British mathematician John Conway
devised a cellular automaton he named the "Game of Life" in 1970.
The game is played on a 2-dimensional grid where each square, or
cell, is either Alive or Dead. The only part of the game that is
interactive is setting up the initial grid of Alive and Dead cells.
Evolution then occurs in steps according to a set of rules.
Generally, 4 rules are listed but for the sake of example, I'll
list 5. The rules all pertain to how many of a cell's neighbors, of
which there can be a maximum of 8, are also Alive.
For cells that are Alive:
A. If just 0 or 1 neighbor is alive, cell becomes Dead.
B. If 2 or 3 neighbors are alive, cell remains Alive.
C. If 4 or more neighbors are alive, cell becomes Dead.
For cells that are Dead:
D. If exactly 3 neighbors are alive, cell becomes Alive.
E. If D is not true, then cell remains Dead.
By way of example, the following
figures show the evolution from an initial state of 8 live cells in
the shape of the letter "C". A small letter in the bottom left
corner describes each cell's state according to the rules listed
above. Once the state has been figured out for each cell, all cells
change simultaneously in one step of evolution. In this example all
life goes extinct by step 5.
The next set of figures show the
same evolution as above but each cell has been numbered according
to the rules listed above to help visualize how evolution occurred
as it did.
Of course, the simple example
above is not so interesting since life ended rather quickly. But,
it is truly amazing how incredibly complex patterns can arise from
various initial configurations guided only by the simple set of
Conway Rules of Life. There are arrangements that lead to stable
configurations, moving patterns, arrangements that alternate
between 2 or more steady states, and so on. An entire lexicon has
arisen describing the kinds of digital life one can create. The
User's Web Page above is great fun to explore and has many links to
viewing Life others have created as well as programs allowing you
to create life.
Now, onto the puzzle for this
cache. Understanding the Rules of Life allows you to take the eight
starting configurations (Column 1) shown below and evolve them to
the end state shown in Column 3. After hours of playing Life I
found these eight relatively simple configurations to evolve in
interesting and unpredictable ways. The end states range from
extinction to stable configurations to alternating steady states,
and so on. You can solve this puzzle using graph paper but that
would likely take up most of your time for the next few months.
Think of that as old school. To quickly solve this puzzle, go new
school and use one of the handy online or downloadable programs
available from the User's Web Page. You could even program this
yourself as many of us did who took engineering classes back in the
1970's. For each initial configuration you have to figure out how
many steps of evolution take place before you arrive for the first
time at the end configuration shown (some of the harder to see ones
have linked higher resolution versions). When you have the eight
numbers you need, do the math below the puzzle to solve for the
cache coordinates
Despite the seeming complexity
here, this is actually a very easy and fun puzzle. A daughter of
mine spent last night playing Conway's Game of Life after I showed
it to her, instead of surfing music videos as is usually her wont.
So, go forth and multiply!
Yellow cells are Alive and Grey
cells are dead. And beware of edge effects - enlarge the game board
and shrink the cell size if necessary - different behaviors ensue
if action reaches a boundary.
|
after A generations becomes
(becomes extinct) |
|
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after B generations becomes
(stable state) |
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after C generations becomes
(The eight outer "gliders" will
continue to move away but the
remainder is at equilibrium. Count steps
until all non-glider movement ceases) |
|
|
after D generations becomes (stable state) |
|
|
after E generations becomes (stable state) |
|
|
after F generations becomes
(becomes extinct) |
|
|
after G generations becomes
(this one ends in a 2-phase
steady state, shown here is the
first state reached. |
|
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after H generations becomes
(becomes extinct) |
|
The coordinates are at:
N 47 (A-25).(A+B+C+D-251)
W 122 (H-6).(E+F+G+H-313)
(geochecker
here)
Shades of old school FTF activity here as SeaC2 scored a late night
FTF - congratulations!