CSCI 150: PreLab 10

In this prelab you will formulate some of the ideas necessary to complete Lab 10. Please turn in your solution on Gradescope. You can either turn it in as a PDF (e.g., saving a document as a PDF in Word), take a picture (e.g., with a smartphone), or scan it (e.g., at the library) to hand it in. Please remember, no late prelabs allowed!

Part 1 - Reading

Part 2 - The Game of Life

The Game of Life, created by mathematician John Conway, is what is referred to as a cellular automaton. It is a set of rules rules which are used to generate patterns that evolve over time. Despite the name, the Game of Life is not a game; it is really a simulation. In some ways, it can be thought of as an extremely simplified biological simulator which produces unexpectedly complex behavior.

The Game of Life is played on an infinite board made up of square cells. It takes way too long to draw an infinite board, so we'll make do with a small finite piece. Each cell can be either live or dead. We'll indicate a live cell as a red square, and a dead cell as a black one. The board begins in some initial configuration, which just mean a setting of each cell to be either live or dead (generally we'll start mostly dead cells, and only a few live cells).

The board is repeatedly updated according to a set of rules, thereby generating a new configuration based on the previous configuration. Some dead cells will become live, some live cells will die, and some cells will be unchanged. This configuration is then updated according to those same rules, producing yet another configuration. This continues in a series of rounds indefinitely (or until you get bored of running your simulation).

Rules of Life

The rules are pretty simple: to figure out whether a cell (x,y) will be live or dead in the following round, you just look at the 8 neighbors of that cell (those that share a corner or an edge, so N, S, W, E, NW, NE, SW and SE). What happens to (x,y) next round depends on the number of its neighbors who are live and whether it is currently live or not. In particular:

• If a cell has 4 or more live neighbors, it dies (overcrowding).
• If a cell has 0 or 1 live neighbors, it dies (loneliness... *sniff*).
• If a cell has exactly 2 live neighbors, nothing changes (if it was live, it stays live, if it was dead, it stays dead).
• If a cell has exactly 3 live neighbors, it comes to life (I don't have a good explanation for this one, but it does seem to make for cool patterns).

For example, consider the following 3 initial configurations, and the two configurations that follow each.

In the first example, both live cells have only one live neighbor, so they both die. Any dead cell has at most two live neighbors, so no new live cells spawn. Thus in one step, there are no live cells. Clearly, at this point, the configuration is stable.

In the second example, two live cells have only one neighbor, so both die. But the third cell lives, and the cell to its immediate left has exactly 3 live neighbors, so it spawns. On the next iteration, we find ourselves in a case similar to the previous example, and all cells die.

Note that we can't set a cell to be live or dead the instant we determine its status for the subsequent round; we will likely need to know whether it is alive or dead on this round to determine the future status of other nearby cells. To see this, consider the second example. We can immediately tell that the top-most live cell will die. But had we set it to dead immediately, then when we got to the second live cell, it would have only had 1 live neighbor and we would have (erroneously) determined that it too must die. Thus it is critical that we first determine for every cell whether or not it will be live, and only after doing so update the status of each.

In the last example, all currently living cells die; the middle cell has too many neighbors, and the other have too few. However, four dead cells have exactly 3 live neighbors, and so those cells spawn. In the following round, there are neither cells that die nor cells that spawn, so we have a stable configuration. In general, a pattern that doesn't change is called a still-life.

While all of these patterns stabilized quickly, some patterns take a long time to stabilize, and some never do. Of those that never stabilize, some at least have a regularity to them; they eventually eventually repeat states. These are said to be oscillators. Others never repeat the same state again, and produce an infinite number of configurations.

Describe the Problem:
The problem you will solve on your lab is as follows.
input: none (although we may may change this later so that there is some way to input an initial configuration)
goal: simulate the game of life on an initial configuration that is hard-coded into your program.

Understand the problem:
Consider the following four intial configurations.

For each of these, you should specify the next four generations of each. You can either draw pictures, or type solutions. If you do the latter, I suggest you use a fixed width-font (like courier) and use a period (.) for a dead cell, and an X for a live cell. For example, the initial configurations would look like:

.....   .....   .....   .X...
.....   .XXX.   .XX..   ..X..
.XXX.   XXX..   .XX..   XXX..
.....   .....   .....   .....
.....   .....   .....   .....

Honor Code

If you followed the Honor Code in this assignment, write the following sentence attesting to the fact at the top of your homework.

I affirm that I have adhered to the Honor Code in this assignment.