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fractint-digest         Sunday, March 22 1998         Volume 01 : Number 142




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

Date: Sat, 21 Mar 1998 03:23:29 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) More Nuclear Fractals

It is verified: Thereare Herman rings in Nuclear! Moreover, there are
Herman rings of a type I have not seen before, where the ring
center...well... I'll let you see for yourself. First two new formula
files, which draw Julia sets of Nuclear in 4 color ranges basedon not only
convergence to infinity but also any finite attractors. Then more PAR
entries, with further Mandelbrot zooms and Julia sets including a Herman
ring and zoom of an intriguing structure...


- ---8<--- Add these to nuclear.frm (from a few posts up) --->8---

Nuclear_JulCol { ; p1, p2, p3 parameters. Use float=y, outside=real, logmap=0,
                 ; periodicity=0. Colors from 4 ranges by finite attractors
                 ; and attracted to infinity.
  a=p1, c=p2, k=p3, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2, a6=3*a2
  r3ac=r3*ac, ack=k*ac
  m=maxit-1, m4=m/2, iter=0, done=0, iter2=0
  qq=0.000001, bail=1000
  IF(notfirstpixel)
    m4=0
  ELSE
    za=-1
    zb=0
    zc=1
    qqa=qq
    qqb=qq
    qqc=qq
  ENDIF
  z=pixel
  :
  IF(iter<m4)
    IF(qqa>0)
      z2=sqr(za)
      z3=za*z2
      za=(r3a2*z3-a6*z2-r3ac*za-ac)/(r3*za+1)+ack
      IF(|za|>bail)
        qqa=0
      ENDIF
    ENDIF
    IF(qqb>0)
      z2=sqr(zb)
      z3=zb*z2
      zb=(r3a2*z3-a6*z2-r3ac*zb-ac)/(r3*zb+1)+ack
      IF(|zb|>bail)
        qqb=0
      ENDIF
    ENDIF
    IF(qqc>0)
      z2=sqr(zc)
      z3=zc*z2
      zc=(r3a2*z3-a6*z2-r3ac*zc-ac)/(r3*zc+1)+ack
      IF(|zc|>bail)
        qqc=0
      ENDIF
    ENDIF
    iter=iter+1
  ELSE
    z2=sqr(z)
    z3=z*z2
    z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack
    iter=iter+1
    iter2=iter2+1
    IF(lastsqr>bail)
      done=1
      color=iter2
      IF(color<1)
        color=1
      ENDIF
      IF(color>66)
        color=66
      ENDIF
    ELSEIF(|z-za|<qqa)
      done=1
      color=iter2
      IF(color<1)
        color=1
      ENDIF
      IF(color>63)
        color=63
      ENDIF
      color=color+66
    ELSEIF(|z-zb|<qqb)
      done=1
      color=iter2
      IF(color<1)
        color=1
      ENDIF
      IF(color>63)
        color=63
      ENDIF
      color=color+129
    ELSEIF(|z-zc|<qqc)
      done=1
      color=iter2
      IF(color<1)
        color=1
      ENDIF
      IF(color>63)
        color=63
      ENDIF
      color=color+192
    ENDIF
    IF(done)
      z=color-iter-7
      notfirstpixel=1
    ENDIF
  ENDIF
  done==0
}

