Let's modify the last rule slightly - simply change the neighborhood-0 output from white to black. The new rule is shown below:
What is the Wolfram code for this rule? With such a slight change in the rule, we ought to expect a sligh change in the output, right? Let's see.
The First Generation:
|All of the neighborhoods to the left of the black cell are , so all cells from the arrow leftward are black/on in the first generation.|
|All neighborhoods from this one are , so all remaining cells in this generation are black/on. This completes the first generation.|
|All neighborhoods to the left of the neighborhood shown follow , so all of those cells produce a white/empty cell. The neighborhood shown at right is , so its successor is black/on.|
|All of the remaining cells are . This completes the second generation.|
The third generation is .
After eleven generations you should have .
Switching to Mathematica (computer), the first 50 generations is:
Making a tiny change in the rule certainly did not make a slight change in the output! This is a completely different pattern!
At this point, you should be able to answer the following questions. Check your answers here.
last update November 24, 2009 by JL Stanbrough