The Center for Research on Concepts and Cognition
In case you've missed out on the desktop publishing craze of the past decade, a font is a style of characters used for printing -- examples are Times Roman and Helvetica, or the Arial in which you are probably viewing this page (if you're on Windows; on a Mac you may well be seeing Helvetica.) The design and appreciation of a font is an enormously complex task, involving both letter style (how well a particular letter's form fits into the font) and letter quality (how well a particular letter's form "looks like" the letter it's supposed to be). This sounds easy, but there is a vast range of variation in both style and quality in the fonts actually used in everyday life.
The notion of a gridfont is an attempt to scale the problem of font design and perception down to the point of implementability. A gridfont character is made up of line segments on a 3x7 grid. Horizontal, vertical, and 45-degree diagonals are allowed. This represents a gigantic simplification of the problem already, as real fonts have curves, serifs, varying thicknesses of strokes, and many other characteristics which are completely ignored in the gridfont paradigm. Moreover, the usual gridfont problem space is also restricted to the 26 lower-case letters, with no capitals, numeral, or punctuation.
However, the gridfont microdomain, like any well-conceived microdomain, still admits to an astounding variety of cognitive phenomena, including beauty, elegance, ugliness, clearness and murkiness, humor, subtlety and blatance. Human-designed fonts (the vast majority of which were designed by Hofstadter during a year of gridfont mania in 1984 after he bought his first Macintosh, complete with drawing program) can exhibit extremely strong coherence of font style without losing much in the way of readability. Here, for example, are sixteen gridfonts lifted straight from Hofstadter's book and also incorporated into John Rehling's thesis on his work implementing Letter Spirit. (There is a wider variety of styles of the letter "a" on page 424 of the book.) John's thesis, available in the publications section of this site, is highly recommended for its coherent and complete analysis of the gridfont domain.