Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)

Part 1 of this series of posts on RCT (reverse caber tosser) patterns described the basic mechanism of storing construction information in very large distances, and extracting it with a mechanism that amounts to repeatedly dividing the distance by two and taking the remainder. The minimum number of gliders needed to produce a working universal construction arm turns out to be ridiculously small -- only 16 gliders as of this writing, and there's no guarantee that this is the cheapest possible mechanism.

However, a construction-arm mechanism can make it possible to build any desired constructible object, without necessarily being very efficient about it. In this case, the RCT's native construction arm needs a very long string of bits to produce an output glider -- over an order of magnitude more bits than we would need with a more efficient encoding mechanism.

The DBCA...

This means that, in our continuing quest to build any possible glider-constructible object using only sixteen gliders, it's now time for an apparently insane diversion. Rather than going ahead and building what we want to build -- the ATBC, or Actual Thing Being Constructed, which is the real goal of any RCT construction -- we instead go through a "bootstrap" stage, where we build a whole new construction arm mechanism that's much more efficient than the original, and then use that new construction arm to do a lot of cleanup ... plus building the ATBC, almost as an afterthought, at the very end.

This extra "bootstrap" mechanism is called the DBCA -- Decoder and Better Construction Arm.

Somewhat counterintuitively, if an RCT pattern takes the time to build a DBCA before doing anything else, it will end up completing its final construction much faster than it would have otherwise. Any given construction -- even if it's only something very small and simple, like the single shillelagh from the example -- will need only a fraction of the number of bits that would have to be stored in the RCT mechanism if it used only the native RCT construction arm.

This first bootstrap stage will also help to enable a second bootstrap stage, which will be even more useful than the first. The DBCA allows for roughly a twelvefold efficiency improvement, but the actual construction and cleanup problem is still painfully difficult: new bits will only keep getting fed into the DBCA while the switch-engines are still producing incoming gliders. We can't do any cleanup until after the four GPSEs have arrived at the epicenter and have been safely stabilized -- but at that point, we won't have any more recipe information coming in to tell the DBCA how to do the cleanup!

... And The BSRD

The idea behind the next bootstrap stage -- called the BSRD, for "Binary Storage and Retrieval Device" -- is to find a way to store incoming information, so that we can delay the last stage of the RCT's complicated construction and cleanup process. We'll still complete the repeated process of dividing the RCT distance by two and taking the remainder, but now we'll store all that information somewhere instead of building anything immediately. Then, after the incoming glider streams have all been absorbed, and the incoming switch engines have all stabilized into very long trails of safe stable ash, we'll make use of the stored information to run the DBCA to do any final construction and cleanup tasks.

The original plan was to construct a BSRD with a static data tape -- a long line of blocks and blanks representing 1s and 0s, let's say, that can be read by an "index elbow" moved by a slide gun type device, similar to the binary tapes in the pi and phi calculators, but rebuilt to make them more easily constructible by slow salvos.

However, it turns out that a storage unit can probably be built that's at least a couple of orders of magnitude cheaper than that. See the "pseudo-BSRD" discussion below.

A complete DBCA recipe

On 27 May 2022, Pavel Grankovskiy completed an RCT recipe for a working DBCA mechanism, including quite a bit of periodic circuitry, based in part on an earlier design by Adam P. Goucher. Periods that are multiples of 8 happen to work well with incoming GPSE glider streams, and it's somewhat cheaper to build a period-8 bumper or bouncer than a stable Snark reflector. It's also cheaper to build a suppressed period-256 shotgun for the common parts of the various salvos for a construction arm, than to build an all-stable synchronized shotgun.

The combined improvements to the original design allow the entire DBCA structure to be constructed at about 60% of the original estimated cost.

... and a complete BSRD, too!

