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Cell[CellGroupData[{
Cell["Solutions to Exercises (7)", "Title"],

Cell["The Game of Life", "Subtitle"],

Cell[TextData[{
 "M. E. Mauel\nColumbia University\n",
 StyleBox["(with help from \nComputer Simulations with ",
  FontSize->12],
 StyleBox["Mathematica",
  FontSize->12,
  FontSlant->"Italic"],
 StyleBox[", \nR. Gaylord and P. Wellin, Springer-Verlag 1995)",
  FontSize->12]
}], "Subsubtitle"],

Cell[CellGroupData[{

Cell["Introduction", "Section"],

Cell[TextData[{
 "In this exercise, you are to write a program to simulate the ",
 StyleBox["Game of Life.",
  FontSlant->"Italic"]
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Cell[TextData[{
 "The ",
 StyleBox["Game of Life",
  FontSlant->"Italic"],
 " was invented by the mathematician John Conway and first published in ",
 StyleBox["Scientific American",
  FontSlant->"Italic"],
 " in 1970. The game made Conway internationally famous and launched a whole \
new field of mathematica research which includes \"cellular automation\". "
}], "Text",
 FontVariations->{"CompatibilityType"->0}],

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 "The basic idea of the ",
 StyleBox["Game of Life",
  FontSlant->"Italic"],
 " is to consider a rectangular domain of square sites, or cells, which can \
be empty or be occupied by no more than one organism. The population of \
\"organisms\" are dynamic since some \"die\" and new organisms are \"born\" \
each generation. Conway's ",
 StyleBox["genetic laws",
  FontSlant->"Italic"],
 " are the \"rules\" for the game of life. Conway devised these rules so that \
(1) it could not be proven that an initial population would grow without \
bound, (2) there are some initial population patterns that appear to grow, \
and (3) some initial patterns have very interesting dynamics."
}], "Text"],

Cell[TextData[{
 "The ",
 StyleBox["Rules of the Game of Life",
  FontSlant->"Italic"],
 " are very simple. They are:\n1. Death by overcrowding: Any site with four \
or more neighbors dies by overcrowding.\n2. Birth: Any empty site with \
exactly three neighbors gives birth to new life.\n3. Death by loneliness: Any \
site with one or none nearest neighbors, dies from loneliness."
}], "Text"],

Cell["\<\
For example, the Cheshire cat proceeds to from a simple up-down asymmetric \
pattern to a smile and finally to a stationary 2x2 block.\
\>", "Text"],

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Cell["\<\
Notice the \"white\" squares correspond to \"life\", and the {1, 1} site is \
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\>", "Text"]
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Cell["Counting Nearest Neighbors (in-class)", "Section"],

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How should we count the number of neighbors for each and every cell?\
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Using your command, the game board evolves in time according to the formula \
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\>", "Text"],

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