LISSAJOU.BAS & LISSAJOU.EXE
Copyright Dan Farmer  January 1991
All rights reserved.

The concept for this program came from the Mathematical Recreations column
in Scientific American, January 1991, authored by A.K.Dewdney.  The column
refers to some remarkable ray-traced "creatures" done by Clifford Pickover
at the Thomas J. Watson IBM Research Center.

After playing around a little with the algorithm mentioned in the article for
producing the spherical Lissajous figures used by Pickover, I decided to
write a program to help me make DKB ray-trace script files of the shapes, hence
this program.

Since I am not very well versed on mathematics, I refer you to the article in
Scientic American for more about the concepts behind this program.  All I know
is that you can produce an endless variety of beautiful and complex shapes.
Even if you don't decide to render the images, the preview feature is neat
just by itself.  Another great anti-productivity tool!

For those who are interested in the internals, Pickover's basic algorithm is:
    X = R1*SIN(A*T)*COS(B*T)
    Y = R1*SIN(A*T)*SIN(B*T)
    Z = R1*COS(A*T)
    Where T (time) is an iterative loop, and R,A,and B are parameters.
    I have added an exponential option for X,Y, and Z.

I have also included a couple of "mutations" of the basic algorithm that
will produce other strange and wonderful forms.  They look like this:

    X = R1*SIN(A*T)*COS(B*T)
    Y = R1*COS(A*T)*COS(B*T)
    Z = R1*SIN(A*T)


    X = R1*SIN(A*T)*SIN(B*T)
    Y = R1*SIN(A*T)*COS(B*T)
    Z = R1*SIN(A*T)

For those with a QuickBASIC compiler, other perversions are easy to add.
Put the variation into a sub-routine named ALGO.FOUR (etc.) and edit
the line   ON ALGO GOSUB ALGO.ONE, ALGO.TWO,ALGO.THREE to include your
new module.  Also modify the variable MAXALGO that is used for bounds
checking.

The DKB script is written using SPHERES of a quantity and size that you
specify.  The color and texture are DECLARED as Atexture and
Acolor to make it easy to modify the whole composite in a single blow.

Hope you have fun with it... but be warned:  It takes a lot of computing
power to render 500 or so spheres.  You will probably find that less than
that amount doesn't make a smooth enough object.

Dan Farmer
1001 E. 80th St.  Apt #102
Bloomington MN 55425
(612) 854-6209

Leave mail on the You Can Call Me Ray BBS (708) 358-5611.

(DKB a ray-tracing program written by David K. Buck with Aaron Collins.)