http://math.stackexchange.com/questions/1425676/gravitational-potential-inside-infinite-grid-of-masses

gravnet.rb

#!/usr/bin/ruby
# gravnet.rb

require "matrix"

# simplified gravitational force (G=m=M=1.0)
# from (i,j) to r
def fij(i, j, r)
  # difference vector
  rij = Vector[i,j] - r
  # length of difference vector
  d = rij.r
  # force
  f = rij / (d**3)
  return f
end

# force summing over the grid square [-n,n] x [-n, n]
def fsum(r, n)
  f = Vector[0.0, 0.0]
  (-n).upto(n) do |i|
    (-n).upto(n) do |j|
      f += fij(i, j, r)
    end
  end
  return f
end

def list(r, n_max)
  # show the last three total forces
  (n_max-2).upto(n_max) do |n|
    f = fsum(r, n)
    puts "n = #{n}: r = #{r}, F = #{f}"
  end
  puts
end


n_max = 100

list(Vector[0.5,0.5], n_max)
list(Vector[0.25,0.25], n_max)
list(Vector[0.25,0.0], n_max)
list(Vector[0.0,0.25], n_max)