Glider reflector in Life

[McIntosh Harold V.-UAP]

The discovery of the still-life glider reflector is
certainly interesting, along with the tale of how it
was finally put together. One can hardly begrudge
the listing of coordinates for its components, but
perhaps its discoverer would be willing to provide
us with some additional verbal description of what
this thing is like.

For example, the coordinates exhibited suggest that
it is an assemblage of strustures which are them-
selves small still lifes occupying an area of about
120x120. Could you save us the trouble of graphing
this out by giving us a rundown on the number and
kinds of constituents, with a description of the
area they occupy and perhaps their distribition
within? Is it uniform, do they cluster around an
axis, or whatever?

Presumably the glider must approach exactly the
right spot to be reflected. Is that true? Also,
one of the things people have sought for the
longest time is a structure which would deflect
a glider 90 degrees. Can one of those five
intermediate gliders be used for that purpose?

All in all, a remarkable accomplishment.

[Paul Callahan]

In article <961118013...@servidor.dgsca.unam.mx>,

>For example, the coordinates exhibited suggest that
>it is an assemblage of strustures which are them-
>selves small still lifes occupying an area of about
>120x120. Could you save us the trouble of graphing
>this out by giving us a rundown on the number and
>kinds of constituents, with a description of the
>area they occupy and perhaps their distribition
>within? Is it uniform, do they cluster around an
>axis, or whatever?

I will write up a more detailed description soon in order to include this
on my web page.

The atomic components (blocks, eaters, etc.) group naturally into stages,
and I can describe these stages briefly. Ideally, I would provide a high-level
schematic of what is going on here, but I'm not sure it is worth the
effort to do this in ASCII graphics. For those who want to see this in
action and have a Java-compatible browser, I refer you again to Alan's
web page, as mentioned in the previous posting. You can also view
the posted pattern in a variety of Life programs.

Stage 0: (Paul Callahan)

In the initial stage, a glider collides with a block to produce a pi
heptomino. This explosive collision is "perturbed" by the permanent
parts of the reflector so that at generation 242, the destroyed block is
restored, a glider is released in the reverse direction, an r-pentomino
is produced some distance from the stage, and a beehive is left in
an awkward position close to the block. In other words, the first
stage is a still life that realizes the following conversion:

glider --> glider + r-pentomino + beehive

Note that nothing is said about the destroyed block. Since it has been
restored in precisely the same place, we can ultimately view it as a
permanent part of the assembly. I'm belaboring the point only to
emphasize that this is the trick that gives us the "space" we need to work
with. You can't do much with one glider, but you can do a lot with a big
explosion, and that includes finding a way to rebuild the initial
"explosive charge."

Stage 1: (David Buckingham)

The next stage converts the r-pentomino to a pattern called the Herschel
(a b heptomino becomes a block and a Herschel after 20 generations). This
is a fairly active pattern that sends off gliders and comes close to
reproducing itself before destroying itself in debris.

Thus the conversion after ths stage (generation 329) is:

glider --> glider + Herschel + beehive

Buckingham very recently found ways to "shepherd" a Herschel through eight
different still life stages, implementing turns, reflections, and translations
of this pattern, and producing excess gliders at most stages. So, given the
above, the question becomes, can we send the Herschel along several stages in
such a way as to emit a glider to delete the unwanted beehive? In other
words, we need to route the Herschel to an appropriate diagonal and
orientation. "Appropriate" depends on the way we obtain the final glider.
However, using only Buckingham's stages, there are an infinite number of
ways to accomplish this. The fastest one is the most desirable, since
the faster we can delete the beehive, the sooner we can reuse the reflector.
Dean Hickerson found the sequence of stages presented here (the fastest
known) and also designed a special-purpose final stage.

Stages 2-6 (David Buckingham):

These stages route the Herschel to the required diagonal. Only
the two fastest of Buckingham's stages are required here. One flips
and translates the Herschel in 77 moves, the other turns it 90 degrees
and translates it in 64 turns. Some gliders are produced in the process.
Some must be eaten to avoid destroying the pattern. The one non-standard
still life in the construction was designed by Dean, and is simply a way
of placing several eater heads where separate eaters would not fit.

After these stages, we have (generation 329 + 77 + 64 + 64 + 77 + 77 = 688):

glider --> 4 gliders + (moved) Herschel + beehive

Stage 7 (Dean Hickerson):

This stage converts the final Herschel into 2 gliders. At stage 757, a
glider is sent off along a path to destroy the beehive. Finally, by stage
788, we have two gliders in place of the Herschel. Or:

glider --> 6 gliders + beehive.

At generation 823, the beehive is finally destroyed. Thus, we have the
clean conversion:

glider --> 5 gliders.

One result of this glider excess is that we can produce several kinds
of glider guns by bouncing gliders between reflectors. It sounds a little
like one of those designs that pop up sometimes for perpetual motion machines.
But there is no "Law of Conservation of Gliders" so it actually works!

Note that I'm using the timing from Alan Hensel's pattern. He left a
lot of steps before the first collision, which is why the final generation
823 above is so much larger than the minimal time between glider, which
is 747, as stated in the last posting.

>Presumably the glider must approach exactly the
>right spot to be reflected. Is that true?

Yes, it has to collide with a block in a specific way to create a pi
heptomino in the appropriate location.

>Also,
>one of the things people have sought for the
>longest time is a structure which would deflect
>a glider 90 degrees. Can one of those five
>intermediate gliders be used for that purpose?

Yes.

One is sent 90 degrees to the right, two are sent 90 degrees to the left.
One is sent back 180 degrees. One last glider is sent out in the same
direction.

However, it must be noted that there is nothing that limits such a construction
to 5 gliders. Buckingham has shown that a Herschel can be sent along a still
life path to produce arbitrarily many gliders. If the path is a loop, you
get infinitely many, or in other words a glider gun. That was Buckingham's
original intention. While Dean Hickerson's final stage destroys the Herschel,
there are a few somewhat slower reflectors that can delete the beehive while
leaving the Herschel intact to send off as many more gliders as you like.
That is, one can easily show that for any choice of m, there is a
glider --> m gliders still-life conversion. These gliders can also be
sent in any direction you like.

--
Paul Callahan (call...@inf.ethz.ch)
Web Page: http://wwwjn.inf.ethz.ch/paul/

[sergio e. martinez casas]

On Sun, 17 Nov 1996, McIntosh Harold V.-UAP wrote:

...

>
> Presumably the glider must approach exactly the

> right spot to be reflected. Is that true? Also,

> one of the things people have sought for the
> longest time is a structure which would deflect
> a glider 90 degrees. Can one of those five
> intermediate gliders be used for that purpose?

several (c. 17) years ago i set up a collision between a glider and a
barber pole of a certain (lost, unrecorded, etc.) length, which, given de
right initial conditions of phase of barber pole and position of glider,
the latter was 'deflected' 90 degrees. the single quotes meaning that the
original glider was destroyed and another was produced after the clearing
of debris. what i fail to remember (among various other thins :( ) is
whether the pole was completely restored. the direction of the incoming
glider was perpendicular to the pole, and the collision produced close to
its central section.

i hope this helps someone to recreate what i found.

-esrgio