100 Degree Theorem: Word Display
This display shows the word you have selected.
The display has 3 modes which you toggle with the
little button in the top left corner. Each word is
some string in the digits 1,2,3.
- mode 1: prints out the digits of the word.
-
mode 2: prints out a compression of the word,
in which 1212=a, 1213=b, .... , 3232=x
(lexicographically) and 12=A,...,32=F. This is the
notation we use in the paper.
-
mode 3: prints out the word hexpath, which
is a combinatorial representation of the word.
You can read about the hexpath in detail by consulting
the documentation for the word window on
the main console. In brief,
we draw a certain hexagonal
path in the plane. The path is made by dividing
the three kinds of edges in the hexagonal grid
into types depending on the direction of the
edge, and then following these edges according
to the digits in the word.
The word display can be one of three colors
- Blue: The word describes a billiard
path which starts out perpendicular to one of
the sides of the triangle. The word is
essentially a palindrome.
- Green:
The word is the square of an odd word.
- Red:
All other words.
This same method of representing words is
used when to display the output of our searches.