A Slice of Life 02-201

More on Slices

Last Time: append() and copy() Operations

s := make([]int, 10)!s = append(s, 5)!

0! 0! 0! 0! 0! 0! 0! 0! 0! 0! 5!0! 1! 2! 3! 4! 5! 6! 7! 8! 9! 10!

c := make([]int, 11)!copy(c, s)!

0! 0! 0! 0! 0! 0! 0! 0! 0! 0! 5!0! 1! 2! 3! 4! 5! 6! 7! 8! 9! 10!

s!

c!

Return to Prime Numbers

func ListPrimes(n int) []int {!!primeBool := PrimeSieve(n)!!primes := make([]int, 0)!!for i:=range primeBool {!! !if !primeBool[i] && i>=2 {!! ! !primes = append(primes, i)!! !}!!}!!return primes!

}!

This stores the primes, which we can print separately.

Return to Prime Numbers

func PrintList(list []int) {!!for _, val := range list {!! !fmt.Println(val)!!}!

}!

This function now works for any slice of ints.

Brainteasers

Exercise: Given a slice a, how could you delete the element at index i?

Brainteasers

Exercise: Given a slice a, how could you delete the element at index i?

a = append(a[:i], a[i+1:])!

Brainteasers

Exercise: Given a slice a, how could you delete the element at index i?

a = append(a[:i], a[i+1:])!

Exercise: Given a slice a, how would you replace the i-th element with the j-th element (thus reducing the length of the slice by 1)?

Brainteasers

Exercise: Given a slice a, how could you delete the element at index i?

a = append(a[:i], a[i+1:])!

Exercise: Given a slice a, how would you replace the i-th element with the j-th element (thus reducing the length of the slice by 1)?

a[i] = a[j]!a = append(a[:j], a[j+1:])!

The Game of Life

Cellular Automata in HW3

The rule

Produces the pattern on the right above, something even more complex.

The Autolab Assignment

Input. You will write a program that takes in a CA rule and produces a given number of iterationsof the CA. Your command should be able to be run using the following command line:

go run ca.go RULE WIDTH STEPS

Where STEPS is the number of steps to run the CA. Since we can’t work with an infinitely longsequence of cells, we will only model WIDTH cells. Finally, RULE is a sequence of 8 ’0’s and ’1’sthat give the outcome of each subrule in the order used in the examples above. For example, therule:

would be given as “11111010” and the rule

2

Rule

Cellular Automata in HW3

The rule

Produces the pattern on the right above, something even more complex.

The Autolab Assignment

Input. You will write a program that takes in a CA rule and produces a given number of iterationsof the CA. Your command should be able to be run using the following command line:

go run ca.go RULE WIDTH STEPS

Where STEPS is the number of steps to run the CA. Since we can’t work with an infinitely longsequence of cells, we will only model WIDTH cells. Finally, RULE is a sequence of 8 ’0’s and ’1’sthat give the outcome of each subrule in the order used in the examples above. For example, therule:

would be given as “11111010” and the rule

2

Rule

Cellular Automata in HW3

The rule

Produces the pattern on the right above, something even more complex.

The Autolab Assignment

Input. You will write a program that takes in a CA rule and produces a given number of iterationsof the CA. Your command should be able to be run using the following command line:

go run ca.go RULE WIDTH STEPS

Where STEPS is the number of steps to run the CA. Since we can’t work with an infinitely longsequence of cells, we will only model WIDTH cells. Finally, RULE is a sequence of 8 ’0’s and ’1’sthat give the outcome of each subrule in the order used in the examples above. For example, therule:

would be given as “11111010” and the rule

2

Rule

Cellular Automata in HW3

The rule

Produces the pattern on the right above, something even more complex.

The Autolab Assignment

Input. You will write a program that takes in a CA rule and produces a given number of iterationsof the CA. Your command should be able to be run using the following command line:

go run ca.go RULE WIDTH STEPS

Where STEPS is the number of steps to run the CA. Since we can’t work with an infinitely longsequence of cells, we will only model WIDTH cells. Finally, RULE is a sequence of 8 ’0’s and ’1’sthat give the outcome of each subrule in the order used in the examples above. For example, therule:

would be given as “11111010” and the rule

2

Rule

Cellular Automata in HW3

The rule

Produces the pattern on the right above, something even more complex.

