Task $1$A: Building Randomly a Society $[10$ marks$]$

In this task, we are going to define the function build$\_$society $(m,n),$ which builds an $mn$ society

randomly populated with live and dead cells.

Assumptions

$,m$ and $n1$

Output must be a list of lists

Note: As long as the result of your function returns an $mn$ society randomly populated by dead and live

cells, your solution will be accepted. There is also no need to set the random seed for computation.

Example Run

$\{$:$[^(\text{'})-^(\text{'}),^(\text{'})^(\text{'})],[^(\text{'})-^(\text{'}),^(\text{'})],[^(\text{'}**),^(\text{'}\text{'})]]...$

$....$

$...$ Task $1$B: Modeling a Society $[15$ Marks$]$

As we have observed from Task $1$A$,$ we have not much control over the life or death of a cell in the society

built. In this task, we instead would like to take control over the life or death of every cell when we build a

society. For instance, the society built in the last sample run of Task $1$A is replicated below:$-**+=$

$....$

$.$

Here, we want to model a society based on this resultant society. We shall take in this resultant society,

which consists three strings of characters, and convert it into proper internal structure of a society: List of

lists of characters of $\text{'}-\text{'}$ and $\text{'}$ cdots $\text{'}.$ To be precise, we copy the printed society and paste it as the argument to

our model$\_$society function.

Sample runs $($outputs are highlighted in blue for clarity$)$:$*+\%.$

$`\text{'}\text{'})=+.=$

$=-.=*$ Task $1$C: Coding the Game$-$Of$-$Life Rules $[15$ Marks$]$

Our next task is to turn the set of Game$-$of$-$Life rules into a function. Specifically, we notice that whether a

cell will be destined to live or die depends on two factors: $(1)$ its current liveness: either it is alive or dead at

the moment; and $(2)$ the number of live neighbors surrounding it$.$

Write a function gol$($cell$\_$value, live$\_$neigh$)$ that takes in $(1)$ a Boolean value representing live $($by True$)$

and dead $($by False$)$; and $(2)$ an integer between $0$ and $8($both inclusive$)$ capturing the number of live cells in

its $($maximum eight$)$ neigbourhood. The function returns True when the cell will be alive in the next

evolution, and False otherwise. Your function should define correctly the game$-$of$-$life rules, as replicated

below:

Any live cell with fewer than two live neighbours dies, as if caused by loneliness.

Any live cell with two or three live neighbours lives on to the next generation, as if sustained by

friendship.

Any live cell with more than three live neighbours dies, as if caused by over$-$crowdedness.

Any dead cell with exactly three live neighbours becomes a live cell in the next generation, as if by

reproduction.

Sample runs:

$$ gol$($True$,3)$ # Current cell is alive, three live neighbor

True # The cell is destined to die in the next evolution

$$ gol$($False$,3)$ # Current cell is dead, three live neighbor

True # The cell is destined to live in the next evolutionTask $1$D: Tabulating Game$-$of$-$Life Rules $[15$ Marks$]$

As we begin to explore different ways of defining game$-$of$-$life rules, we want to be certain about the effect

of our defined rules. A way to ascertain the effect is to display the results of the rules given the current cell

value and the number of live neighbours.

Write a function tabulate$($rules$)$ that takePart $1$: Conway's Game$-$of$-$Life $[100$ marks$]$

The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician

John Horton Conway in $1970.$ It is a zero$-$player game, meaning that its evolution is determined by its initial

state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and

observing how it evolves.

$--$ Wikipedia

We are interested in observing the state of a Game$-$of$-$Life simulation.

The simulation begins with a rectangular society of size $mn(m$ rows, $n$ columns$),$ with any of $mn$ cells

may be dead or alive. Our task is to monitor the evolution of the cells in this society for several generations

$($as determined by the user$)$ based on the following four Game$-$of$-$Life Rules:

Any live cell with fewer than two live neighbours dies, as if caused by loneliness.

Any live cell with two or three live neighbours lives on to the next generation, as if sustained by

friendship.

Any live cell with more than three live neighbours dies, as if caused by over$-$crowdedness.

Any dead cell with exactly three live neighbours becomes a live cell in the next generation, as if by

reproduction.

Note that cells can have up to $8$ neighbours, where a neighbour is a cell that is directly adjacent or diagonal

to the cell.

For example, given the following demography of a $65$ society $($here a dead cell is represented by $\text{'}-\text{'},$ and

a live cell is represented by ${?}^{\text{'}}*\text{'}$ respectively$)$