A co-worker recently implemented Mandelbrot on a system at work, and I was
impressed with the results.  So I figured, why not try it on my you-know-what.
I was very pleased with the results, never expecting such a tiny program to
create such a nice display.  

For any neo's out there, the algorithm is to test the magnitude of imaginary
numbers as they are repeatedly squared (sort of) and plot a color depending
on the number of times the number was squared before its magnitude exceeded the
value 2.  (Numbers that will never exceed a magnitude of 2 are numbers in the
"Mandelbrot Set".)  This program simply uses gr.11 which has 16 colors.  The
color selected by the algorithm is the color selected to plot.  If the point
has exceeded 15 squarings and has still not exceeded the limit, it is assumed
in the Mandelbrot set and drawn as black.  This is, of course, an
approximation.

There are no bells and whistles (add them yourself!) but here goes.  
In BASIC, of course!

10 REM MANDELBROT PATTERNS
20 RS=1/40 : IS=RS/4 : REM INCREMENTS FOR REAL AND IMAGINARY AXES
30 ORGR=1.5 : ORGI = 0.6 : REM DEFINES WHERE IN THE COMPLEX PLANE TO PLOT
100 GRAPHICS 11
200 FOR S=0 TO 79
205  R=S*RS-ORGR : REM SCALE HORIZ (REAL) AXIS
210  FOR T=0 TO 191
215   I=T*IS-ORGI : REM SCALE VERT (IMAGINARY) AXIS
220   C=1 : REM INITIALIZE
225   COLOR 1 : PLOT S,T : REM JUST TO SHOW WHERE CURRENT POINT IS
230   R1=R : I1=I : REM LOCALS FOR ITERATIVE CALCULATIONS
235    IF ABS(R1)<1.0E-49 THEN R1=0 : REM STUPID ATARI TAKES UNDERFLOW TRAPS
236    IF ABS(I1)<1.0E-49 THEN I1=0
239    R12=R1*R1 : I12=I1*I1 : REM SQUARE REAL&IMAG PARTS
240    IF R12+I12>4 THEN 300 : REM CHECK MAGNITUDE. COMPARE TO 4 TO AVOID SQRT
250    R2=R12-I12+R : I2=2*R1*I1+I : REM SQUARE AND ADD IN ORIG VALUE
260    C=C+1 : IF C>15 THEN C=0 : GOTO 300 : COUNT INTERATIONS, TEST TERM VALUE
270    R1=R2 : I1=I2
280    GOTO 235
300   COLOR C
305   PLOT S,T
310  NEXT T
320 NEXT S
400 GOTO 400

Under Turbo, it takes approx. 1 hour to render a screen.

The values RS, ORGR and ORGI scale the drawing and select origin coordinates.
The values in the program draw most if the Mandelbrot set, but is very slow
because of all the black.  Some other values:

 RS    ORGR    ORGI     Picture
1/10   2.5     2.4      Small version of the full set, centered on the screen
1/20   2.5     1.2      Larger version of the set
1/40   1.5     0.6      Full screen of the set, with a little offscreen
1/60   1.4     0.5      Close-up of the upper left corner of the set*

* Make sure you do this one!

Try it!  You will be impressed.

Possible bells, whistles, etc.:
1) Save/restore pictures to disk
2) Select and area to blow up, using paddle or joystick
3) "Quick draw" at lower resolution to preview patterns
4) Calculate all 4 points in a gr.11 pixel, and average the result

Another thing you may want to know - The patterns get more interesting at
higher resolution (smaller and smaller values of RS).  As far as I know,
more and more detail can be seen at arbitrarily small values.

Have fun! -Stan

/ hpclkms:comp.sys.atari.8bit / lac@Alliant.COM (Stan Lackey) /  8:07 am  Aug 24, 1988 /

Allow me to quote from the Atari Tech Ref.

     "When any one of the joystick trigger lines (pin 6) is pulled low, the
ANTIC chip takes the current VCOUNT value and stores it in PENV.  The
horizontal color clock value (0-227 decimal) is stored in PENH.  The least
significant bit is inaccurate and should be ignored.  Since there are a
number of delays involved in displaying the data and changing the light
pen register, each system must be calibrated.  Software which uses the
light pen should contain a user-interactive calibration routine.  For
example, the user could point the light pen at a crosshair in the center
of the screen and the program could compute the required horizontal offset.
PENH will wrap around from 227 to 0 near the right hand edge of a standard
width display because of the delay.  The pen will not work if it is pointed at a
black area of the screen, since the electron beam is turned off.  It is
a good idea to read two (or more) values and average them, since the user
will probably not hold the pen perfectly steady."

End of quote.  Now, for your enjoyment pleasure, I shall add some (probably
obvious) commentary.

In addition to using the trigger line, the gun will also need to use the
power and ground lines.  There is some limit on the current draw from the
joystick, but I can't seem to find it right now.  Just exercise caution
as you hook up more things to one port.  If you really need to now, send
me e-mail, and I will try to locate the info.

Of course, someone will need to know what locations PENV and PENH and VCOUNT
and their shadows live in, so here is the list.

NAME      LOCATION       SHADOW
----      --------       ------
PENH      $D40C          $234
PENV      $D40D          $235
VCOUNT    $D40B          N/A

Good luck with the project, and let us know how it turns out.  I don't have
time to do the project myself, or I would give it a shot.

