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- Newsgroups: comp.theory.cell-automata
- Path: sparky!uunet!paladin.american.edu!gatech!bloom-beacon!INTERNET!dont-send-mail-to-path-lines
- From: ACW@RIVERSIDE.SCRC.Symbolics.COM (Allan C. Wechsler)
- Subject: Birth only from antipodal parents
- Message-ID: <19920817171305.1.ACW@PALLANDO.SCRC.Symbolics.COM>
- Sender: daemon@athena.mit.edu (Mr Background)
- Organization: The Internet
- References: <=07mx3-.pdh@netcom.com>
- Distribution: inet
- Date: Mon, 17 Aug 1992 17:13:00 GMT
- Lines: 27
-
- Mr. Howard expresses interest in a (binary, Moore-neighborhood) rule
- where birth occurs when there are exactly two live neighbors, in
- antipodal positions. (A rule for survival is also given, but is not
- relevant to my initial point.)
-
- Such a birth-rule is unlikely to generate interesting behavior, because
- the bounding octagon cannot grow. If the configurations we want to
- study have finite support, then there are no moving oscillators
- (spaceships) and no patterns that grow without limit. Therefore (in the
- domain of finite patterns) the automaton can't be universal.
-
- The rule Mr. Howard proposes has a fairly rich survival environment (115
- environments out of 256 lead to survival) but an extremely poor birth
- environment (4 out of 256). My intuition is that almost all initial
- configurations will stabilize very rapidly, leaving a fixed framework
- that is consistent with the survival environment, punctuated with a few
- "spark gaps" of approximately this form:
-
- o...o
- ooxoo
- o...o
-
- in which the cell marked "x" flashes. Any more complex dynamics would
- surprise me.
-
- Has Mr. Howard actually tried this rule, say on a 50x50 toroidal board
- seeded with random bits?
-