Nuclear_JColLog { ; p1, p2, p3 parameters. Use float=y, outside=real, logmap=0,
                  ; periodicity=0. Colors from 4 ranges by finite attractors
                  ; and attracted to infinity. Uses a "logmap".
  a=p1, c=p2, k=p3, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2, a6=3*a2
  r3ac=r3*ac, ack=k*ac
  m=maxit-1, m4=m/2, iter=0, done=0, iter2=0
  qq=0.000001, bail=1000
  IF(notfirstpixel)
    m4=0
  ELSE
    za=-1
    zb=0
    zc=1
    qqa=qq
    qqb=qq
    qqc=qq
  ENDIF
  m3=m-m4
  z=pixel
  :
  IF(iter<m4)
    IF(qqa>0)
      z2=sqr(za)
      z3=za*z2
      za=(r3a2*z3-a6*z2-r3ac*za-ac)/(r3*za+1)+ack
      IF(|za|>bail)
        qqa=0
      ENDIF
    ENDIF
    IF(qqb>0)
      z2=sqr(zb)
      z3=zb*z2
      zb=(r3a2*z3-a6*z2-r3ac*zb-ac)/(r3*zb+1)+ack
      IF(|zb|>bail)
        qqb=0
      ENDIF
    ENDIF
    IF(qqc>0)
      z2=sqr(zc)
      z3=zc*z2
      zc=(r3a2*z3-a6*z2-r3ac*zc-ac)/(r3*zc+1)+ack
      IF(|zc|>bail)
        qqc=0
      ENDIF
    ENDIF
    iter=iter+1
  ELSE
    z2=sqr(z)
    z3=z*z2
    z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack
    iter=iter+1
    iter2=iter2+1
    IF(lastsqr>bail)
      done=1
      color=66*(log(iter2)/log(m3))
      IF(color<1)
        color=1
      ENDIF
      IF(color>66)
        color=66
      ENDIF
    ELSEIF(|z-za|<qqa)
      done=1
      color=63*(log(iter2)/log(m3))
      IF(color<1)
        color=1
      ENDIF
      IF(color>63)
        color=63
      ENDIF
      color=color+66
    ELSEIF(|z-zb|<qqb)
      done=1
      color=63*(log(iter2)/log(m3))
      IF(color<1)
        color=1
      ENDIF
      IF(color>63)
        color=63
      ENDIF
      color=color+129
    ELSEIF(|z-zc|<qqc)
      done=1
      color=63*(log(iter2)/log(m3))
      IF(color<1)
        color=1
      ENDIF
      IF(color>63)
        color=63
      ENDIF
      color=color+192
    ENDIF
    IF(done)
      z=color-iter-7
      notfirstpixel=1
    ENDIF
  ENDIF
  done==0
}


- --->8--- Add these to nuclear.par ---8<---

fracmini_zoom3     {
  reset=1960 type=formula formulafile=nuclear.frm
  formulaname=nuclear_m_k passes=t
  center-mag=6.69587/-1.21995/1.400751 params=0.2/0.4/-0.3/0.3/0/1.2
  float=y maxiter=257 inside=0 outside=real periodicity=0
  colors=000zzz<64>000K0e<61>hlze0K<61>zhqU0U<61>zcz
  }

fracmini_zoom4     {
  reset=1960 type=formula formulafile=nuclear.frm
  formulaname=nuclear_m_k passes=t
  center-mag=6.62916/-1.67046/10.29964 params=0.2/0.4/-0.3/0.3/0/1.2
  float=y maxiter=257 inside=0 outside=real periodicity=0
  colors=000zzz<64>000K0e<61>hlze0K<61>zhqU0U<61>zcz
  }

fracmini_zoom1a    {
  reset=1960 type=formula formulafile=nuclear.frm
  formulaname=nuclear_m_k passes=t center-mag=7.08534/2.64775/3.387863
  params=0.2/0.4/-0.3/0.3/0/1.2 float=y maxiter=257 inside=0
  outside=real periodicity=0
  colors=000zzz<64>000K0e<61>hlze0K<61>zhqU0U<61>zcz
  }

fracmini_zoom1b    {
  reset=1960 type=formula formulafile=nuclear.frm
  formulaname=nuclear_m_k passes=t
  center-mag=+6.90457180794366800/+2.71575563221129500/67.75727
  params=0.2/0.4/-0.3/0.3/0/1.2 float=y maxiter=4000 inside=0
  outside=real periodicity=0
  colors=000zzz<64>000K0e<61>hlze0K<61>zhqU0U<61>zcz
  }

herman_ring_01     {
  reset=1960 type=formula formulafile=nuclear.frm
  formulaname=Nuclear_Jul passes=t
  center-mag=0.703812/-0.0857366/0.136612
  params=0.2/0.4/-0.3/0.3/7.019340119066568/2.534415006977062 float=y
  maxiter=4000 inside=0 logmap=yes periodicity=0
  colors=000zlh<64>VKC00e<61>hlze00<17>kDFKA0kEH<41>zhq0e0<30>MoRNoRNpSNpS\
  <27>lzh
  }

