Cellular Automata

Implement an elementary cellular automata step function for a 2D grid of size $n \times m$ using a von Neumann neighborhood.

The von Neumann neighborhood of a cell $(i,j)$ consists of the cell itself and its 4 orthogonal neighbors: $(i-1,j)$ (above), $(i+1,j)$ (below), $(i,j-1)$ (left), and $(i,j+1)$ (right).

Given input grid A, compute output grid B by applying your own custom function $f$ to each cell's von Neumann neighborhood:

$$B_{i,j} = f(A_{i,j}, A_{i-1,j}, A_{i+1,j}, A_{i,j-1}, A_{i,j+1})$$

Design $f$ to create the most visually interesting simulation possible!

Input

• A: Input grid of integers of size $n \times m$
• n: Number of rows
• m: Number of columns

Output

• B: Output grid of integers of size $n \times m$

Notes

Use zero-flux (Neumann) boundary conditions at all edges:

• At $i=0$ (first row): treat $A_{-1,j} = A_{0,j}$
• At $i=n-1$ (last row): treat $A_{n,j} = A_{n-1,j}$
• At $j=0$ (first column): treat $A_{i,-1} = A_{i,0}$
• At $j=m-1$ (last column): treat $A_{i,m} = A_{i,m-1}$