

Article 242 of comp.theory.cell-automata:
Path: mimsy!haven!purdue!tut.cis.ohio-state.edu!bloom-beacon!fermat.UUCP!r
>From: [email-masked] (Richard Schroeppel)
Newsgroups: comp.theory.cell-automata
Subject: Some recent Life results
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Date: 26 Oct 89 22:10:38 GMT
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Some recent new stuff in (Conway) Life:

Dean Hickerson at Penn State University wrote an Apple II program to look
for oscillators and spaceships.  (The guts are in 6502 assembly code.)
His program models a small rectangle (say 6*10) for a few time steps
(typically 4).  The number of layers is one more than the number of time steps.
Usually the first and last layers are connected by a mapping relationship.
This can be identity, a reflection, rotation, or a shift (for spaceships).
He supplies initial values for a few cells and the border, and sets the
search code loose, filling in cells and making inferences about adjacent
cells, and about successor and predecessor cells.  He frequently
intervenes in the searches, since the program can only search small
configurations to exhaustion.  He has turned up some amazing stuff:

A set of spaceship construction parts:  There are about a dozen parts,
typically fitting in an 6*10 rectangle.  Each part is period 2 and moves
orthogonally at speed c/2.  The parts can be strung together to make
spaceships of arbitrary width; the minimum is about 25 cells.  The
spaceships look like a row of threshers harvesting a field of wheat;
the thickness in the direction of motion is only about 10 cells.
There is a set of rules for the assembly, similar to a finite state
machine.  [Start with part A on the left.  Part A may be followed with
either B, D, or I; ...]

He also has a period 3, speed c/3 spaceship construction kit.

He has turned up a number of new oscillators of periods 2,3,4,5,6, & 8.

Robert Wainwright (of Lifeline) has studied Hickerson's oscillators (by hand!)
and taken them apart into useful pieces, coming up with a potpourri of new
oscillators.  An example:

        ..oooo..
        ..o..o..
        ooo..ooo
        o......o
        o......o
        ooo..ooo
        ..o..o..
        ..oooo..

Gosper has also found new, improved glider guns & logic gates, probably
leading to a smaller proof of Turing Machine equivalence.

Rich Schroeppel
[email-masked]