James Gilbert had an idea based on John Conway's Game of Life.  If a cell is intelligent, how long can it survive? Andrea Gilbert turned it into a maze, and it's very good.  You can see the Maze of Life at www.clickmazes.com .  At her home page, you can also see her new NEWS and RULES mazes.  The Maze of Life idea suggests a lot of new problems in cellular automata.  For example, start with the F-pentomino.  If one of these cells is intelligent, and can move one space (or stay) each turn, how far can it journey away from the starting area before dying or getting trapped?  How much of a mess can this intelligent cell create?  What is the smallest initial set of cells that would allow this smart cell to build a glider gun?
Sorry - This puzzle is a JAVA Applet
Adrian Fisher and I have both been intrigued by Andrea Gilbert's Life Maze.  I've managed to get back home again in all the mazes.  Adrian has managed to demolish the neighborhood in Maze 5 (I haven't figured out how he did it, yet).  Anyone who finds new objectives (and solutions for them) should send them to Andrea.

Gerry Quinn was intrigued by the Game of Life, right below.  He has a different Life game (shareware) at his site bindweed.com.  His game is called Zen.

You can see more links at my old Life page.  If you like all of these cellular automata links, you can preorder A New Kind of Science for \$40 at www.wolframscience.com.

And now, part of a correspondence between myself, Carl Hoff, and Andrea Gilbert.

From: "Carl Hoff"
To: <ed@mathpuzzle.com>, "Andrea Gilbert"
Subject: RE: Life

Ok,

I've been doing a little more playing.  How is this for a new
objective.  Try to create a stable position with the most live
cells.

Those with 4 live cells: (that I've been able to create)

+ + + + + + +    + + + + + + +
+ + + + + + +    + + + + + + +
+ + + + + + +    + + + O + + +
+ + + O O + +    + + O + O + +
+ + + O O + +    + + + O + + +
+ + + + + + +    + + + + + + +
+ + + + + + +    + + + + + + +

Those with 5 live cells: (that I've been able to create)

+ + + + + + +
+ + + + + + +
+ + O O + + +
+ + O + O + +
+ + + O + + +
+ + + + + + +
+ + + + + + +

Those with 6 live cells: (that I've been able to create)

+ + + + + + +    + + + + + + +    + + + + + + +
+ + + + + + +    + + + O + + +    + + + + + + +
+ + + O + + +    + + O + O + +    + + + + + + +
+ + O + O + +    + + + O + O +    + O O + + + +
+ + O + O + +    + + + + O + +    + O + O + + +
+ + + O + + +    + + + + + + +    + + O O + + +
+ + + + + + +    + + + + + + +    + + + + + + +
Goal 7

Those with 7 live cells: (that I've been able to create)

+ + + + + + +
+ O + + + + +
O + O + + + +
O + O + + + +
O O + + + + +
+ + + + + + +
+ + + + + + +

Those with 8 live cells: (that I've been able to create)

+ + + + + + +
+ O O + + + +
+ O O + + + +    Here the relation of the two sets of
+ + + + + + +    4 isn't really important
+ + + + + + +
+ + + O O + +
+ + + O O + +

Those with 9 live cells: (that I've been able to create)

+ + + + + + +
+ + + + + + +
+ + + + + + +
+ O + + + + +
O + O + + + +
O + + O + + +
O O O O + + +

Those with 10 live cells: (that I've been able to create)

Still looking for one.

Those with 11 live cells: (that I've been able to create)

+ + + + + + +
+ + + + + + +
+ + O + + + +     By the way, the time I stumbled across
+ O + O + + +     this one the Blue one was the one
O + O + O + +     'inside' your retirement home, Ed.
O + + O + + +
O O O + + + +

Those with 12 live cells: (that I've been able to create)

+ O + + + + +
O + O + + + +
O + O + + + +
+ O + + + + +
+ + + + O O +
+ + + O + + O
+ + + + O O +

For all of these the orientation does not matter, nor which is the
blue cell.  Some of the these though do need to be up againt an edge
or corner of the board to be stable.  Can anyone find a 10 cell stable
position?  Can anyone do better then 12?

goals 5 & 6 - a useful addition. Must go devise some more starting
positions now... let us now if you find any good ones!"

About finding some good starting positions, yes I've sort of found a
few but at the moment they can all be made from yours.  If you

+ + + + + + +   Key:  \U/
+ + + + + + +         LSR
+ + O + O + +         <D>
+ + + B + + +
+ + + O + + +
+ + + + + + +
+ + + + + + +

and do this:

SS>U>DULUUU/S<><\D
123456789012345678

You'll be at a position were i've started at to find some
of these new solutions, like to new 6 cell solution and the
11 and 12 cell solutions.  I'm almost starting to think that
just about any good starting position that you could come
up with could be reached from this one.  By the way, I once
got from this position back to the exact same start position
minus one, i.e. what the board looks like after S.  I found
that interesting.  I guess you could also make it a goal to
come up with the longest path that repeats.

Could I also make a couple suggestions?  Could you please
add a feature to the program to allows it to display a log
of your moves?  Many of the above positions I've gotten to
just by moving around at whim and say after 30 or 40 moves
I see something start to form that looks interesting that
I can mold into one of the above.  The problem is after the
fact, its almost imposible for me to recreate what I did.
If you could undo more then one move that would also allow
me to recreate the solution.  If you can't tell I really enjoy
this little puzzle.  And no Ed I'm NOT retired.

Well back to more playing,
Carl

P.S.  I just found a shorter solution to the new 6 cell
solution (I guess you can call it goal 7)

Here it is:

SS>U>DU<RL>\<
1234567890123

> -----Original Message-----
> From: ed pegg
>
>
> P.S.  Here is another position I've been able to reach
>
>        + O + + + + +
>        O + O + + + +
>        O + O + + + +
>        + O + + + + +
>        + + + + O O +
>        + + + O + + O
>        + + + + O O +
>
> Very nice!  I'm thinking this particular puzzle might be called
>
> Y Retire
>
> Since you need to retire to finish the puzzle.  It makes me wonder what
the
> largest possible retirement home might be.
>
> --Ed!