Creating Large Life Forms with Interactive Life

Ever since John Conway introduced the game of Life in 1970 [2], amateur and professional mathematicians have been obsessed by finding new complicated structures, and finding new applications for the seemingly chaotic behavior of Life forms. Perhaps its addictive nature stems from the simplistic rules: each cell on a square lattice is either on (alive) or off (dead). The Moore neighborhood of a cell is the eight surrounding cells (counting diagonals) [3]. If a dead cell has exactly three neighboring cells which are alive, then the cell becomes alive in the next generation. On the other hand, a living cell must have either two or three living neighbors to remain alive, otherwise the cell will die in the next generation. Figure 1 shows four generations of the Life form known as the “glider.” Because every four generations, this glider moves one space diagonally, we say that this glider moves at 1/4 the speed of light. (In the Life model, light is said to travel at 1 square per generation.) The first open problem that Conway asked was whether any Life form could be proven to have unbounded growth. This was solved by Bill Gosper’s discovery of the glider gun, a formation that spews a glider every 30 generations [4]. Other glider guns have since been discovered, but none have been as efficient as the original, now referred to as the “p30 glider gun.” Using glider guns, one in fact can engineer even more complex Life forms. Any computer circuit, and even a Turing machine, can be con-