hring_01_col       {
  reset=1960 type=formula formulafile=nuclear.frm
  formulaname=nuclear_julcol passes=t
  center-mag=0.703812/-0.0857366/0.136612
  params=0.2/0.4/-0.3/0.3/7.019340119066568/2.534415006977062 float=y
  maxiter=1000 inside=0 outside=real periodicity=0
  colors=000zlh<64>VKC00e<61>hlze00<17>kDFKA0kEH<41>zhq0e0<30>MoRNoRNpSNpS\
  <27>lzh
  }

hring_01_col_b     {
  reset=1960 type=formula formulafile=nuclear.frm
  formulaname=nuclear_julcol passes=t
  center-mag=-0.860841/0.620496/0.7041856
  params=0.2/0.4/-0.3/0.3/7.019340119066568/2.534415006977062 float=y
  maxiter=1000 inside=0 outside=real periodicity=0
  colors=000lhz<12>gbugbufate`s<17>LEWJCUJCU<20>53G75I<6>00Ahlz<44>12f00e0\
  0c<14>000zhq<44>f12e00c00<14>000lzh<44>2f10e00c0<14>000
  }

near_hring_01      {
  reset=1960 type=formula formulafile=nuclear.frm
  formulaname=nuclear_jcollog center-mag=1.25716/-0.0284745/0.1666
  params=0.2/0.4/-0.3/0.3/7.05/2.534415006977062 float=y maxiter=5000
  inside=0 outside=real periodicity=0
  colors=000<15>I09K0AK0B<47>zcz00e<61>hlze00<17>kDFKA0kEH<41>zhq0e0<30>Mo\
  RNoRNpSNpS<27>lzh
  }

near_hring_01a     {
  reset=1960 type=formula formulafile=nuclear.frm
  formulaname=nuclear_jcollog center-mag=-1.10546/0.566287/0.8009615
  params=0.2/0.4/-0.3/0.3/7.05/2.534415006977062 float=y maxiter=5000
  inside=0 outside=real periodicity=0
  colors=000zrz<29>n2Wm0Ul0U<31>20B00A00e<61>hlze00<17>kDFKA0kEH<41>zhq0e0\
  <30>MoRNoRNpSNpS<27>lzh
  }

nukej_2            {
  reset=1960 type=formula formulafile=nuclear.frm
  formulaname=nuclear_jcollog passes=t
  center-mag=1.25716/-0.0284745/0.1666
  params=0.2/0.4/-0.3/0.3/6.91038/2.72676 float=y maxiter=5000
  inside=0 outside=real periodicity=0
  colors=000<15>I09K0AK0B<47>zcz00e<61>hlze00<17>kDFKA0kEH<41>zhq0e0<30>Mo\
  RNoRNpSNpS<27>lzh
  }

- ---8<--- End --->8---

- --
    .*.  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]

- -
- ------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
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------------------------------

Date: Sat, 21 Mar 1998 03:33:40 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) Doing lengthy computations once per image in Fractint 19.6

Many have lamented the lack of a "per-image" initialization in Fractint
formula files. Lament no more. It can be done! Here's how:

To do something simple only once per image:

foo {
  stuff
  IF(!notfirstpixel)
    slow_stuff_not_pix_dependent
    notfirstpixel=1
  ENDIF
  stuff
  :
  stuff
}

If you want to do something looping, such as iterating some critical
points to find finite attractors (as done in my newest Nuclear Julia
formulas above):

foo {
  stuff
  m=maxit
  m2=maxit/2
  IF(notfirstpixel)
    m2=0
  ELSE
    initialize some variables where results will go
    (za, zb, zc, qqa, qqb, and qqc in the Nuclear_Jul_Col's)
  ENDIF
  stuff
  iter=0
  notfirstpixel=1
  :
  IF(iter<m2)
    Newton's method, iterate some critical points, you name it
    Won't execute when m2=0 when notfirstpixel is true
  ELSE
    Normal iteration
    (Note: First pixel will only get 1/2 normal iterations. Should not be a
    problem.)
  ENDIF
  iter=iter+1
  stuff
}