Kenneth Sumrall
ken%hpcl@hplabs.hp.com
...!hplabs!hpclkms!ken

   Has anyone else had a problem using a light pen with the ICD MIO? Mine
just won't work when it is hooked up. Any ideas?

                               Gary Duzan
                               Time  Lord
                           Third Regeneration
                        Atari Enthusiast Extreme

   I am not including any of the previous messages but I will summarize the
one I am refering to.
   There was a question about why the XF551 would not boot up immediately from
a double sided boot disk.  This problem also occurs on single sided double
density disks.  
   The reason for the problem is because Atari wrote the OS (yep, that means
operating system) for the drive and told it that everytime it powers on it
should pretend that it is an 810.  When you power on your computer and it
attempts to boot, it thinks it is looking at a single density disk.  The
computer then recieves an error when it tries to read the disk.  This error
always occurs with Spartados, I haven't tested it with a different dos but I
suspect it would happen then also.
  As soon as the drive encounters the error, it reconfigures itself to the
correct density.  Then when you hit RESET or turn your computer off and then
back on again, the drive is properly configured.
  If the problem only occurs with Spartados then perhaps ICD will correct it
by forcing the boot program to configure the drive correctly.  If the problem
is with the drive not doing an autoconfigure than all DOS's will have to be
modified to boot correctly.

Hello,

   I get my messages from info-a16 in digest format, and would like to know if
anyone has a undigester?  Or if there is something that can take the digest
apart and put it into seperate mail messages?  Does anyone know of such a
beast?  Any help would be appreciated....

John Bunch

Does anyone know where I can obtain Daisy Dot II?

The name and address of the person or company would do nicely,
or a BBS number if it is posted in the public domain would also do.

Thanks,

 Scott Parish

PARS@KSUVM.BITNET
PARS@KSUVM.KSU.EDU

Check out the August(?) issue of Antic ("Newsroom comes for the 8-bit Ataris"
on the cover). There's an article on DaisyDot II, and an address.

                                                --R.J.
                                                B-)

P.S. Sorry, no cute sign-off yet...I just got my account back up.

Daisy Dot II is available by sending $10 to:

        Roy Goldman
        2440 S. Jasmine
        Denver, Colorado 80222

If you own a standard 9-pin printer such as an Epson, you'll love it.
I tried it on my 24-pin printer and would LOVE to have a 24-pin version,
but the present 9-pin version isn't much use to me at present.  If anybody
knows about any plans to develop a 24-pin version, I'd love to hear about it.
Without hesitating, I would send in $24 (or $23, or whatever) for my copy
of a 24-pin version with font editor.

-John Sangster, j@mitre-bedford.arpa

By popular demand, I've changed the name of the proposed group to
rec.games.micro.  This should make it clear what the purpose of
the newsgroup is, without implying that the group is for the IBM
PC family only.

I'd like to address some of the comments that have been made
regarding the newsgroup.  First of all, there has been the
comment that rec.games.misc is sufficient for handling the
traffic in microcomputer game help.  I agree with this, but the
problem is that everyone doesn't seem to know that that is where
they should post help messages for microcomputer games.
Therefore, they post in the .sys groups, or occasionally
rec.games.frp or other groups.  If there was such a group as
rec.games.micro then it would be clear where the messages were to
be posted.  I do not propose that the rec.games.micro group
include games originally programmed for UNIX/VAX systems, since
there are already several newsgroups (rec.games.rogue,
rec.games.hack, rec.games.moria) that support those games.
Rec.games.misc can now be a repository for games that don't have
their own newsgroup such as Omega or Phantasia or Xword.

There has also been the comment that this group won't cut down on
net traffic.  I believe it will cut down on net traffic because
there won't be the same messages about the same games throughout
the .sys groups.  Most microcomputer games have been converted to
more than one system, and therefore the same messages about these
games can (and do) appear in more than one .sys group.  A clear
example of that is Bard's Tale.  There is an advantage to the
person playing these games also, in that if he's playing a game
that is a later conversion from the original, then in
rec.games.micro, he can probably find someone who's played on a
different computer but who's finished the game.  The advantage to
the people reading the .sys groups is that they don't have their
group cluttered with game messages that should really go into the
rec area.

There was a comment about moderation--if someone wants to
moderate this group, fine.  _I_ can't moderate it, and really, I
don't see the group as having too much "noise" so I don't think
moderation is necessary.  The only thing I can see moderation
doing is to prevent the requesting of copyright information, and
currently rec.games.misc readers don't do much of that.

Now for the current vote tally-73 YES 15 NO.  I will post another
tally in two weeks.
--
Jennifer Schlickbernd (Lorini) Jet Propulsion Laboratory
jenni@jato.jpl.nasa.gov or elroy!jato!jenni@csvax.caltech.edu
CIS: 72466,3413  Voice:(818) 354-8617
"Great leaders are rare, so I'm following myself."

The 'emacs' editor under Un*x has a feature to let you read digested mail
one message at a time, and even delete or keep individual messages from the
digest.
I don't know the details (I've just gotten started on Un*x, and our Ethernet
is busted so I'm not gonna go and look it up now), but it's in the manual
somewhere of course.  When our Ethernet is fixed, I'm going to subscribe
to digested lists on that machine (this machine can gateway), so I can
use emacs to read my mail.  It's much nicer than hacking out the stuff you
don't want with an ordinary editor prior to, say, throwing the file on the
printer (and infinitely superior to throwing the *whole* file on the printer).