The R (or F) pentomino, unlike the other eleven, has a story which deserves to be told and which is told almost nowhere. While not particularly famous, this pentomino has its own small importance in both the computer and mathematical worlds. You'll have to follow me through two simple concepts before we begin:

The first is the pentomino. A domino is a figure made from two equal squares, a triomino is made of three squares, and a tetromino (think Tetris) is made of four; therefore, a pentomino is a figure made from five equal squares. And, unlike the domino, it comes in twelve varieties, all named after letters. (This does not count chirality: pentominoes are the same no matter which way they're rotated.) Here they are:

 00  0  0    0   0   000  0 0  0    0     0   0    00
00   0  0   00   00   0   000  0    00   000  00   0
 0   0  0   0    00   0    U   000   00   0   0   00
F/R  0  00  0    P    T         V    W    X   0    Z
     0  L   N                                 Y

The pentominoes, like tangrams, are largely recreational: it is an interesting exercise to fill, for example, a 6 by 10 box with one of each kind. Each pentomino has its own interesting properties (for example, its ability to tesselate), but they are not usually studied in detail. And so we continue...

The second concept is the Game of Life.In 1970, John Horton Conway invented this zero-player "game", a simple cellular automaton (and practically the first of its kind) where the "player" draws an configuration of cells which continue to "live" independently under several simple rules. For those who aren't acquainted with the game, here's a short synopsis:

The game is played on an infinite grid (usually simulated by graph paper. Each cell in the grid has two states — alive and dead (or filled and empty). Now, each cell has eight "neighbors" surrounding it to the sides and diagonally. If a dead cell has exactly three live neighbors, it becomes alive. However, it will die again if its number of neighbors becomes one or less, or four or greater.

So Conway played with his patterns on his reasonably-priced infinite paper for a while. He may have begun investigating simple shapes like the 2 by 2 block and the 3 by 1 blinker, and moving up to the 10 by 1 strip that becomes an oscillator known as the pentadecathlon. All of these shapes end in a fixed or oscillating, predictable structure. But with the R pentomino, he finally met his match. Although it starts with just five cells, the simple figure blossoms into an array of figures Life fans know as blocks, beehives, and boats, throwing off several gliders in the process. In other words, it expands without limit. Although I can't draw the entire sequence for you, I can show you a few examples (0 is alive, a blank space is dead):

 00    0    00   00     0     0   
 00   0 0   0 0  0 0   0 0    0   000     0 0    0 0     0 0
      0 0    00   0    0  0   0         000 000000 000   00
       0                00                0 0    0 0      0

From left to right, we have the block, beehive, and three versions of the boat (all are unmoving); the two stages of the oscillating blinker; a stage of the pentadecathlon, which will visit this formation every fifteen moves (hence the name); and the glider, which will continue diagonally forever. (The glider is also a hacker emblem). I suggest you Google "Conway Game of Life" to find more patterns like these.

But to return to my point, the results were threefold. As Conway could not finish the design on paper, Life changed from graph paper doodles into an miniature computer industry, resulting in programs like Mirek's Cellebration, Life32, XLife, Hashlife, et cetera. The F pentomino became known (as Conway called it) as the R pentomino, possibly making it the most ubiquitous of the pentominoes. (Or, at least, it soon will be). And, finally, Life was given the reputation and ultimate meaning it has today with the symbolism of chaos from order, life from death, the simple from the complex. The science of cellular automata continues to endure, be it on paper, on a screen, or in the mind.
