Part 16 (2/2)

”By all means.” He drew in the fourth dot: And waited.

She looked at it, then up at him. ”That's all?”

”That's the essence.”

”Cal, I'm just a little slower than you. I don't quite see how this relates to comprehension of the so-called 'pattern ent.i.ties' and travel between alternate worlds.”

He raised an eyebrow. ”You don't?”

”You're teasing me!” she complained, making a moue.

So he was learning already! ”There's pleasure in it.”

”You've changed. You used to be so serious.”

”I am stronger -- thanks to you.” On Nacre he had been almost too weak to stand, contemplating death intellectually and emotionally. He still had a morbid respect for death -- but Veg and Aquilon had helped him in more than the physical sense.

”Let's take your square another step,” she suggested. ”I know there's more. There always is with you.”

He looked at the square. ”We have merely to formulate the rule. Three dots are incomplete; they must generate the fourth. Three adjacent dots do it -- no more, no less. Otherwise the resultant figure is not a -- ”

”All right. Three dots make a fourth.” She took his marker and made a line of three: ”What about this?”

”Double feature. There are two locations covered by three adjacent dots. So -- ” He added two dots above and below the line:

”So now we have a cross of a sort.” She shook her head. ”I remain unenlightened.”

”Another rule, since any society must have rules if it is to be stable. Any dot with three neighbor-dots is stable. Or even with two neighbors. But anything else -- more than three or less than two -- is unstable. So our figure is not a cross.”

”No. The center dot has four neighbors. What happens to it?”

”Were this the starting figure, it would disappear. Cruel but necessary. However, the five-dot figure does not form from the three-dot figure because the ends of the original one are unstable. Each end-dot has only a single neighbor.” He drew a new set: Then he erased the ends, leaving one:

”But what of the new dots we already formed?”

”Creation and destruction are simultaneous. Thus our figure flexes so.” He numbered the stages:

1 2 3 4 ”We call this the 'blinker.' ”

She looked at him suspiciously. ”You mean this has been done before?”

”This is a once-popular game invented by a mathematician, John Conway, back in 1970. He called it 'Life.' I have often whiled away dull hours working out atypical configurations.”

”I haven't seen you.”

He patted her hand. ”In my head, my dear.”

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