Question $5(20$ Pts$.)$

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 the best$-$known example of a cellular automaton.

This game uses an m x n grid of cells, and each cell begins with one of two states: alive $($noted by a $1)$ or dead $($noted by a $0).$ Each cell then interacts with the eight cells that surround it $($these can be horizontal, vertical, or diagonal$)$ based on these four rules:

Any live cell with fewer than two live neighbors dies, as if caused by underpopulation.

Any live cell with two or three live neighbors lives on to the next generation.

Any live cell with more than three live neighbors dies, as if by overpopulation.

Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.

The next state is created by applying the above rules simultaneously to every cell in the current state, where births and deaths occur simultaneously. Write a function to compute the next state of the following states with Matlab$/$Octave$.$

Note that you can take the border of the grid as dead cells.

Examples: