Monster Media 1993 #2/Image.iso/math/attract.zip/ATTRACT.DOC

Text File | 1993-07-03 | 8KB | 177 lines

          Documentation file for ATTRACT.EXE by Eric Deren  7/2/93

TOC:

Part 1 - What is it?
Part 2 - How do you use it?
Part 3 - Why did I write it?
Part 4 - Who am I?
Part 5 - Bibliography

                            Part 1 - What is it?

   ATTRACT is a program that calculates in real-time Poincaré sections of
chaotic (or "strange") attractors in phase space (sometimes called a
multiple-body phase portrait).  Currently supported are the Damped and
Driven Pendulum (DDP) model and the Duffing Two-Well Oscillator (DTWO).
   Phase space is a coordinate system used for motion analysis where,
rather than showing displacement vs. time, velocity vs. displacement is
shown.  One point in the DDP simulation represents the phase portrait of
a pendulum that is allowed to flip an entire 360° (2π).  Displacement (x axis)
is given by the angle, in radians, and the velocity (y axis) is velocity
in radians per second.  A phase portrait of a standard everyday pendulum
with friction would resemble a spiral to the origin of the coordinate system,
as the pendulum slowed down, changed direction, sped up, passed 0
displacement, slowed down and changed direction again.  The interesting
thing about the DDP is that it is also driven by a force that comes at
a specific frequency.  If this frequency is out of phase with the pendulum's
natural movement, chaos takes over and we have a non-linear dynamical
system.
   In much the same way as the Lorenz attractor, the particles in these
simulations never run over the same path twice.
   For more information, see the bibliography.


                        Part 4 - How do you use it?

   Usage:

   ATTRACT [options]

         options:                  abbreviations:
        step=(step size)                 i=
   particles=(# of particles)            p=
   attractor=(attractor #)               a=
       style=(style #)                   s=
distribution=(dist #)                    d=

   Attractor numbers:

   1)  Damped and Driven Pendulum
   2)  Duffing Two-Well Oscillator

   Style Numbers:

   1)  Erases old points and redraws new at the same time.  Reduces flicker.
   2)  Clears screen and then draws new points.  Useful if you are doing
       large numbers of points and the erase/redraw looses all illusion
       of movement.
   3)  Just draws points and doesn't erase them.  Useful if you want to run
       just one or two points and view their path.  You will probably want
       to turn down the step size so you get a solid line.

   Distribution Numbers:

   1)  Starts with an evenly distributed row of points.  Similar to Merge2.
   2)  Starts with an evenly distributed block of points.
   3)  Starts with a random scattering of point positions.

   Hints:

   Attract without arguments will function using the default values.  Type
an something not listed to get a command list.

   I wouldn't try to run more than 16000 points if I were you.  The program
is supposed to be making sure that you have memory for these points, but
for certain numbers above around 16000 strange things start to happen; more
strange than the display.

   Because of all of the floating point calculations going on here, this
program really drags on anything less than a 386 with a math coprocessor.
I haven't seen it on a 486sx, but it should be fine.  If the standard
setup looks more like a repainting line than an animation, you will want
to see this program on a faster computer.

   Increasing the number of points has the effect of slowing down the
display for those of you with computers too fast.

   For a neat display of unpredictable chaotic behavior, run
ATTRACT p=1 s=3 i=0.002
Watch it for a few minutes and try to predict where it's going next.
Good luck.   The above with i=0.005 is kinda neat too.

   Because chaos is so dependent on starting conditions, small things
like changing the step size will create a different display.  After about
a minute, a point with a step size of i=0.002 will be moving completely
different from a point started with a step size of i=0.001.  This is because
you are giving it different numbers of chances for round-off error to occur,
and those little numbers add up in a chaotic system.


This program is released as shareware.  It may be freely distributed as long
as it remains unmodified.  Peace.

Disclaimer:  You use ATTRACT at your own risk.  I won't be held responsible
             if it screws anything up.


                        Part 3 - Why did I write it?

   I wrote the original program because I've always been fascinated by
the processes involved in getting a computer to simulate reality.  As
you can see by most of my raytraced art and animations, I strive for
realism, not just for realism's sake, but to get my viewer wondering
whether it's real.  Then, as soon as it could almost be real, I do something
bizarre.  In much the same way as Industrial Light and Magic works.
   Now, personally, I don't see this thing looking like a pendulum at all.
But it makes one heck of a can of paint with two colors being mixed together.
Or maybe some smoke in turbulent air.
   This version is here because I didn't want the code to sit on my computer
and rot.  I added a command line interface, and made the systems user
selectable, so now other people can enjoy the picture.  If you saw Merge2,
Hype, or Htorus, those were other cases of this same situation.  Of course,
my other programs were in color, but hey, black & white is classy.  (read:
I couldn't figure out a nice way to color the dots)


                            Part 4 - Who am I?

  I'm Eric Deren.  I usually do computer animation, but programming is
one of my other hobbies.  (along with bike riding, swimming, and weight
lifting)  I also do video editing and camera work.  At the time of this
writing I'm just out of high school (at the NC School of Science & Math,
a public school in Durham, NC) and preparing for school at Georgia Tech.

  Anyway, if you've used and liked Attract, and you have questions/comments/
suggestions/money/employment for me, I can be reached as ERIC DEREN by Email
via the PCGnet, or The Graphics Alternative BBS [phone], or
The Leo Graphics BBS [phone].  I don't know my internet address for
next year yet, but it will probably be @hydra.gatech.edu.

   Obviously, when I was writing this thing, I wasn't thinking about money.
But if you wish to send me some money or some hardware (sugg: SIMMS ;-) or
something please feel free.  I will accept gladly. :-)

Thanks for your support!
Eric Deren
Rt 1 Box 401
Andrews, NC 28901



                            Part 5 - Bibliography

  Just a little something for those of you who are intrigued as I was when
I was trying to figure this stuff out.  There are also several good general
fractal books in this list.

  J. Gleick, CHAOS: Making a New Science (New York: Viking Penguin, 1987)

  S.N. Rasband, Chaotic Dynamics of Nonlinear Systems (New York: John Wiley
           & Sons, 1990)

  K. Briggs, "Simple Experiments in Chaotic Dynamics," Am. J. Phys. 55 (12)
           (December 1987)

  E.C. Zeeman, F.R.S. in Dynamical Chaos, ed: M.V. Berry, I.C. Percival, and
           N.O. Weiss (Princton: Princton University Press, 1987)

  Devaney, Robert L., Chaos, Fractals, and Dynamics: Computer Experiments in
           Mathematics  (Menlo Park, CA: Addison-Wesley, 1990)

  Peitgen, H. -O and P.H. Richter, The Beauty of Fractals: Images of Complex
           Dynamical Systems  (New York: Springer-Verlag, 1986)

  Pickover, Clifford A., Computers, Patterns, Chaos and Beauty (New York:
           St. Martin's Press, 1990)