I was prompted into action today by an email from Alex Bellos, who is publishing a recreational maths book soon which includes a chapter on Life. Here is my reply, with his original email at the bottom.
----- Original Message -----
From: "Paul Chapman" <redacted>
To: "Alex Bellos" <redacted>
Sent: Monday, November 25, 2013 12:24 AM
Subject: Re: new life replicator: geminoid
> I have not been following or assisting Dave Greene's Gemini-related research for
> some months. Indeed, and since I will copy this email to the ConwayLife forums,
> let me say that I am embarrassed and ashamed that it took an email from you to
> prompt me to take a look at his latest work, rather than any of the many emails
> he has sent me.
> I had no idea how far he had progressed, nor how much the basic design had
> changed since the last time we discussed variations of and/or improvements to
> the Gemini. The patterns in the post you linked to are astounding. I have
> spent much of today watching and understanding them.
> So, in answer to your specific question: *the* Gemini is a specific pattern, the
> original knightship designed by Andrew Wade. *A* Geminoid is a Gemini-like
> pattern, ie a pattern based on two components, one at each end of a glider
> "program tape" which bounces between them. Andrew was the first to come up with
> the basic Geminoid idea, and I believe Dave Greene coined the term Geminoid.
> The patterns in Dave's post are (strict!) self-replicators rather than
> spaceships. Dave makes a reference to a true spaceship based on the same design
> principles, but I haven't yet hunted that down.
> I would characterize the advances of this Geminoid over the original Gemini as
> almost entirely - but not quite entirely - breakthroughs (and quite breathtaking
> breakthroughs) in design, rather than in engineering, mostly relating to the
> radical reduction in the *population* of the pattern. These can be summarized
> as follows:
> - Gemini had two identical copies of the constructor, one at each end of the
> glider tape. This Geminoid has only one, at the NW end. It is used not only to
> build a copy of itself, but also to build a new reflector at the SE end of the
> tape from very far away. This is a significant innovation.
> - A single glider tape contains the construction program rather than the 12
> tapes of Gemini. This was one of Dave's original ideas for re-engineering the
> Gemini, and dates back years. (Forgive the vagueness in specifying time
> intervals - you will find as you get older and the frequency of significant
> events in your life drops, that it'll be harder and harder to remember when more
> recent events took place. You can call that wisdom if you like. Hah! :)
> - The tape goes through the replicator twice (three times in the case of the
> third version) each replication cycle, and the duplication of the tape is done
> in a separate pass from the construction.
> - The construction itself is done entirely with gliders from a single direction,
> whereas Gemini used pairs of gliders meeting at 90 degrees. Unidirectional
> slow-glider (ie one at a time) construction is something Dave and I have been
> researching for many years. It requires more low-level instructions to build
> the same pattern, but saves on infrastrusture in the constructor itself, which
> thus requires less time to build. It's a tradeoff.
> - My original design for the "shoulder shotgun", three copies of which Andrew
> Wade used in the Gemini, produced four different glider "salvos" to move the
> "elbow" and/or dispense gliders along the "forearm" to the "hand" at the
> construction site; the elbow was always a single block aligned with the
> shoulder, and the construction could only take place on one side of the elbow.
> This Geminoid instead uses a (completely different) shoulder which shoots a pair
> of side-by-side gliders towards the elbow, in any relative phase. (I followed
> Dave's work on this at the time.) This gives far greater flexibility in the
> control of the elbow, which may adopt many forms between 2-glider salvos; in
> turn, this makes for more efficient elbow moves and forearm outputs. It also
> allows construction to occur on both sides of the elbow (which I refer to as
> Laura Palmer construction - "Sometimes my arms bend back" - Google if you don't
> know the reference :), which in particular allows the construction of the new
> reflector at the SW (EDIT: SE) end of the tape.
> However, for me, the most remarkable new thing here is what Dave refers to as
> the semi-Snark, the discovery of which a search of the forums reveals was
> announced on July 1st in this post by Guam:
> http://conwaylife.com/forums/viewtopic. ... 8383#p8383
> It is the small Spartan (ie easily-constructible - as opposed to the Snark qv)
> period-doubling reflector two copies of which can be seen along the SW edge of
> the pattern at the NW end of the tape. What this means is that it reflects
> every other glider arriving along a single input path.