- --
    .*.  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]

- -
- ------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
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------------------------------

Date: Sat, 21 Mar 1998 03:41:05 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) How I found it out

I have discovered that Fractint zeros all the formula variables once *per
image* but keeps them from pixel to pixel. How I did it: First I had, in
making a goof (missing a something=0 in an initializer ina formula)
observed that Fractint remembered a formula variable from one pixel to
another. (A counter had kept counting pixel by pixel, resulting in a
striped image!) I realized I could speed up my first attempt at the
Nuclear_Jul_Col if it turned out to zero them at the start of the image.
(It originally did the SAME ~2000 iterations of the 3 critical points
every pixel! This was slow and ledto hour long calctimes on "simple" Julia
sets. Ouch.) So I did this:

fuddle {
  IF(adq==0)
    adq=3
  ELSE
    adq=14
  ENDIF
  :
  z=adq-8
  done=1
  done==0
}

If adq was zero, it would become 3. Then z would be set on first iteration
to 3 - 8, and the loop would immediately exit, yielding a cyan pixel (using
the default color map and outside=real). If instead adq was nonzero, it would
go to 14, yielding a yellow pixel. I ran this with outside=real, logmap=0,
maxiter>255, and passes=1, and got a single blue pixel in the upper left
corner of an otherwise yellow screen, thus demonstrating 2 of the 3 things
I was hoping to verify: that variables are set to zero sometime before use,
and that they are definitely kept unchanged from the end of one
pixel to the start of the next. They were zeroed at most once per image.
But maybe they were only zeroed less often, e.g. per use of the formula?
That would be no good.
I then upped maxiter  (specifically from 2000 to 6000) to force a
regeneration of the image. Same deal, thus showing that the variable is
indeed zeroed again at the start of a new image, not only zeroed for one
run of the formula or for one run of the 'z' parameters or for one run of
Fractint.

It works.


- --
    .*.  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]

- -
- ------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
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------------------------------

Date: Sat, 21 Mar 1998 03:58:02 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Nuclear Explosion

>hi, can someone tell me what that Julia's doing inside that piece of an
>M-set.  i haven't seen this before, but maybe it's common? if so ignore,
>but otherwise, cld someone explain this. the formula is longish and was
>posted early this morning so i won't post it again.
>thank you

Heh. :)
That's coloring by all critical points, just to get neat effects like
that. It superimposes the pictures for all 3 critical points. The red buds
are where one of them is going to finite attractors and is determining
them; the orange Julia inside is where one of the other 2 is being sucked
into the attractor picked by the first. (Elsewhere it was going to infinity.)
Note that the Julia set fits with the bud's period and location. This neat
effect occurs with all the multicolored Nuke Mandelbrot formulas, as well
asthe tricolor and 4color formulas posted ages ago.


- --
    .*.  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]

- -
- ------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
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------------------------------

Date: Sat, 21 Mar 1998 04:10:00 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Fractals Just Went Nuclear!

>These are incredible!

Thanks :-)

>(has any tried them?). But the cool/weird thing is
>that if I set outside color to summ I get pictures of M-sets and Julias
>within M-sets. Paul, can you explain?

It's supposed to do that... the comments should make that clear; the
Mandel ones without a specific critical point use all 3 to make a "triple
exposure" picture using color ranges. The comments say to use
outside=real; outside=summ will work identically (since the z value
emitted has imaginary component 0). Best results without using a logmap,
but there's an ersatz logmap builtin with 2 real parameters, which affect
the "compressed" you usually use logmap=2 to achieve, and the rate of
decline (not an option using the normal logmap!). It uses not a log but an
nth-root, like the square root alternative logmap, but using any n. Bigger
n means more colors for lower iterations. n smaller than 1 means colors
pushed toward higher iterations. Either way all iterations are used.

The new Nuclear_J_ColLog uses a logmap similar if not equal to the builtin
one, with no compression. (No tweaks because no spare parameters!)

