Life on the Edge
Fran...@netscape.net
defined on the edges of a square grid: each edge has six neighbors,
three at each end.
Like Conway's Life, each edge can be in one of two states: on or off;
and its state in the next generation depends only on the current state
of the edge itself and how many of its neighbors are on. The rule for
this automaton is that an edge that was off becomes on when exactly
two of its neighbors are on; and an edge that was on remains on only
if exactly one of its neighbors is on. Or, more simply put, an edge is
on in the next generation iff exactly two of the edges in its seven
edge neighborhood - including the edge itself - are on.
Small patterns with this automaton are a bit more fragile than in
Life. For example, a row of two edges (you'll need a fixed-width font
to properly view these pictures):
-.-
goes in the next step to
_|_
.|.
which then dies out.
The alternator is a simple period 2 pattern, alternating between
|.|
and
._
._
It is difficult to construct stable patterns, as they must be composed
of pairs of lines, with their growth blocked off. I believe the
smallest is
...|.....
_|.|.|_..
.._....._
...|.|.|.
.....|...
However, the really interesting part is what happens when we start
with 3 sides of a square:
..._
..|_
This goes in the next generation to:
._|_.
._._|
..|..
which looks like an airplane (which is what I call this pattern). The
next generation it seems to fall apart:
....|_
|...._
....|.
but the next generation is
..._|_.
..._._|
....|..
and it flies!
Can anyone find other interesting patterns? It would be especially
interesting if someone can find an "airplane gun", which generates
airplanes at regular intervals. Any other patterns that move, and any
other periodic patterns - especially with a period greater than two -
would also be of interest.
Vend
> I have discovered an interesting cellular automaton. This automaton is
> defined on the edges of a square grid: each edge has six neighbors,
> three at each end.
Is that actually an exagonal cellular automaton?
Doctroid
"Vend" <ven...@virgilio.it> wrote:
I think it can be mapped to a CA on cell centers of a hexagonal grid
with a compound neighborhood:
(view with non proportional font):
Number the rows as follows:
. __ __ __ __
1 / \__/ \__/ \__/ \
2 \__/ \__/ \__/ \__/
3 / \__/ \__/ \__/ \
4 \__/ \__/ \__/ \__/
5 / \__/ \__/ \__/ \
6 \__/ \__/ \__/ \__/
. \__/ \__/ \__/
Cells in odd-numbered rows (corresponding to horizontal edges in the
edges of square grid model) have this neighborhood:
. __ __
2 __/ \__/ \__
3 / \__/ \__/ \
4 \__/ \__/ \__/
. \__/ \__/
Cells in even-numbered rows (corresponding to vertical edges) have this
neighborhood:
.. __
2 __/ \__
3 / \__/ \
4 \__/ \__/
5 / \__/ \
6 \__/ \__/
. \__/
Furthermore I think it can be mapped to cell centers of a square grid
with neighborhoods
. __ __
. __|__|__|
. |__|__|__|
. |__|__|
for the odd *diagonals* (i.e. the black cells in a checkerboard pattern)
and
. __ __
. |__|__|__
. |__|__|__|
. |__|__|
for the even diagonals (white cells of a checkerboard).
--
- Doctroid Doctroid Holmes
It's too confused to make sense, so let's make nonsense.
-- Chris McG.