The "Game of Life" was invented by John H. Conway to simulate the birth and death of cells in a society. It really isn't a "game", but a simulation of population growth that is displayed over time.

Game Rules:

The game is played on the rectangular board. Each square at time T could contain 1 that indicates the presence of the organism (life) or 0 that indicates the absence of the organism (death).

The following rules govern the birth and/or death of these organisms between two consecutive time periods. At time T, for each square:

Birth: An organism is born if there was none at time T-1 and exactly three of its neighbors were alive.

Survival: An existing organism remains alive if at time T-1 there were either two or three neighbors.

Death: An organism dies from isolation if at time T-1 there were fewer than two neighbors.

Death: An organism dies from overcrowding if at time T-1 there were more than three neighbors.

At time T the situation on the board is called configuration.

The Game is over when there is no change in configuration between two consecutive time periods or the program performed certain number of iterations.

See example below:

Table

Write the following functions to complete the Game. There are different levels to implement the game. Level 1, Level 2, Level 3, Level 4

Pay attention: you always need to work with TWO boards: oldBoard (configuration at time T-1) and newBoard (configuration at time T), since while creating configuration at time T you cannot change configuration at Time T-1. The initial configuration is configuration at time 0. I suggest you work in the same file you worked in lab 8, add additional functions and change the main

Level 1 and Level 2

def make_new_board(oldBoard, row, col) which has three parameters, 2D list with configuration at time T-1. The function creates and returns a new board - configuration at time T, using the rules of the game. This function will use function neigh from lab 8.

MAIN function for Level 1: Ask user to enter 1 to randomly generate initial configuration, and 0 for user input. Create a new configuration for Time 1 using function make_new_board. Find if it was change in configuration and print the number of live organisms at Time 0 and Time 1.

MAIN function for Level 2: Ask user to enter 1 to randomly generate initial configuration, and 0 for user input. Create a new configuration for Time 1, then at Time 2 and Time 3. Find if it was change in configuration at each time and print the number of live organisms at each time.

Level 3. In addition to function make_new_board, write the following function and complete the main
def play_game_simple(board, row, col, max_time) which has three parameters, initial configuration (Time 0), number of rows and number of columns. This function plays the Game by creating new configurations starting at Time 1 and moving up to max_time. Function prints the board for each time level. The function returns the number of live ogranisms after max_time configurations are done.

MAIN function for Level 3: Ask user to enter 1 to randomly generate initial configuration, and 0 for user input. Ask user to enter the max_time - the maximal number of iterations for your game. Call function play_game_simple to play the game. Print the number of live ogranisms at the end of the game. Pay attention, this function will use functions from lab 8: copyBoard and count.

Level 4. In addition to function make_new_board, write the following functions and complete the main.
def play_game(board, row, col, max_time) which has three parameters, initial configuration (Time 0), number of rows and number of columns. This function plays the Game by creating new configurations starting at Time 1 and moving up to max_time or until no change in configuration is occured. Function prints the board for each time level. The function returns True if the game was over at max_time and False otherwise. Pay attention, this function will use functions from lab 8: copyBoard and change.

def endMessage(status) - the function pints the final message according to the value of the parameter result. The value of the parameter result will be the value that was returned by function play_game. If the value of the parameter result is False, it means that the game was over because there is no change in configuration. And if the value of the parameter result is True, it means that the game was over after max_time configurations (which will be user input). The function should print an appropriate message.

MAIN function for Level 4: Ask user to enter 1 to randomly generate initial configuration, and 0 for user input. Ask user to enter the max_time - the maximal number of iterations for your game. Call function play_game to play the game. Call function endMessage to print the fincal messsage. Call function count(from lab 8) to find the number of live ogranisms at the end of the game.