The Game Of Life Part

So much has been discovered about Conway's "Life" since I first wrote the last two chapters, that it was impossible to summarize the highlights in an addendum. A book could and should be written about the game, an Encyclopedia of Life, or a Handbook of Life, that would put all the important known Life forms on record and thereby save Lifenthusiasts the labor of rediscovering them. The eleven issues that appeared of Robert Wainwright's periodical Lifeline continue to be the main repository of such data. Wainwright is said to be working on a book, and there are rumors of other books about "Life" that are in the making. In the meantime, I will try in this chapter to pull together some of the significant developments in "Life" since my second column on the game ran in Scientific American in 1971. Because so many basic forms were independently discovered by many people, I shall not often attempt to credit first discoverers.

The earliest and most important group of Lifenthusiasts was at M.I.T., centering around William Gosper who is now working for Xerox at their Stanford research headquarters. In the mid-70s the most active "Life" group was in the computer control division of Honeywell, Inc., Framington, Mass. It included (alphabetical order) Thomas Holmes, Keith McClelland, Michael Sporer, Philip Stanley, Donald Woods, and his father William Woods. In the late seventies, an active group of "Life" hackers formed at the University of Waterloo, in Canada, with John Abbott, David Buckingham, Mark Niemiec, and Peter Raynham as the leaders. Most of what I shall report comes from these three groups.

All still lifes with 13 or fewer bits have long been known. The block and tub are the only 4-bit stable forms, and the boat aircraft carrier mm


More still lifes is the only one with 5 bits. Figure 128 caught four of the five 6-bit still lifes, missing only the aircraft carrier shown in Figure 147. There are four 7-bit stable forms: the loaf, long boat, long snake, and fishhook. The fishhook or "eater" is the smallest still life lacking any kind of symmetry. Note that forms such as the boat, barge, ship, and sinking ship can be stretched to any length, and lakes can be made as large as you like, with any number of barges, boats, and ships at anchor on the water. There are nine 8-bit still lifes, ten 9-bit forms, 25 with 10 bits, 46 with 11 bits, 121 with 12 bits, and 149 with 13 bits. The stable pool table in Figure 148 was constructed out of long sinking ships and parts of ponds by William Woods.

Figure 148

Figure 148

The stable pool table

Low-period oscillators

Hundreds of elegant oscillators have been found. Figure 149 shows a few of small size, with short periods. The M.I.T. group, early in the history of "Life," found easy ways to construct giant flip-flops (period-2 oscillators) such as the one shown in Figure 150. It oscillates between the patterns shown in black dots and circles.

Figure 150

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A flip-flop pattern that alternates between states shown in black and with circles

Chapter 22

Another large class of "Life" forms that have been intensively investigated are what the Honeywell group named the fuses. These are stems one or more bits wide, either diagonal or orthogonal, usually infinite in length, that burn steadily from one end toward the other. The simplest is the fuse shown in Figure 151 a, a diagonal of bits that either rises to infinity or has a stable top as shown. It simply burns itself out without producing any sparks or stable smoke. If you put another bit to the left of the lower end, it forms a tiny flame that travels along with the burning.

Figure 151

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