- --
    .*.  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]

- -
- ------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
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------------------------------

Date: Sat, 21 Mar 1998 04:24:50 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Colormaps Ahoy

wizzle wrote

>Good idea and you can do it in very little space as one file containing
>only pars required to create the images. The color part can be copied
>out into any other par we need it for.

Heck, then why not keep all 120? ;-)

Better yet: Put them in a PAR that renders a full-on Mandelbrot with each
map in turn. Then supply with Fractint a few maps already, the PAR, and a
maps.key .key file (you do know about the autokey feature, don't you?
;-)) that draws them one at a time and saves the maps, and cycles them for
effect. The key file, even with map names and stuff, won't be big either.


- --
    .*.  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]

- -
- ------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
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------------------------------

Date: Sat, 21 Mar 1998 15:51:16 -0800
From: Peter Jakubowicz <[e-mail]>
Subject: (fractint) Hardware

Hi,
Has anyone run Fractint w/a Diamond Permedia II video card. I am about to
purchase a new computer that comes with that and wld be interested if I wld
have a problem with Fractint w/ that. The salesperson has never heard of
Fractint. Also, is a Sony 17'' monitor w/ .25 dot pitch that runs at
1600x1200 sufficient for viewing fractals. Pls answer me personally, so as
not to clog up the list, as I have just done.
Thank you


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

Date: Sat, 21 Mar 1998 18:25:00 -0500
From: "Peter Gavin" <[e-mail]>
Subject: Re: (fractint) Sqrt(3) in the Mset

Hehe..  I had that program, but the 48g is pretty much RAM-less..  :)


- -----Original Message-----
From: Ryan Jameson <[e-mail]>
To: [e-mail] <[e-mail]>
Date: Saturday, March 21, 1998 2:02 AM
Subject: Re: (fractint) Sqrt(3) in the Mset


|At 06:55 PM 3/20/98 -0500, you wrote:
|>Jeez, you're right, it is close!  But what I wanna know is, how the *&^$
did
|>you figure THAT out?!!
|>:)
|
|Hmm... I remember from some time ago that there is a program written for
|the HP48 calculator that would solve funky numbers like that for thier
|fractional equivalent. It even inluded such numbers like square roots.
|perhaps that is how he did it....
|
|Ryan
|
|-
|------------------------------------------------------------
|Thanks for using Fractint, The Fractals and Fractint Discussion List
|Post Message:   [e-mail]
|Get Commands:   [e-mail] "help"
|Administrator:  [e-mail]
|Unsubscribe:    [e-mail] "unsubscribe fractint"


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

Date: Sat, 21 Mar 1998 16:43:02 -0800
From: Ryan Jameson <[e-mail]>
Subject: Re: (fractint) Sqrt(3) in the Mset

At 06:25 PM 3/21/98 -0500, you wrote:
>Hehe..  I had that program, but the 48g is pretty much RAM-less..  :)
>

Heh.. I guess you should have bought the gx. I have an sx, and I went and
put a 128 card in it. (160 total) I've yet to run out of room.

Ryan

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

Date: Sat, 21 Mar 1998 22:07:28 -0800
From: kathy roth <[e-mail]>
Subject: (fractint) formula

I've been learning to write formulas for a while now, randomly
changing things,  having fun at it but have not come up with
anything particularly interesting- I guess this is not too surprising-
You drop a watch on the floor and... most of the times it's worse!
          There's been talk of a contest based on coloring methods
and I was looking at a fractal in "The Science of Fractal Images"
with a very simple formula but a different coloring method.  (page 160
if you have it).    This is waaayyy past my level of knowledge of this
but I was trying to write a formula and found it was worthwhile for the
basics of it- like is the initialization right and what is the bailout
here and how does Fractint assign a color really, aside from hitting
the "x" screen  and hitting "iter"....
     So can anyone put this into a fractint formula?  It's a cool
picture.  (Sorry about the length of this.)
     " ...the Julia set of 1/e*e^x (in white) approximated by points
that escape to infinity according to the following criteria: A point
z(0) is colored white if the orbit of z(0) contains a point z(k) with
real part Re z(k) greater than 50 within the first 25 iterates and if
cos (Im z(k)) >= 0.0 (i.e. the next iterate z(k+1) will be very
large...."  (from The Science of Fractal Images " by Peitgen et.al.)
         This is what I tried:
    {z=pixel
        IF (real(z)>50) && (cos(imag(z))>=0)
      ???what next
Would the k =25 iterates be the bailout value?
How do you get it to assign a color?
Thanks in advance to anyone who read this far.








