul's 4th fr

Angela,

>>I'm only a beginner...where do I put what????? I have no idea what to d=
o
with ifs....  So far I've stuffed the pars I find here into a web1.par fi=
le
and the accompanying .frm into a separate file in my \fractint
directory.....help!!!!!!  <<

And that is exactly what you do with those - 1 frm and 1 par each in thos=
e
postings from Paul.  There are no IFS's there - the if's are just part of=

the formula.

Lee

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Date: Sun, 28 Dec 1997 19:54:49 PST
From: "Martin Hecko" <[e-mail]>
Subject: (fractint) Fractal encryption

Greetings fellow fractal addicts...

I don't know if this topic has been discussed on this list before, but
here is my question.

Could it be possible to use fractals as a way to encrypt information?
How strong the encryption would be?

I have thought of very simple method. For simplicity's sake lets use the
regular mandelbrot formula. The password (or the passphrase) would be
the initial parameters for an iteration.
Then take the first part of plain text, make first iteration of the
formula, run the result through some convenient hash algorithm and xor
the result with the plain text. Repeat the above steps for the rest of
the plaintext.

I don't know if it would work (due to the fact that  the floating point
calculations would have to be converted to integers and this could cause
inaccuracies in results).

I realize that this is not exactly a topic about Fractint itself, but I
think there are many knowledgable people on this list that have
potential to contribute to this discourse.


Martin
(the sunny side of life)
______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com

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Date: Sun, 28 Dec 1997 21:57:42 -0800
From: "Jay Hill" <[e-mail]>
Subject: Re: (fractint) Fractal encryption

Hi Martin,

- ----------
> From: Martin Hecko <[e-mail]>

> I don't know if this topic has been discussed on this list before, but
> here is my question.
> Could it be possible to use fractals as a way to encrypt information?
> How strong the encryption would be?

It has not appeared here, but has been discussed on sci.crypt. Usually
getting a general brush off.

> I have thought of very simple method. For simplicity's sake lets use the
> regular mandelbrot formula. The password (or the passphrase) would be
> the initial parameters for an iteration.
> Then take the first part of plain text, make first iteration of the
> formula, run the result through some convenient hash algorithm and xor
> the result with the plain text. Repeat the above steps for the rest of
> the plaintext.

I have thought about this at length. Here are some specific ideas.
You are suggesting a stream cipher using the MSet as a pseudo-random
number generator.  The key you use is, as you say, the coordinates,
c, in the equation z[n+1]=z[n]*z[n]+c, z[0]=0.

> I don't know if it would work (due to the fact that  the floating point
> calculations would have to be converted to integers and this could cause
> inaccuracies in results).

Floating point must be done with plenty of precision, double (64 bit)
is a minimum.

The main weakness is that the values z[n] are not uniformly distributed.
Although this may be offset by a hash function, it can limit the search
space of the attacker.  Even worse, key values not carefully chosen
lead quickly to divergence to infinity or to a periodic attractor. Only
chaotic c are acceptable. While marginally chaotic c are known
on the boundaries of the components, the only really chaotic values
can be found accurately on the real line.  This greatly limits your key
space - to one dimension.

A possibility of a two dimensional key space might be to include the
initial z[0] as part of the key rather than using z[0]=0.  Care must be
taken that c is in fact not in a bud or cardioid (a component).

For every point that is truly chaotic, a periodic point (in a component)
is only an infinitesimal distance away.  If c is in a component, then
the z[n] sequence is doomed to periodicity.

The Lyapunov exponent is a measure the chaos. But it can only be
estimated by following the sequence to great lengths.  The Lyapunov
exponent will indicate chaotic behavior right up to the point where the
first period is reached. It will then drop in one iteration into non-chaos
values - a disaster if it occurs in your message! Since, at that point
your sequence may start repeating.