In regards to completing a proof-of-concept RCT design, a further pleasant surprise showed up on May 27th, when Grankovskiy pointed out that only a few small circuits needed to be added to produce a completely functional BSRD -- or rather, a "pseudo-BSRD", since the structure is not really a binary storage device. Instead of writing data to a static binary tape near the epicentre, the pseudo-BSRD will simply deflect the gliders coming in from the RCT mechanism, sending them out to faraway reflectors near the southeast GPSE launch point.

By the time the first gliders get back to the epicentre, the incoming GPSEs have safely finished their work and have been caught by carefully placed absorbers, all the stored bits have been sent to the pseudo-BSRD, and the DBCA can begin the incredibly long process of cleaning up the GPSEs' ash trails. The original pseudo-BSRD design used p8 reflectors and Snarks, which was more expensive than strictly necessary. A stable rebuild was completed a few days later, and for the time being there seems to be a consensus that that's a good enough option to implement. The pseudo-BSRD is probably somewhere between two and three orders of magnitude simpler than the original projected BSRD design, so this was a massive reduction in the complexity of the full RCT prototype.

Highlights of the DBCA

Some of the key details of the new Goucher-Grankovskiy construction arm are summarized in an earlier forum post in the same thread. The DBCA recipe pattern is too big to be readily animated with LifeViewer, but several key moments are highlighted in that post. The full pattern can very easily be run to completion using Golly.

Here are a few items that weren't called out in detail in the forum post. Zoom in toward the upper left corner below, and you'll see labels appear for the nine possible output signals from the unary counter there. The following LifeViewer pattern places nine single-glider signals that produce each of those nine outputs (one right after the other, instead of separated by vast amounts of time as in a real RCT pattern). There are four types of glider output (even and odd color-changing and color-preserving 90-degree gliders), followed by INC16, DEC8, INC4, DEC2, and INC1.