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Date: Sun, 22 Mar 1998 03:02:49 -0500
From: "Peter Gavin" <[e-mail]>
Subject: (fractint) HP-48G fun!  (aka Sqrt(3) in the Mset)

Well, my Calc teacher got a massive grant from HP (I think it was them, or
maybe it was the school board.. i dunno) and got about a hundred 48g's and
she lends them out to the students in her classes who want/need them.  So,
naturally, I borrowed one, after I saw how nifty they really are.  Actually,
I wrote a fractal renderer on it, in RPL, since I didn't have a clue about
its assembly language, let alone have the time to figure it out.  It was
pretty cool.  I built in external formula capability, and I was working on
adding a zoomer, when I realized, hmm, is it really worth paying for a new
set of batteries every other week just to have something to do in school?
(sounds like  ti-85 zshell tetris, huh? <g> )  And besides, (needless to
say) it was slower than a Yugo, and my ram was running short, too (hehe...),
which slowed it down, a lot.  I think the HP uses some kind of paging mode
or something, so it can use cheap ram for storage, and good ram for
calculations... My friend demonstrated this by repetitively copying a number
onto the stack... about 2 bazillion times.  It got to the point where it
took about 10 seconds just to begin reacting to a key-press.  Anyways, I
thought a fractal renderer would be cool, but I didn't know they were
available anywhere.  How much I've learned since... :)  Of course, since
then, I've done more with fractint than I could've in 10e(10e5) years with
the hp, and in 1024x768 resolution and 256 colors!       [LOL :) ]

Pete

- -----Original Message-----
From: Ryan Jameson <[e-mail]>
To: [e-mail] <[e-mail]>
Date: Saturday, March 21, 1998 7:45 PM
Subject: Re: (fractint) Sqrt(3) in the Mset


|At 06:25 PM 3/21/98 -0500, you wrote:
|>Hehe..  I had that program, but the 48g is pretty much RAM-less..  :)
|>
|
|Heh.. I guess you should have bought the gx. I have an sx, and I went and
|put a 128 card in it. (160 total) I've yet to run out of room.
|
|Ryan
|
|-
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Date: Sun, 22 Mar 1998 04:17:12 -0600
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Celtic formula and pars

This is a multi-part message in MIME format.

- --------------3B8E4221EC9
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit

Paul and/or Joyce Carlson wrote:
>
> I call this formula my Celtic formula because about a year
> ago I posted the image produced by the first par to the
> abpf newsgroup and Noel Giffin wrote to me saying he really
> liked it because it reminded him of some kind of Celtic
> symbol (I don't remember what).
>

I enjoyed the formula and images, but I made a change to the colors to
be more appropriate for last Tuesday's Holiday festivities.  They are
attached as MAP files.

P.N.L.

- -------------------------------------------------
     Why do most folks hate cynics so much?
       Because we're almost always right.
- -------------------------------------------------
http://home.att.net/~Paul.N.Lee/PNL_Fractals.html

- --------------3B8E4221EC9
Content-Type: text/plain; charset=us-ascii; name="Irish_01.map"
Content-Transfer-Encoding: 7bit
Content-Disposition: inline; filename="Irish_01.map"

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- --------------3B8E4221EC9
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- --------------3B8E4221EC9--


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

Date: Sun, 22 Mar 1998 05:09:33 -0800 (PST)
From: "James R. McKenzie" <[e-mail]>
Subject: Re: (fractint) Celtic formula and pars

