    This disk contains programs discussed in the book
"Fourfield, Computers, Art, & the 4th Dimension. First make a backup
of this disk using DISKCOPY or by copying this diskette to your
hard disk. The programs are given in executable form, which
means that you can run the programs just by typing the name of
the program: make sure that the programs is in the active
(default) drive, and type, for example, "Quasi" to run
quasi.exe. One program, hyper.pas, is given in Pascal source
code as well as executable form, so that programmers can
understand how the programs were made, and what it means to
have hypercubes rotating in four dimensional space. These
programs will self-adjust to the type of hardware that you have
installed; for example if you have an IBM or compatible system
and either CGA, EGA, VGA, or graphics capable monochromatic
graphics cards and monitors installed, the programs will
automatically test the system you are running and make the
necessary modification to run with optimum resolution and
smoothness of your equipment. You do not have to be concerned
with ordering the proper disk or with initializing the programs.

The programs are:
    Hyper.exe.  A single four dimensional cube, a hypercube, is
shown on the screen. You have the option of seeing the hypercube in
perspective projection or not (isometric projection). If you have
a color monitor you will have the option of seeing the hypercube in
stereo projection using the red and blue, 3D glasses included in
your book. Perspective and stereo together is a particularly
effective combination.  There are 12 (count them, 12) distinct
rotations: three regular 3-dimensional rotations abound the
x,y,z axes, three more 4-dimensional rotations around the x-w,
y-w, z-w planes, and these six again with the coordinate system
attached to the figure rather than straight up/down, left/righ
t, up/down. These last six rotations, called body-centered rotations,
are like the pitch, roll, yawl of an airplane independent of the
direction of flight. There is the option of turning
on or off coordinate axes. One final option is "movie,"
which automatically rotates the figure on the screen 360 degrees
in all 12 ways. These options are activated by pressing keys on
the alpha numeric keyboard. (see below).

    Hypers.exe. This program is just like the one above, except
that there is a cluster of nine interlocking hypercubes, a
tessellation where each cell of each hypercube is a cell in precisely
two hypercubes. Options are: perspective, stereo, axes, 12 rotations.


      Quasi.exe and Quasi.dat. This program allows you to
select and rotate of one 4 quasicrystal structures: a sphere
(actually a triacontahedron) made up of 10 fat and 10 thin cells,
the 10 ways, and the 15 ways that a quasicrystal element (the
rhombic dodecahedron) can be assembled to make a quasicrystal spaceframe,
and the quasicrystal dome reproduced in your book. Optionss are:
three dimensional rotations to see the multiple symmetries discussed
in the text, zoom in and out, pan left/right/up/down to view small
sections of the figure, toggle perspective on or off, and use the
stereo glasses. You can dump out to a text file on your disk the
x,y,z coordinates and a list of the connections between vertices so
that you can build, plot,or study the figure in another program.
When dumping out text files of the vertices and connects, the program
will give you the orientation of the figure on the screen (ie. side
view, plan). The program will not give you the two dimensional
perspective projection (for use with a plotter, say), but will
instead always give you true three dimensional coordinates.  Quasi.dat
is a binary data file used by quasi.exe. Quasi.dat is not readable or
useable by humans, but with out it quasi.exe will not run.
You should name your text files of specific figures something
else so that the program does not get confused. By using the
text dump option repeatedly you will have access to all the
information in Quasi.dat.

    Nonlin.exe and nonclid.exe. These are two related
non-Euclidean geometry programs. Both show a 3 x 3 x 3
pattern of boxes from the space where distances are measured
by a non-Euclidean formula. In Nonlin, the corners of the boxes
are connected with straight lines, and with a fast computer
the figure can be turned quickly so that the form is comprehensible.
In Nonclid the corners of the boxes are connected with smooth curves,
so that the nonEuclidean character of the space can be seen. However
this "spline" between corners is very,very slow, and one can lose
the sense of the figure. Options are x,y,z rotations, and a reset button.


    As much a possible, the menus for these programs are identical;
you only have to learn one set of commands for all the programs.
After you see the figure on the screen, or unless you are specifically
told to do so by an instruction of the screen thatlooks like this:
<-- , all commands are in the keyread format; this means that you
do not have to press the return button, no letter or number will
appear on the screen, and as you continue to press the button the
command will be repeated.  For example, to rotate around the x axis,
press the number 1 on the alphanumeric keyboard. Like all the numbers
used, this one is found as part of the typewriter keyboard; the
numbers to the left or right or way on top of the typewriter keys
are not used. As long as you press this key, the figure will continue to
rotate.  You may hear a loud screech from you computer, signifying
that too many future rotations are requested for your computer to
be able to keep track of. If this happens, the program will not crash,
just remove your finger for a few moments until your commuter can
catch up. If you go too far, press the A key (in this case) to unrotate
the figure. The letter keys will work the same in either the upper or
lower case. If you have a fast computer, and you keep your finger on the
perspective toggle switch, the key "P", the screen will flash back
and forth between the two options of perspective or isometric projection,
so you will have to learn to strike the key just once.

    The programs have been set up so that you wear the glasses
just as you did when looking at the "3d" picture in the book,
RED ON RIGHT. A viewer planted on the x_z plane, as we all are,
has a left eye view and a right eye view as is presented on the screen
(or on the printed page). Dave Brisson, a researcher in four-dimensional
stereograms, thought that the left and right eye views should be
given the views of someone standing on the x_w plane (as we could
very well be, in four dimensional space). However, the 3d effect
is much harder for the viewer to accomplish this way, and I do not
think the slight extra information gained is worth the sacrifice.

    One final word, most of the "movie" options take a long time,
 perhaps as long as ten  minutes, and there is no way to stop them
 short of turning off the computer. If the program seems to just run
 on and on, it is not broken; it is just a long movie. If you do
 restart the computer you will not ruin the program.

    It is a good idea to print out these menus. I hope these programs
fill you with wonder as they do me.

Menu for Hyper and Hypers:
1:XW 2:YW 3:ZW 4:XY 5:XZ 6:YZ 7:BXW 8:BYW 9:BZW 0:BXY -:BXZ =:BYZ
A:-XW S:-YW D:-ZW F:-XY G:-XZ H:-YZ J:-BXW K:-BYW L:-BZW ;:-BXY ':-BXZ
R: RESET, START OVER
M: MOVIE, FROM CURRENT POSITION
O: AXES TOGGLE
B: BINOCULAR (STEREO) TOGGLE
P: PERSPECTIVE TOGGLE
Z: ZOOM
U: UNZOOM
Q: QUIT

Menu for Quasi:
1:X rotate  2:Y rotate  3:Z rotate
A:-X rotate S:-Y rotate D:-Z rotate
5: PAN UP
6: PAN DOWN
7: PAN LEFT
8: PAN RIGHT
B: BINOCULAR (STEREO) TOGGLE
P: PERSPECTIVE TOGGLE
L: LOAD FROM LIST OF OBJECTS
Z: ZOOM
U: UNZOOM
Q: QUIT AND COPY TO TEXT FILES

Menu for Nonlin and Nonclid:
1:X rotate  2:Y rotate  3:Z rotate
A:-X rotate S:-Y rotate D:-Z rotate
R: RESET
Q: QUIT



Menu for Nonlin and Nonclid:
1:X rotate  2:Y rotate  3:Z rotate
A:-X rotate S:-Y rotate D:-Z rotate
