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2008 February 09

Glider Constructions
Glider Collisions With 16 Bit Objects

I've recently completed a run of all possible collisions between a Glider and a 16 Bit Object (both stable and oscillating). Presented in the extended entry are about 500 collsions which may be useful in the contruction of other objects, where a single Glider quickly transform the object into another unsual object, or transform in place to a common object. (In some cases, I've added a second Glider to clean up any other extraneous objects.) Not included are those cases in which there is a simple transformation which can also be exhibited by a similar collision with a smaller object.

16 Bit Collisions - Age Record The longevity record was established by these two collisions. They both converge on the same resulting census, but the one on the right takes 17408 generations while the one on the left takes 17641.

16 Bit Collisions - 2 LWSS Among the results of this collision are, after 526 Generations, two Lightweight Spaceships heading off at right angles, and a single Glider in the opposite direction.

A number of rare or unsusal objects also appeared in the final census for some collisions. Shown here are those cases where 3 or fewer cases for a particular object are found.

16 Bit Collisions - Unsual Part 1

16 Bit Collisions - Unnusual Part 2

16 Bit Collisions - Unnusual Part 3

16 Bit Collisions - Unnusual Part 4


Turns out that I'd improperly included two collsiions as producing 14.487, when they actually produced a 16.487. Instead of deleting them, I've just properly relabeled them and left them in place. Thanks to Bobby Baum for noticing this.

16 Bit Collisions - Part 0 16.4 — 16.648

16 Bit Collisions - Part 1 16.654 — 16.1437

16 Bit Collisions - Part 2 16.1441 — 16.2197

16 Bit Collisions - Part 3 16.2199 — 16.2366

16 Bit Collisions - Part 4 16.2367 — 16.3271

16 Bit Period 2 Oscillator Collisions 16P2

I can also provide a full .zip file of all these collisions, each in a separate file, and including all objects up to 16 bits, upon request. Just use the email contact address. (I could just post this, but I'd like to actually know who finds all this of more than passing interest.)

2008 February 01

Logic Elements
New p5 Herschel technology

reduced p5 fountain for Lx73 Herschel conduit
Scot Ellison's smaller p5 fountain
for the p5 73-step Herschel conduit
Scot Ellison's search for a smaller p5 oscillator to support the 73-step Herschel conduit was successful, back in May of last year -- though he says that even smaller, perhaps asymmetrical, sparkers are likely to exist.

This smaller p5 fountain is included in an updated version of Hersrch, Karel Suhajda's Herschel-track search and construction program.

adjustable p5 conduit and period doubler
Adjustable p5 tandem-glider conduit
Another p5 Herschel conduit that showed up in 2007 was an adjustable diagonal track in which two gliders to travel an arbitrary distance diagonally between a transmitter and a receiver, similar to Paul Callahan's stable "tandem glider" circuits. It's constructed from known pieces: a stable converter that produces two gliders on the same lane from an input Herschel, and a p5 "doubler" that produces one output glider and/or Herschel from each pair of input gliders.

The circuit's p5 limitation is somewhat mitigated by its reversibility -- there are two mirror-image ways to receive the two gliders, whereas most tandem gliders need either a left- or right-handed receiver. (Some pairs of gliders with two-cell separation, usually produced with the assistance of a boojum reflector, can be received ambidextrously by standard receivers -- but this significantly alters the timing of the circuit.)

Depending on the position of the block, either of the two gliders can be chosen to trigger the Herschel output, while the other one resets the circuit. The circuit can also be hooked up to any glider output of a Herschel track for use as a period doubling fanout device, or a two-state track switch (two circuits on two glider outputs with alternating block positions).

p5, p7, p22, p36, p46, and p104 pulse divider reference collection.
Original p5 pulse divider by Dietrich Leithner.
p7 and p46 versions: Stephen Silver, 31 May 2001.
p22 version: David Eppstein, 1 June 2001.
p104 version: Scot Ellison, 24 March 2003.
p36 version: Jason Summers, 26 March 2003.
Substituting oscillators of other periods (p7, p22, p36, p46) opens up other possibilities -- especially the p7 variant, since the tandem gliders are separated by 119=7*17 ticks, so the double glider stream can be reflected.

It would be nice to have p6, p8, or p9 versions, but unfortunately no pipsquirter or other sparker below p10 seems to work with the current mechanism -- p7 is a special case.

Pulse dividers can be used as period doublers, but the "reset" glider is actually period-independent. The p104 case shows how the necessary one-bit spark can come from any periodic glider source.