A Slightly Different Cellular Automaton

The New Rule:

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:

Action	Result
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.

The Second Generation:

Action	Result
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.

Moving On:

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!

Exercises:

At this point, you should be able to answer the following questions. Check your answers here.

1. Convert these binary (base-2) numbers to base-10:
   1. 10
   2. 101
   3. 10110010
   4. 11111111
2. Convert theses base-10 numbers to base-2:
   1. 6
   2. 11
   3. 100
   4. 148
3. Construct the first 5 generations of the following CAs, starting with a single "live" (black) cell: (Hint: Convert the rule number to binary, then convert the binary digits (bits) into a rule.)
   1. Rule 28
   2. Rule 150

last update November 24, 2009 by JL Stanbrough