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Local Communication

$X(t+1)$_i,j=(4X^(t)_i,j+X^(t)_i-1,j+X^(t)_i+1,j+X^(t)_i,j-1+X^(t)_i,j+1)/(8)

for t = 0 to T-1
  send X(t)(i,j) to each neighbor
  receive from neighbors 
    X(t)(i-1,j), X(t)(i+1,j), 
    X(t)(i,j-1), X(t)(i,j+1)
  compute X(t+1)(i,j)
end

Improvement: Gauss-Seidel strategy

$X(t+1)$_i,j=(4X^(t)_i,j+X^(t+1)_i-1,j+X^(t)_i+1,j+X^(t+1)_i,j-1+X^(t)_i,j+1)/(8)

(See Foster, Figures 2.4 and 2.5)