> At first sight, this would seem a large disadvantage. Two input gliders are
> needed to create each output glider at ninety degrees: one to reflect, and one
> to reset the semi-Snark so it is ready to reflect again. Worse still, since the
> input glider must be reflected twice, by two semi-Snarks, four input gliders are
> needed for each output.
> (NB, the large Herschel-conduit component has a terminator which is a period
> quadrupler; ie it outputs one glider for every four input gliders. I believe it
> is pretty old technology.)
> The first two patterns in Dave's post show that this problem can be halved
> because two tape gliders are in any case required for each 2-glider salvo aimed
> at the elbow, and one of these can be harmlessly duplicated to perform one of
> the four resets. (Indeed, it is cheaper to duplicate it than not to.)
> The third pattern brilliantly halves this again by interleaving 2-glider
> instructions on the tape, as follows.
> Suppose there are 2n-1 instructions in total (it must be an odd number, but a
> NOP instruction is available if required), numbered 0 to 2n-2. Then the
> instructions are ordered on the tape thus:
> 0 n 1 n+1 2 n+2 3 n+3 ... n-2 2n-2 n-1
> On the first pass through the constructor, instructions 0, 1, 2, ... are
> executed, while instructions n, n+1, n+2, ... are ignored, BUT are split to
> perform the other two necessary semi-Snark-pair resets. On the second pass,
> instructions n, n+1, n+2, ... are executed and instructions 0, 1, 2, ...
> ignrored but split to perform the resets.
> At first you might also think (or I did when I thought hard but not hard enough
> :) that the larger standard reflectors could simply replace the semi-Snarks for
> the same functionality, at the cost of extra construction time. This is true,
> but the period-doubling behaviour would still have to be implemented somewhere,
> since each of the two gliders on the input tape, which finally produce the
> 2-glider salvo aimed at the elbow, must be suppressed on one or other of the two
> paths through the constructor. So both the second reflector and the main
> Herschel conduit would still need period-doubling output gates, making the
> former a little larger. This would certainly have been possible without the
> semi-Snark: period-doubling Herschel-to-glider converters are well-known. But
> (in the third version), miraculouly, the semi-Snark offers the advantage of a
> smaller overall pattern without any penalty for its period-doubling effect.
> (I've left out some details about how the tape replication is turned on and
> Do I think that you should write an addendum?
> I'm not sure. I would probably want it to contain some equivalent of the above
> analysis (including the enthusiasm!), but that may be too technical for your
> readership. And of course an annotated diagram - or perhaps several showing the
> state at each significant milestone of the replication cycle - of the business
> end of the Geminoid.
> Personally, I would love to see Dave's work here published in hard copy, but
> with due continued recognition of Andrew's original design breakthrough.
> But even though Life moves slowly, compared with hard copy publishing it moves
> fast. It may be best not to try to play catch-up.
> I'm afriad it has to be your decision. But perhaps I can help further...
> As Dave will attest in spades, I am notoriously unreliable when it comes to
> continued email conversations. I am surprised at myself for writing this email
> rather than avoiding the subject again, since I am still short on energy for
> Life-related thinking. This is the longest piece of writing I have attempted
> for many months. But if you want to discuss further a possible addendum in the
> light of my comments here, please write again. I hope I will reply. :)
> Cheers, Paul
> ----- Original Message -----
> From: "Alex Bellos" <redacted>
> To: "Paul Chapman" <redacted>
> Sent: Sunday, November 24, 2013 10:27 AM
> Subject: new life replicator: geminoid
> Hi Paul,
> I just saw this
> http://conwaylife.com/forums/viewtopic. ... 9908#p9901
> I dont really understand how geminoid is different from gemini? Could you let me
> my book is at the typesetters, and it might be worth putting an addendum to the
> Game of Life chapter if geminoid has taken Life to a new level...