A large Lyapunov exponent indicates chaos, which is desirable in the
sequence. However, it also indicates divergence when a very small
perturbation (one bit) occurs incorrectly in the arithmetic. Therefore, the
message sender and receiver must use exactly identical arithmetic
processing. This can be a problem across platforms.

> I realize that this is not exactly a topic about Fractint itself, but I
> think there are many knowledgable people on this list that have
> potential to contribute to this discourse.

> Martin


Jay

PS Taking an off topic penalty.....

brain              { ; A brain after too much crypto thinking
                     ; by Jay Hill, 1997
  reset=1960 type=phoenixcplx
  center-mag=1.1175e-005/-8.65e-007/0.6666663
  params=0.27/0.02/0.25/0.1/0 float=y maxiter=256 outside=atan
  colors=000<62>wwwwwwvvv<61>KKKKKKKKL<76>bbvccwccv<43>112000000000
  }



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Date: Mon, 29 Dec 1997 21:36:01 +1300
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Jay's variation - the fem counterpart?

At 15:51 28/12/97 -0800, Wizzle wrote:
>P. S.
>
>I do think Jay managed to find a "sexist" variation on my
>image....<<<<snikker>>>>> Nice ....um....phrallic choice of colors.  I'm
>gonna have to go find a fem counterpart....I didn't know phractals could be
>so stimulating.
>
>Angela
>
Funnily enough I did once come across a fractal using one of my own formuas
that had a certain - shall we say - gynecalogical look to it.
(Un)fortunately, I didn't save the parameters, and you know what THAT means...
I have a few leads on where I might find it, and if I find it I'll post it up.

MLO



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Date: Mon, 29 Dec 1997 17:02:27 +0800
From: "Vince Easton" <[e-mail]>
Subject: Re: (fractint) Homepage Bargain

Wizzle (as far as I recall, you are a wimmin, handle Angela ?)

I subscribed to your list just before Christmas, and have
been inundated with stuff I have no time to read, as well
as rather inappropriate for your focus, exploding ham
(maybe we could apply that to Spam).

Since I have to separate IETF stuff from yours, how do
I go about changing my mailbox for fractint related to
: [e-mail]  (sorting wheat from the chaff ?).

I like your group, from what I've seen, but using raptop
platform, albeit 2GB disks, I don't space for exploding
ham (Spam might be a different proposition) ...


Thanks, regards,

Vince


- ----------
> From: Wizzle <[e-mail]>
> To: [e-mail]
> Subject: (fractint) Homepage Bargain
> Date: Monday, December 29, 1997 10:43 AM
>
> If anyone wants to set up a fractal homepage.....I highly recommend
>
> www.simplenet.com
>
> For a piddly $10 per month you get unlimited...that's right...space for a
> homepage.  With fractal gifs taking up the space they do.... one can use
> all the space available.
>
> I have two other providers who dole out 5 and 2 megs.....<<<hurmpf>>> for
> homepages.
>
> The $10 is just for homepage space...no email or connect time.  But if
you
> already have a competitive way to connect.... this can be a bargain. I
> think I have about 30 megs of junk at simplenet and they haven't made any
> waves.  Note that the files there must be connected to the web...they
can't
> just be for storage. And for the most part the server is fast and stable.
>
> Angela aka wizzle
>
> -
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Date: Mon, 29 Dec 1997 04:18:42 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) test

Test, please ignore.

IUf this makes it, I'll post a PAR as penance. :-)


- --
    .*.  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: Mon, 29 Dec 1997 07:36:43 -0800
From: Peter Jakubowicz <[e-mail]>
Subject: Re: (fractint) test

At 04:18 AM 12/29/97 -0500, Paul Derbyshire wrote:


>IUf this makes it, I'll post a PAR as penance. :-)

Maybe a new Quartz?