Code: Select all

x = 1319, y = 2156, rule = B3/S23
583b2o$583b2o$569bo$569b3o$572bo9bob2o$571b2o9bobo$583bo$576bo6b2o$
575bobo5b2o$575bo2bo4b2o$576b2o11$550b2o81bo$546b2obo2bob2o8b2o66b3o$
546b2o2bo4bo7bobo65bob3o$551bo13bo55bo8bo3bo$552bobo66b3o5bo3bo$624bo
3b3obo$623b2o4b3o$555bo74bo$554bobo69bo$553bo2bo68bobo$554b2o65b2o2b2o
$621b2o2$550b2o$549bobo$549bo$548b2o5$598b2o$591b2o5b2o$591b2o3$593b2o
27b2o$593b2o27b2o$587b2o$587b2o$628b2o$628b2o$624b2o$624b2o$550b2o51bo
$550b2o51b2o$536bo65bobo$536b3o90b2o$539bo11b2o76b2o$538b2o9bob2o105b
2o5b2o$549bo75bobo30b2o5bo$543bo5bo76b2o35bobo$542bobo4bo2bo73bo36b2o$
542bo2bo4b2o107b2o$543b2o114bobo$588b2o70bo$587bo2bo$586b6o71b2o$586b
6o71b2obo$586b2o79bo$585b3o76bo$585b2o78bob2o$582b2ob2o80b2o$582bobobo
11b2o46bo$583b4o6b2o2b3o2b2o40b2o$584b2o7bo2bobo4b2o40b2o$589b2o3bo3bo
b2obo$588bo2bo5bo3b2o28bo$587bo3bo40b2o$583b2o2bo2bo40b2o$583b2o2bo2bo
$624b2o$624b2o$588bo2bo26b2o$589b2o27b2o3$620b2o$519b2o92b2o5b2o$520b
2o91b2o$519bo6$636b2o3b2o$635bo2bobo2bo$630bo5b2o3b2o5bo$629bobo15bobo
$630bo17bo2$600b2o$601bo$601bobo$602b2o3$606b2o18bo$605bo2bo16b3o$606b
obo15b3obo$607bo17bo3bo8bo$626bo3bo5b3o20b3o$533b2o92bob3o3bo26bo$533b
o70b2o22b3o4b2o21bo3bo$531bobo70b3o22bo18bo8bobo2bo$516b2o13b2o65b2o2b
o2bobo25bo14b3o4bo2bobo$516b2o80b2o2b2o2b2o24bobo16bo3bo3bo$602b2o29b
2o2b2o11b2o3bo$637b2o17b3o$496b2o155bo$496b2o154bobo$648b2o2b2o$648b2o
$495bo193bobo$494bobo193b2o$495bo194bo$492b3o$492bo$629bobo$630b2o$
630bo61bo$535b2o153bobo$535b2o154b2o7$532b2o$532bo$533b3o$535bo6$503b
2o$503b2o2$455b2o23b2o$456b2o22b2o$455bo46b2o$502bo186b2o5b2o$460b2o
38bobo186b2o5bo$460b2o38b2o192bobo$694b2o$690b2o$459bo230bobo$458bobo
230bo$459bo$456b3o235b3o$456bo237b3o$694b3o$697b3o$697b3o$499b2o196b3o
$499b2o7$496b2o$496bo$497b3o$499bo6$467b2o$467b2o2$444b2o307bobo$444b
2o308b2o$466b2o286bo$466bo$424b2o38bobo$424b2o38b2o227bobo$694b2o$694b
o61bo$423bo330bobo$422bobo330b2o$423bo$420b3o$420bo4$463b2o$463b2o6$
744bo$460b2o281bobo$460bo281bo3bo$461b3o277bo3bo$463bo276bo3bo$391b2o
346bo3bo$392b2o346bobo$391bo349bo$737bo$736bobo$431b2o303b2o$431b2o
307b2o$740bobo$408b2o325b2o5bo$408b2o325b2o5b2o$430b2o$430bo$388b2o38b
obo$388b2o38b2o3$387bo$386bobo$387bo$384b3o$384bo124bo$507b3o$506bo$
505bobo$427b2o76bobo$427b2o77bo42bo$547b3o$546bo$546b2o2$490b2o99bo$
490b2o97b3o$424b2o162bo$424bo100b2o60bobo$425b3o96bobo60bobo$427bo82b
2o12bo63bo$510bobo10b2o292bobo$512bo305b2o$503b2o7b2o304bo$503b2o23b2o
$527bobo42b2o$395b2o96bob2o30bo44b2o183bobo$395b2o94b3ob2o29b2o230b2o$
