The 16 vertexes of the hypercube in the program are numbered from 0 to 15
according to a simple scheme. If each number is rewritten in binary form
and converted into an array of four bits, a miniature coordinate system
emerges. The binary digits of 13, for example, are 1 (that is, one 8), 1
(one 4), 0 (zero 2's) and 1 (one 1). The binary number can then be written
as the array
Dimensions seem to creep in everywhere as HYPERCUBE
is
written. A two-dimensional matrix, or array, called vert
preserves the vertexes as they are initially defined. Since there are 16
vertexes with four coordinates each, vert is a 16-by-4 matrix of 64
numbers; vert(i,j)
is the jth coordinate of the
ith vertex. The program HYPERCUBE
holds the matrix
vert
inviolate; vert
is defined at the beginning
of the program and its contents are then transferred to a second 16-by-4
matrix called cube
. The matrix cube
can be
thought of as a working matrix; its contents are continually altered by the
rotations carried out in the program.
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