The Autolab Assignment

Input. You will write a program that takes in a CA rule and produces a given number of iterationsof the CA. Your command should be able to be run using the following command line:

go run ca.go RULE WIDTH STEPS

Where STEPS is the number of steps to run the CA. Since we can’t work with an infinitely longsequence of cells, we will only model WIDTH cells. Finally, RULE is a sequence of 8 ’0’s and ’1’sthat give the outcome of each subrule in the order used in the examples above. For example, therule:

would be given as “11111010” and the rule

2

Rule

Cellular Automata in HW3

The rule

Produces the pattern on the right above, something even more complex.

The Autolab Assignment

Input. You will write a program that takes in a CA rule and produces a given number of iterationsof the CA. Your command should be able to be run using the following command line:

go run ca.go RULE WIDTH STEPS

Where STEPS is the number of steps to run the CA. Since we can’t work with an infinitely longsequence of cells, we will only model WIDTH cells. Finally, RULE is a sequence of 8 ’0’s and ’1’sthat give the outcome of each subrule in the order used in the examples above. For example, therule:

would be given as “11111010” and the rule

2

Rule

2-D Cellular Automaton: The Game of Life

1.  A live cell (dark) with < 2 live neighbors dies. 2.  A live cell with 2-3 live neighbors lives on. 3.  A live cell with > 3 neighbors dies. 4.  A dead cell (light) with exactly three live

neighbors becomes live.

Neighborhood

2-D Cellular Automaton: The Game of Life

1.  A live cell (dark) with < 2 live neighbors dies. 2.  A live cell with 2-3 live neighbors lives on. 3.  A live cell with > 3 neighbors dies. 4.  A dead cell (light) with exactly three live

neighbors becomes live.

Quick Quiz

Exercise: What is the next iteration of this board?

Stable Forms

Quick Quiz

Exercise: Carry out the next few iterations of this board. What happens?

Oscillators

Getting More Complicated …

The Strange Behavior of the R-Pentomino

John Conway’s Question

Think: Is it possible for the number of live cells to grow without bound as time goes on?

Courtesy: Thane Plambeck!

Bill Gosper’s Glider

Courtesy: Thane Plambeck!

Hacking the Game of Life

Game of Life Problem: •  Input: An initial configuration of the Game of Life

board, and an integer n. •  Output: All configurations of this board over n

generations.

Recall: Multidimensional Arrays

0 1 2

3 4 5 6

0 1 2 3 var a [7][4]int!a[1][2] = 19!y := a[3][0] // gives 0!x := len(a) // gives 7!

7 rows

4 columns

Think of as “an array of length 7, where each array contains an array of length 4”.

Creating a 2-D Slice

var field [][]bool = make([][]bool, m)!

2-D slices are also “slices of slices” – we must define the outer slice first.

0 1 2

3 4 5 6

0 1 2 3

m rows

n columns

Creating a 2-D Slice

var field [][]bool = make([][]bool, m)!

2-D slices are also “slices of slices” – we must define the outer slice first.

0 1 2

3 4 5 6

0 1 2 3

m rows

n columns

for row := range field {! field[row] = make([]bool, n)!}!

To initialize the slices in field, write an explicit loop.

Creating a 2-D Slice

var field [][]bool = make([][]bool, m)!

for row := range field {! field[row] = make([]bool, n)!}!

var x = len(field)/2!var y = len(field)/2!field[x][y] = true!

2-D slices are also “slices of slices” – we must define the outer slice first.

To initialize the slices in field, write an explicit loop.

Can use as 2-D array now

0 1 2

3 4 5 6

0 1 2 3

m rows

n columns

Storing all n Generations

Think: How do we store all n generations of a Game of Life Board (which we are storing as a 2-D slice of boolean variables)?

Storing all n Generations

Think: How do we store all n generations of a Game of Life Board (which we are storing as a 2-D slice of boolean variables)?

Answer: A 3-D slice!