- ---"Paul N. Lee" <[e-mail]> wrote:
>
> Paul and/or Joyce Carlson wrote:
> >
> > I call this formula my Celtic formula because about a year
> > ago I posted the image produced by the first par to the
> > abpf newsgroup and Noel Giffin wrote to me saying he really
> > liked it because it reminded him of some kind of Celtic
> > symbol (I don't remember what).
> >
>
> I enjoyed the formula and images, but I made a change to the colors to
> be more appropriate for last Tuesday's Holiday festivities.  They are
> attached as MAP files.
>
> P.N.L.
>
> -------------------------------------------------
>      Why do most folks hate cynics so much?
>        Because we're almost always right.
> -------------------------------------------------
> http://home.att.net/~Paul.N.Lee/PNL_Fractals.html


Am I supposed to replace a color map and if so which one?  I've never
cracked open the maps all that much, damn they're huge.  BTW do you
actually "type" this stuff in by hand?  If so you must go through
<TAB> keys quite quickly.


Before anyone says anything know this, I don't program, I don't hack.
If I can't run it straight off the shelf I don't run it.  That's not
to say I don't use Spreadsheets and Wordprocessors, I mean I don't
re-write programs from the inside-out nor do I alter add-ins.  PARS,
FRMS and MAPS are add-ins.  I run 'em don't hack 'em.  I just need to
know which file[s] do I replace, if any, in order to use the map
originally sent in this message.

I don't mean to sound curt but when I get more verbose I digress,
unfortunately I'm no good at balancing this out, sorry to sound this
way I honestly don't mean to.


                         T H A N K   Y O U


                         James R. McKenzie


                         [e-mail]
==

_________________________________________________________
DO YOU YAHOO!?
Get your free @yahoo.com address at http://mail.yahoo.com


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

Date: Sun, 22 Mar 1998 10:15:35 -0600 (CST)
From: [e-mail] (Paul and/or Joyce Carlson)
Subject: (fractint) 3-way Halley formula

comment {
Here's my "3-way" rendering applied to a 7th-order Halley method
fractal.  After you run the 3wayhal1 par, press the @ key and
select halmap1 for the filled-in rounded image.  Press the @ key
again and select halmap2 for the folded image.  Pressing the @ key
again and selecting halmap3 returns you to the original image.

Paul Carlson
}

frm:Halley7_3Way {; Copyright (c) Paul W. Carlson, 1998
    ; Alyways use float=y, outdide=summ
    ; real(p1) = escape circle radius squared
    ; imag(p1) = number of iterations to skip
    ; real(p2) = number of color ranges
    ; imag(p2) = number of colors in a range
    ; p3       = relaxation factor
    z = k = iter = range_num = bailout = 0
    w = pixel
    prev_modw2 = 1.0e20
    rad2 = real(p1)
    skip_iters = imag(p1)
    num_ranges = real(p2)
    colors_in_range = imag(p2)
    colors_in_range_1 = colors_in_range - 1
    :
    w5 = w^5, w6 = w * w5, w7 = w * w6
    w = w - p3 * (w7-w)/((7*w6-1)-(42*w5)*(w7-w)/(14*w6-2))
    ;
    IF ((prev_modw2 < rad2) && (|w| > rad2))
    bailout = 1
    IF (iter > skip_iters)
        k = 1
    ENDIF
    index = colors_in_range_1 * (rad2 - prev_modw2) / rad2
    z = (index + range_num * colors_in_range + 1) * k
    ENDIF
    prev_modw2 = |w|
    range_num = range_num + 1
    IF (range_num == num_ranges)
    range_num = 0
    ENDIF
    iter = iter + 1
    z = z - iter
    bailout == 0 && |w| < 1.0e10
}

