How to resolve the algorithm Conway's Game of Life step by step in the R programming language
How to resolve the algorithm Conway's Game of Life step by step in the R programming language
Table of Contents
Problem Statement
The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is the best-known example of a cellular automaton. Conway's game of life is described here: A cell C is represented by a 1 when alive, or 0 when dead, in an m-by-m (or m×m) square array of cells. We calculate N - the sum of live cells in C's eight-location neighbourhood, then cell C is alive or dead in the next generation based on the following table: Assume cells beyond the boundary are always dead. The "game" is actually a zero-player game, meaning that its evolution is determined by its initial state, needing no input from human players. One interacts with the Game of Life by creating an initial configuration and observing how it evolves.
Although you should test your implementation on more complex examples such as the glider in a larger universe, show the action of the blinker (three adjoining cells in a row all alive), over three generations, in a 3 by 3 grid.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Conway's Game of Life step by step in the R programming language
Source code in the r programming language
# Generates a new board - either a random one, sample blinker or gliders, or user specified.
gen.board <- function(type="random", nrow=3, ncol=3, seeds=NULL)
{
if(type=="random")
{
return(matrix(runif(nrow*ncol) > 0.5, nrow=nrow, ncol=ncol))
} else if(type=="blinker")
{
seeds <- list(c(2,1),c(2,2),c(2,3))
} else if(type=="glider")
{
seeds <- list(c(1,2),c(2,3),c(3,1), c(3,2), c(3,3))
}
board <- matrix(FALSE, nrow=nrow, ncol=ncol)
for(k in seq_along(seeds))
{
board[seeds[[k]][1],seeds[[k]][2]] <- TRUE
}
board
}
# Returns the number of living neighbours to a location
count.neighbours <- function(x,i,j)
{
sum(x[max(1,i-1):min(nrow(x),i+1),max(1,j-1):min(ncol(x),j+1)]) - x[i,j]
}
# Implements the rulebase
determine.new.state <- function(board, i, j)
{
N <- count.neighbours(board,i,j)
(N == 3 || (N ==2 && board[i,j]))
}
# Generates the next interation of the board from the existing one
evolve <- function(board)
{
newboard <- board
for(i in seq_len(nrow(board)))
{
for(j in seq_len(ncol(board)))
{
newboard[i,j] <- determine.new.state(board,i,j)
}
}
newboard
}
# Plays the game. By default, the board is shown in a plot window, though output to the console if possible.
game.of.life <- function(board, nsteps=50, timebetweensteps=0.25, graphicaloutput=TRUE)
{
if(!require(lattice)) stop("lattice package could not be loaded")
nr <- nrow(board)
for(i in seq_len(nsteps))
{
if(graphicaloutput)
{
print(levelplot(t(board[nr:1,]), colorkey=FALSE))
} else print(board)
Sys.sleep(timebetweensteps)
newboard <- evolve(board)
if(all(newboard==board))
{
message("board is static")
break
} else if(sum(newboard) < 1)
{
message("everything is dead")
break
} else board <- newboard
}
invisible(board)
}
# Example usage
game.of.life(gen.board("blinker"))
game.of.life(gen.board("glider", 18, 20))
game.of.life(gen.board(, 50, 50))
You may also check:How to resolve the algorithm Singly-linked list/Element definition step by step in the Odin programming language
You may also check:How to resolve the algorithm Get system command output step by step in the BASIC programming language
You may also check:How to resolve the algorithm Benford's law step by step in the Picat programming language
You may also check:How to resolve the algorithm Show the epoch step by step in the Common Lisp programming language
You may also check:How to resolve the algorithm Bitmap/Bézier curves/Cubic step by step in the ALGOL 68 programming language