Re: game of life question
- From: spiantado <spiantado@xxxxxxxxx>
- Date: Mon, 30 Jul 2007 20:47:31 -0000
On Jul 30, 9:58 am, Allan Adler <a...@xxxxxxxxxxxxxxxxxxxx> wrote:
Let L denote the set of all points of the plane with integer coordinates
and let P denote the set of all subsets of L. Conway's game of life
determines a mapping T from P to itself. Call an element x of P timeless
if there is a sequence x0=x, x1, x2, ... of elements of P such that, for
every positive integer n, we have T(x(n)) = x(n-1).
Is there any characterization known of the set of timeless elements of P,
other than the definition?
--
Ignorantly,
Allan Adler <a...@xxxxxxxxxxxxxxxxxxxx>
* Disclaimer: I am a guest and *not* a member of the MIT CSAIL. My actions and
* comments do not reflect in any way on MIT. Also, I am nowhere near Boston.
Not sure what you mean exactly. Do you mean that P is the set of cells
that are "ON" and the game of life determines a mapping from a set of
ON cells to another set of ON cells (ie, subsets of ZxZ to subsets of
ZxZ)?
If this is what you mean, then I'm not sure I understand what sequence
you are looking for--does T(x(n)) = x(n-1) mean T(x_n) = T(x_{n-1}) ?
If so, it sounds like you are just asking for a way to characterize
fixed points under T, meaning you want to know when an element x in P
has the property that T(x) = x ?
Is that the question?
.
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