490bo267bo61bo$372b2o117b3ob2o254b3o64bobo$372b2o119bobo96b2o160bo64b
2o$394b2o97bobo96bobo155bo3bo$394bo99bo99bo145bo8bobo2bo$352b2o38bobo
142b2o46b2o7b2o144b3o4bo2bobo$352b2o38b2o143b2o46b2o156bo3bo3bo$545b2o
195b2o3bo$545bo29bob2o169b3o$351bo194b3o24b3ob2o166bo$350bobo150b2o43b
o23bo171bobo$351bo151b2o68b3ob2o161b2o2b2o$348b3o196bo27bobo162b2o$
348bo197bobo26bobo$546bobo27bo$490bo54b2ob3o$489bobo59bo$391b2o96bobo
53b2ob3o$391b2o94b3ob2o52b2obo$486bo$487b3ob2o44b2o46b2o$327b2o160bob
2o35b2o7b2o46b2o$328b2o199bo$327bo201bobo$530b2o$388b2o182bo$388bo182b
obo$389b3o96b2o81bobo$391bo95bobo60b2o17b3ob2o$487bo62b2o16bo$486b2o7b
o73b3ob2o$494bobo74bob2o$495bo$502b2o$359b2o141b2o31bo$359b2o173bobo$
534bobo$336b2o197bo34b2o$336b2o194b3o34bobo$358b2o172bo36bo$358bo209b
2o7bo$316b2o38bobo217bobo$316b2o38b2o219bo$554b2o28b2o$554b2o28b2o195b
2o5b2o$315bo253bo211b2o5bo$314bobo237bo12b3o216bobo$315bo237bobo10bo
49b2o168b2o$312b3o238bo2bo9b2o48b2o164b2o$312bo241bo2bo73bo150bobo$
562bo53bo12b3o151bo$554bo2bo3bobo51bobo10bo$554b2o4bo2bo51bo2bo9b2o
156b3o$355b2o204b2o53bo2bo166b3o$355b2o267bo161b3o$616bo2bo3bobo163b3o
$616b2o4bo2bo163b3o$623b2o164b3o89bobo$882b2o$588b2o292bo2$352b2o233bo
3bo$352bo233bo4bo229bobo$353b3o229bobobo232b2o$355bo228bobobo233bo61bo
$582bo4bo294bobo$517b2o63bo3bo118bo177b2o$517bo15bo9bo159b3o$515bobo
15b3o5b3o37bo2b2o116bo$515b2o19bo3bo39bobo119b2o$323b2o210b2o3b2o38b2o
$323b2o259b2o161bo$584bobo158b3o163bo$300b2o192b2o83b2o5bo157bo164b3o$
300b2o192b2o83b2o5b2o93b2o60bobo162bo$322b2o356bobo60bobo162b2o$322bo
357bo63bo$280b2o38bobo356b2o$280b2o38b2o204b2o$526b2o$538b2o144b2o$
279bo257bo2bo142bobo42b2o$278bobo257b2o4b2o137bo44b2o$279bo264bobo135b
2o$276b3o267bo$263b2o11bo269b2o$264b2o270b2o210b2o$263bo242b2o29bo210b
obo$506bo27b3o213bo$319b2o186b3o11b2o11bo140bo17b2o46b2o7b2o120b2o$
319b2o188bo11b2o2b2o147bobo16b2o46b2o129b3o$525bobo145bo3bo23b2o163b2o
2bo2bobo$526bo145bo3bo24bo29bob2o131b2o2b2o2b2o$530bo140bo3bo26b3o24b
3ob2o135b2o$523b2o4bobo138bo3bo29bo23bo$524bo3bo3bo138bobo55b3ob2o$
521b3o5bo3bo138bo30bo27bobo$316b2o203bo8bo3bo133bo33bobo26bobo132bo$
316bo214bo3bo131bobo32bobo27bo132bobo$317b3o212bobo132b2o32b2ob3o135b
2o21bo2bo$319bo213bo137b2o34bo134b2o22b2o$671bobo27b2ob3o$666b2o5bo27b
2obo$666b2o5b2o195b2o$693b2o46b2o127bobo$684b2o7b2o46b2o129bo$287b2o
312bo83bo186b2o$287b2o310b3o83bobo$598bo87b2o$264b2o332b2o128bo58b3o$
264b2o461bobo56bo$286b2o439bobo56bo3bo$286bo419b2o17b3ob2o55bo2bobo91b
3o$244b2o38bobo139b2o278b2o16bo63bobo2bo91bo$244b2o38b2o291b2o146b3ob
2o58bo3bo90bo$424bo3bo147bobo148bob2o62bo$424bo4bo146bo213b3o$243bo
