Conway's
|
Corderships and switch engines
Contents
When Life was first published in October 1970, people tried
to make infinite-growth patterns, ones that grow without
limit. Conway realised that there are two ways that such a
pattern can grow:
Moving source - This encompasses puffers and rakes
Stationary source - These are guns and slide guns
The first infinite growth pattern was made by Bill Gosper,
and it was a gun (a stationary object that emits gliders).
This particular example emits one glider every 30 gens:
Later, a puffer train (moving object that emits debris)
was found. It moves at c/2 and has a period-140 output:
However, a much smaller, simpler puffer train exists.
It is completely different to anything else, and is
called the switch engine. It exists in two different
forms, both of which are known to occur naturally:
It was discovered by Charles Corderman. The computer he
used to find it was an unusual hybrid computer, the only one
of its kind. He did a systematic search for all polyominos
(patterns consisting of orthogonally-connected cells). When
running a particular decomino (10-cell polyomino), he noticed
something strange. The pattern appeared to create itself
again, 48 generations later, whilst leaving debris. After
another 48 generations, the pattern is returned to its
original orientation, translated 8 cells diagonally.
What if these switch engines could mutually stabilise
each other to leave no material behind? That is exactly
what Dean Hickerson did when he created the first
Cordership, which had 13 switch engines. This was soon
optimised to 10:
An improved Cordership was built using a similar method.
This one only requires 7 switch engines:
A 6-engine Cordership with an interesting termination
was built:
This can be synthesised repeatedly using a gun, but the
resulting gun is extremely large. It operates at p784:
Much more recently, in 2004, Paul Tooke built a Cordership
using only 3 switch engines:
This one can be synthesised much more easily, at p690:
A switch engine can travel through a lane made of boats.
This is called a swimmer track, as the switch engine appears
to "swim" down it at the slow speed of c/12. The following
oscillator was made by David Bell in June 2005:
Dave Greene built a stable device that can convert a Herschel
into a swimmer and back. He made a mistake in the construction,
so he had to bolt an extra track on. It still works, but is
reduced to a minimum compression of 629 ticks (generations):
A Cordership can be quickly transformed into two swimmers.
The following pattern demonstrates this:
In 2009 I built a converter to turn a single glider
into a Cordership. You can read about it on this page:
http://b3s23life.blogspot.com/2009/02/first-complete-glider-to-cordership.html
The switch engine, since it occurs naturally, can be incorporated
into a quadratic growth pattern. Such a pattern would synthesise
a block-laying or glider-producing switch engine at a regular rate.
One notable example consists of just 38 cells (by Mitchell Riley):
It produces a switch engine every 140 generations (notice the
similarity with the puffer train mentioned at the start of
this article).
A more traditional breeder that synthesises switch engines uses
glider collisions. This was the method used in the very first
quadratic growth pattern, made by Bill Gosper. Whereas his
design spawned copies of his gun, the switch engine breeder
creates switch engines periodically. This example was built
in 1997 by Helmut Postl:
It fills space more densely than Riley's breeder, synthesising
a switch engine every 80 (instead of 140) generations.
The smallest (in terms of bounding box) quadratic growth pattern
does not rely on the switch engine, but instead stretches a
uniform agar. It is unimaginatively called the spacefiller:
Switch engine technology is not restricted to linear and
quadratic growth. Other growth rates are possible, such
as Bill Gosper's linear-logarithmic growth pattern.
The pattern is very slow, so I suggest using a very
powerful program to run it. Personally I would reccomend
Golly, but Hashlife is equally equipped to simulate it.
Corderships can be used to build diagonal puffers and
rakes. These are moving objects that leave behind
other objects. A simple example is this puffer which
builds heavyweight switch engines:
LWSS and MWSS rakes can be made using a different
method:
Standard spaceships aren't the only things that can
be built. A more complex construction generates switch
engines, resulting in another quadratic-growth pattern:
And taking the idea one step further, David Bell has
built an arrangement of Corderships which synthesises
more Corderships, travelling perpendicular to the
rake.
By Calcyman
Back to home page
E-mail me
The discovery of the switch engine