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Date: Mon, 29 Dec 1997 07:57:44 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) The par I promised :-)

; color_var.par
; Copyright (C) 1997/1998 PGD. Use as you please so long as you
; don't charge money for it (distribution media maybe but not the file)
; and retain this notice on all copies and state how and where if anywhere
; it is modified from the original.
;
; Shows the same fractal (an interesting M-set zoom) with various different
; color schemes and coloring options.

MetallicRibbons    { ; Metallic ribbons in blue hues
  reset=1960 type=mandel
  center-mag=-0.04246747495000000/+0.79409885450000010/9336.24
  params=0/0 maxiter=2000 bailout=400 inside=0 decomp=256
  colors=000K0A<125>zzzzzzyyz<76>BLzAKyAKyAKx<45>F0K
  }

Field_Lines        { ; Field lines decked out in rainbow colors.
  reset=1960 type=mandel
  center-mag=-0.04246729615000000/+0.79409885450000010/9336.24/0.9996
  params=0/0 maxiter=2000 bailout=400 inside=0 decomp=256
  colors=000e00L00000<3>000c0z000<4>00000V00z00W000<4>000c0z000<4>0000V00z\
  00W0000<4>000c0z000<4>00000V00z00W000<4>000c0z000<3>000<2>zz0<2>000<3>00\
  0c0z000<4>00000V00z00W000<4>000c0z000<4>0000V00z00W0000<4>000c0z000<4>00\
  000V00z00W000<4>000c0z000<3>000<2>zU0<2>000<3>000c0z000<4>00000V00z00W00\
  0<4>000c0z000<4>0000V00z00W0000<4>000c0z000<4>00000V00z00W000<4>000c0z00\
  0<3>000<2>zz0<2>000<3>000c0z000<4>00000V00z00W000<4>000c0z000<4>0000V00z\
  00W0000<4>000c0z000<4>00000V00z00W000<4>000c0z000<2>000<2>z00
  }

Candy_Pastels      { ; Looks good enough to eat!
  reset=1960 type=mandel
  center-mag=-0.04246711730000000/+0.79409885450000010/9336.24/0.9996
  params=0/0 maxiter=2000 bailout=400 inside=0 logmap=77
  colors=zAK<15>zzz<15>zUA<14>zwvzzzzzw<14>zz0<15>zzz<15>0zA<15>zzz<15>0Kz\
  <15>zzz<14>e4zc0zd3z<13>xvzzzzzwz<14>z0z<15>zzz<15>z00<15>zzz<14>zHP
  }

Goldilocks         { ; Goldi-something, anyways
  reset=1960 type=mandel
  center-mag=-0.04246699810000000/+0.79409885450000010/9336.24/0.9996
  params=0/0 maxiter=2000 bailout=400 inside=0 logmap=77
  colors=zAKA0K<80>000000100<74>U00U00V10V20<92>zz0
  }

Furfur             { ; Weird
  reset=1960 type=mandel
  center-mag=-0.04246646165000000/+0.79409885450000010/9336.24/0.9996
  params=0/0 maxiter=2000 bailout=400 inside=0 outside=real logmap=77
  colors=000<126>zzzzzzyyz<43>PXzPWzOVzOVzOVy<77>A0K
  }

Arcs               { ;
  reset=1960 type=mandel passes=b
  center-mag=-0.04246610404999999/+0.79409885450000010/9336.24/0.9996
  params=0/0 maxiter=2000 bailout=400 fillcolor=1 inside=255 logmap=77
  colors=000<126>zzzzzzyyz<43>PXzPWzOVzOVzOVy<77>A0K
  }

Distance_Estimator { ;
  reset=1960 type=mandel passes=t
  center-mag=-0.04246568680000000/+0.79409885450000010/9336.24
  params=0/0 float=y maxiter=2000 bailout=400 inside=0 logmap=77
  distest=-1/20/800/600
  colors=000<126>zzzzzzzyy<43>zXPzWPzVOzVOyVO<77>K0A
  }



- --
    .*.  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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End of fractint-digest V1 #47
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