3wayhal1           { ; Copyright (c) Paul W. Carlson, 1998
  reset=1960 type=formula formulafile=hal3way.par
  formulaname=halley7_3way passes=t
  center-mag=-4.44089e-016/2.22045e-016/0.8912656
  params=1/0/8/30/3/0
  float=y maxiter=252 inside=253 outside=summ
  colors=0000C4<6>0zR<6>0C4000<13>0000CC<6>0zz<6>0CC000<13>00000O\
  <6>GGz<5>33U00O000<13>000O6U<6>eNx<6>O6U000<13>000O08<6>z0f<6>O\
  08000<13>000O00<6>w77<6>O00000<13>000c40<6>zW0<6>c40000<13>000a\
  G0<6>zz0<6>aG0000<27>000O08
  cyclerange=1/240
  }

halmap1            { ; Copyright (c) Paul W. Carlson, 1998
  colors=0000C4<15>0zR<12>0C40CC<15>0zz<12>0CC00O<14>FFwGGzFFw<11>0\
  0OSA`<14>eNxfOzeNw<10>K2OO08<15>z0f<12>R0BO08O00<15>z88<11>R11c40\
  <14>vS0xU0wT0<12>c40aG0<14>xw0zz0yw0<11>aG0000<13>000
  cyclerange=1/240
  }

halmap2           { ; Copyright (c) Paul W. Carlson, 1998
  colors=0000zR<3>0nL0kK0gJ0dI0aG<7>0C4<12>0zR0zz<15>0CC<12>0zzGGz<\
  14>11R00O11R<11>GGzfOz<14>M4RK2OL3R<11>fOzz0f<14>O08<13>z0fz88<15\
  >R11<12>z88xU0<13>e60c40d50<12>xU0zz0<15>aG0<12>zz0000<13>000
  cyclerange=1/240
  }

halmap3           { ; Copyright (c) Paul W. Carlson, 1998
  colors=0000C4<6>0zR<6>0C4000<13>0000CC<6>0zz<6>0CC000<13>00000O<6\
  >GGz<5>33U00O000<13>000O6U<6>eNx<6>O6U000<13>000O08<6>z0f<6>O0800\
  0<13>000O00<6>w77<6>O00000<13>000c40<6>zW0<6>c40000<13>000aG0<6>z\
  z0<6>aG0000<27>000O08
  cyclerange=1/240
  }


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

Date: Sun, 22 Mar 1998 08:44:33 -0800
From: kathy roth <[e-mail]>
Subject: re: (fractint) Celtic formula and pars

Here's a celtic variation.  I can't get it to take out that double
space.

celtic-monolith    { ; kathy roth
                     ; frm by Paul Carlson
                     ; map by wizzle
  reset=1960 type=formula formulafile=celtic~1.frm
  formulaname=mandel_3way passes=t
corners=-0.45691884/-0.73072927/-0.15972509/0.20535548/-0.73072927/0.205\

  35548 params=4/2/2/125 float=y maxiter=512 inside=253 outside=summ
  invert=1/0/0
 colors=C0CdPR<33>ylqzmrzmq<52>K00F00A00<55>zcmzcmybl\
<67>A00K00<31>`KNaLO\
  bMPcNPcOQ
  }

Celtic_Julia {; Copyright (c) Paul W. Carlson, 1998
    ;****************************************************
    ; Always use floating point math and outside=summ.
    ;
    ; Parameters:
    ;   p1       = Julia set coordinates
    ;   real(p2) = a factor controlling the width of the stalks
    ;   imag(p2) = maximum iterations for stalks
    ;   real(p3) = number of color ranges
    ;   imag(p3) = number of colors in a color range
    ;****************************************************
    w = pixel
    c = p1
    z = 0
    bailout = 0
    iter = 0
    range_num = 0
    stalk_width = real(p2)
    max_iter = imag(p2)
    num_ranges = real(p3)
    colors_in_range = imag(p3)
    ratio = (colors_in_range - 1) / stalk_width:
    ;
    w = w * w, wr = real(w)
    w = w - wr + abs(wr) - c
    ;
    IF (abs(real(w)) <= abs(imag(w)))
        min_dist_to_axis = abs(real(w))
    ELSE
        min_dist_to_axis = abs(imag(w))
    ENDIF
    IF (min_dist_to_axis < stalk_width && iter > 1 && iter <= max_iter)
        z = ratio * min_dist_to_axis + range_num * colors_in_range + 1
        bailout = 1
    ENDIF
    range_num = range_num + 1
    IF (range_num == num_ranges)
        range_num = 0
    ENDIF
    iter = iter + 1
    z = z - iter
    bailout == 0  && |w| < 4
}











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