SYMMETRY. Figure/Ground tessellation by translation.
INSPIRATION. Created in response to an assignment in a graphic design class. First reproduced in Godel, Escher, Bach by Douglas Hofstadter,
STORY. The following story is excerpted from the introduction to my book Inversions.
My first inversion was in fact one of the most unusual. I was quite lucky to have started with such a challenging theme. In 1975 I attended Matt Kahn’s Basic Design course in the art department at Stanford University. One of the assignments was the following:
Produce a flat design in two or more colors that has no background: that is, one in which the spaces between forms are as positive as the forms themselves (as in a checkerboard). The objective is to make all of the parts of your composition interretlate — use all of the space and make it all work.
Foreground and background are also known as figure and ground, respectively. One way (but by no means the only way) to interrelate figure and ground is to make them exactly the same shape. in the figure on the left , for instnace, the spaces between the black arrows form white arrows. If we repeat this pattern, we can cover the whole plane with alternating black and white arrows.
Of course there are many other shapes besides arrows that will fit together to cover the plane. The artist M. C. Escher devised many ingenious human and animal forms that interlock with copies of themselves to fill space. Discovering such a shape is a fascinating and often frustrating experience, a real exercise in give and take. On the one hand, the outline must make a recognizable shape; on the other hand, it must fit snugly with copies of itself — for every “in” there must be an “out”.
Most of the students in my design class chose to work with animal or other pictorial shapes. As the teacher had encouraged adventurous solutions, and as letterforms had always attracted me, I decided to work with the words figure and ground.
The first possibility that suggested itself was for the spaces within the FIGURE to form the GROUND — a nice visual pun. After repeated failures at this combination, I arrived at the intermeshing of FIGURE with itself shown above. If you turn this design over, you will see that the spaces between the letters in the white FIGURE make an upsdie-down black FIGURE. (It ma take a few moments for your eye to “lock” on the word.) Notice how F first with E, I with R, and G with U. Notice also how some of the letters have been run together. R has been almost lost. The F/E combinations works particularly well; a similar technique would work for F/F or E/E.
Forcing a word to mesh with itself can cause strange things to happen to the letters. In a figure/ground inversion, every line must serve as the boundary of two different letters. Occasionally the two letters fit into each other perfectly, but more often than not they tend to push the boundary in two different directions. Most of the time I spent developing FiGURE went into finding compromises that would still yield legible letterforms.
The letter that suffered the most was the I. Unfortunately, straightening out the unwanted bump would destroy the recognizability of the R. “Wouldn’t it be nice,” I wished, “if the I and R were both right side up, so that the bowl of the R would contain the dot of the I?”
I decided to follow this possibility further. If I were to fit with R, with both letters upright, then working backward, F would have to fit with U, and working forward, G with E. This eventually gave rise to the repeating pattern shown above. The letters jostle around quite a bit but maintain their legibility surprisingly well.
As you look at this inversion, you rmind will oscillate between two different interpretations: black letters on white background, and white letters on black background. Which do you see first? If you practice, you will find that you can “flip” your interpretation at will — a good demonstration that the meaning of a picture is in the mind of the beholder. It is nearly impossible, however, to blanace your perception on the edge of ambiguity, so that both words appear equally dominant.
The evolution of an inversion contains another sort of oscillation: As you develop an inversion, you must constantly switch attention between the demands of legibility and the demands of symmetry. Putting legibility in the foreground tends to make the letters shapes grow more distinct. For instance, I tried to put the correct serifs on the letters in FIGURE wherever possible. Letting symmetry dominate your perception tends to make the letter shapes grow more similar. For instance, the outside of the E was rounded to match the inside of the G. Out of this process of give and take often emerges a visual style that is as much a surprise to the inventor as it is to the viewer.
For the presentation in class, I cut out two copies of FIGURE, one in white cardboard and one in black. Before class, I placed the two words on a table at the front of the room, spelling out the word figure twice, one in white and once in black, without any of the letters interlocking. When it came time to present my project, I pointed to the two words. I said nothing, but soon the implicity challenge was understood.
First my classmates noticed repeated curves. Perhaps the letters were meant to fit together. Different theories were batted around as the shapes were assembled. eventually the black word and the white word were assembled into separate solid masses. But what did this have to do with an assignment on figure/ground relationships? Someone recognized that black and white were to alternate, and finally the desired pattern was revealed.
I never did solve FIGURE/GROUND. But in retrospect, the FIGURE/FIGURE combination seems more fitting after all — a picture that is all FIGURE and no GROUND. The solution was fine; all that needed adjustment was my statement of the problem. This unexpected twist of expectations was a lovely lesson and has remained with me in my explorations. I hope that you, too, will discover new inversions as you explore your own worlds within the magic universe of letterforms.