Project 3 – Conway’s Game of Life

A kind of cellular automaton

Proposed by the mathematician John Conway in 1970.

Complex behavior emerges from simple rules.

The Game of Life itself is not a realistic simulation of any actual phenomenon

However, researchers have used cellular automata to model the spread of weeds, fire, urban sprawl, and other phenomena

Project 3 – Purpose

Experience with one kind of simulation

Experience using arrays (including 2 dimensional arrays)

Experience modifying an existing program

The Rules of the Game

A game in the sense of a simple set of rules that can give rise to complex behavior, rather than in the sense of several players competing.

The game is played on a 2 dimensional array of cells.

Each cell is either alive or dead. We are given some starting configuration of live and dead cells.

At each step, we compute the next state of the array.

The game continues indefinitely, although obviously you'll want to stop it at some point.

Computing the Next State

For each cell, calculate how many live neighbors it has. Each cell has 8 neighbors:

Computing the Next State (2)

For each cell, calculate how many live neighbors it has out of its 8 neighbors.

If the cell is alive:

If it has 2 or 3 live neighbors, it remains alive.

If it has 0 or 1 live neighbors, it does of loneliness

If it has 4 or more live neighbors, it dies of overcrowding.

If the cell is dead:

If it has 3 live neighbors, it comes alive

Otherwise it remains dead.

Computing the Next State (3)

The next state for each cell is computed using the current states of its neighbors. (You'll get wrong results if you update a cell and then use the updated state of that cell when computing the state of its neighbors.)

One and Two Dimensional Arrays

ooops ….. Visual Basic does allow you to declare both the lower and upper bounds of an array:
           Dim a(1 To 100) as Integer

You can have two dimensional arrays as well as one dimensional ones. This is much more natural for the Game of Life
      Dim cells (0 To 31, 0 To 31) As Integer
      Dim i As Integer
      cells(2,3) = 1
      i = cells(4,5)

Visualizing a 2-D Array

Dim a (1 To 3, 1 To 3) As Integer

We’ll regard the first subscript as the row, and the second as the column

More on Declaring Arrays

Unless you do something special, the bounds of an array in the declaration must be constants:
           Dim a(1 To 100) as Integer

We can declare constants though for easier modification:
    Const nRows As Integer = 30
    Const nCols As Integer = 30
    Dim newCells (1 To nRows, 1 To nCols) as Integer

For Loops

Do while is going to get pretty tedious for the Game of Life, because we iterate through arrays all the time

Equivalent constructs:

Mini-Exercise

What does this print?

Write a for loop that prints the integers between 0 and 10 inclusive.

Mini-Exercise – Answer

What does this print?

Write a for loop that prints the integers between 0 and 10 inclusive.

Mini-Exercise

What does this print?

Mini-Exercise -- Answer

What does this print?

Nested For Loops

Just as with Do While loops, we can nest one for loop inside another. This is very common when dealing with 2-dimensional arrays

Mini-Exercise

What does this print?

Mini-Exercise – Answer

What does this print?

Mini-Exercise

What does this print?

Mini-Exercise – Answer

What does this print?


	A kind of cellular automaton
	Proposed by the mathematician John Conway in 1970.
	Complex behavior emerges from simple rules.
	The Game of Life itself is not a realistic simulation of any actual phenomenon
	However, researchers have used cellular automata to model the spread of weeds, fire, urban sprawl, and other phenomena


	Experience with one kind of simulation
	Experience using arrays (including 2 dimensional arrays)
	Experience modifying an existing program


	A game in the sense of a simple set of rules that can give rise to complex behavior, rather than in the sense of several players competing.
	The game is played on a 2 dimensional array of cells.
	Each cell is either alive or dead. We are given some starting configuration of live and dead cells.
	At each step, we compute the next state of the array.
	The game continues indefinitely, although obviously you'll want to stop it at some point.


	For each cell, calculate how many live neighbors it has. Each cell has 8 neighbors:


	For each cell, calculate how many live neighbors it has out of its 8 neighbors.
	If the cell is alive:
		If it has 2 or 3 live neighbors, it remains alive.
		If it has 0 or 1 live neighbors, it does of loneliness
		If it has 4 or more live neighbors, it dies of overcrowding.
	If the cell is dead:
		If it has 3 live neighbors, it comes alive
		Otherwise it remains dead.


	The next state for each cell is computed using the current states of its neighbors. (You'll get wrong results if you update a cell and then use the updated state of that cell when computing the state of its neighbors.)


	ooops ….. Visual Basic does allow you to declare both the lower and upper bounds of an array: Dim a(1 To 100) as Integer
	You can have two dimensional arrays as well as one dimensional ones. This is much more natural for the Game of Life Dim cells (0 To 31, 0 To 31) As Integer Dim i As Integer cells(2,3) = 1 i = cells(4,5)


	Dim a (1 To 3, 1 To 3) As Integer We’ll regard the first subscript as the row, and the second as the column


	Unless you do something special, the bounds of an array in the declaration must be constants: Dim a(1 To 100) as Integer
	We can declare constants though for easier modification: Const nRows As Integer = 30 Const nCols As Integer = 30 Dim newCells (1 To nRows, 1 To nCols) as Integer


	Do while is going to get pretty tedious for the Game of Life, because we iterate through arrays all the time
	Equivalent constructs:


	What does this print?
	Write a for loop that prints the integers between 0 and 10 inclusive.


	Just as with Do While loops, we can nest one for loop inside another. This is very common when dealing with 2-dimensional arrays