182bobobo144b2o218bo$242bobo182bobobo259bo102bobo$243bo184bo4bo256bobo
102b2o$240b3o186bo3bo94b2o50b2o108bobo98b2o85b2o$240bo286bo2bo4b2o42bo
bo109bo34b2o62bobo84bo2bo4b2o$430b2o2bo92bobo5b2o42bo108b3o34bobo62bo
5b2o79bobo5b2o$433bobo92bo49b2o108bo36bo63b2o5b2o80bo$434b2o288b2o7bo
151bo$283b2o145b2o91b2o9b2o196bobo138b2o9bobo$283b2o144bobo92bo9b2obo
195bo140bo9bo2bo$429bo5b2o84b3o13bo172b2o28b2o129b3o11bo2bo$428b2o5b2o
84bo15bo172b2o28b2o129bo$534bo2bo51b2o134bo159bo2bo$535b2o52b2o119bo
12b3o159b2o$597b2o110bobo10bo198b2o20b2o$597bo111bo2bo9b2o193b2o2b2o2b
2o16b2o$280b2o316b3o109bo2bo203bobo2bo2b2o$280bo319bo117bo199b3o$281b
3o426bo2bo3bobo199b2o$283bo315bo110b2o4bo2bo$598bobo116b2o$454b2o142bo
bo316bo$450b2o2b2o141b2ob3o313bobo$449bobo75bo75bo312bo2bo$450bo76b3o
67b2ob3o314b2o9b2o$251b2o277bo66b2obo327b2o$251b2o192b3o4b2o75b2o213b
2o$445b3o4bo91b2o43b2o330b2o$228b2o215b3o5b3o88bo35b2o7b2o152bo3bo173b
obo$228b2o212b3o10bo86bobo36bo160bo4bo175bo$250b2o190b3o86bo10b2o37bob
o157bobobo177b2o$250bo191b3o85bobo49b2o156bobobo$199b2o7b2o38bobo279bo
bo205bo4bo$200b2o6b2o38b2o275b2o4bo141b2o63bo3bo$199bo324bobo15b2o129b
o15bo9bo$524bo17bobo57b2o67bobo15b3o5b3o37bo2b2o206b2o$207bo305b2o8b2o
19bo57b2o67b2o19bo3bo39bobo209bo$206bobo304b2obo27b2o145b2o3b2o38b2o
211b3o$207bo309bo222b2o209bo$204b3o307bo225bobo$204bo310bob2o131b2o83b
2o5bo$517b2o68bo62b2o83b2o5b2o176b2o5b2o$586bobo332bo5b2o$521bo11b2o
51bobo332bobo$247b2o271bobo10b2o52bo334b2o$247b2o272b2o61b3o95b2o242b
2o$517b2o65bo97b2o241bobo10b2o$516bobo175b2o230bo11b2o$516bo5b2o90b2o
77bo2bo$515b2o5b2o170b2o4b2o220b2o$612bo3bo83bobo217bob2o$612bo4bo84bo
216bo$244b2o300bo67bobobo83b2o218bo$244bo299b3o68bobobo72b2o134b2o88b
2obo27b2o$245b3o295bo72bo4bo40b2o29bo109bo9bo15bo88b2o8b2o19bo$247bo
295b2o72bo3bo40bo27b3o110b3o5b3o15bobo97bo17bobo$663b3o11b2o11bo115bo
3bo19b2o97bobo15b2o$618b2o2bo42bo11b2o2b2o122b2o3b2o118b2o4bo$621bobo
57bobo251bobo$622b2o58bo252bobo$618b2o66bo164b2o83bo10b2o$215b2o305b2o
93bobo59b2o4bobo163b2o94bobo$215b2o306bo93bo5b2o55bo3bo3bo260bo$191b2o
330bobo90b2o5b2o52b3o5bo3bo259b2o$187b4o4b2o327b2o151bo8bo3bo243b2o$
187b3ob2o2b2o490bo3bo127b2o114bo$192bo495bobo128b2o111b3o$146b2o541bo
117b2o123bo$139b2o5b2o658bo2bo$79b2o58b2o660b2o4b2o$79b2o58b2o55bo603b
obo$65bo74b2o3b2o48bobo602bo$65b3o71bo2bo2b2o23b2o22bo2bo601b2o$68bo9b
ob2o58bo2bo26b2o23b2o445b2o165b2o$67b2o9bobo54b2o6bo494b2o2b2o165bo29b
2o$79bo55b2o3bo2bo6b2o386b2o97bobo170b3o27bo$72bo6b2o59bobo33b2o13b2o
345b2o98bo173bo11b2o11b3o$71bobo5b2o60bo34b2o12bobo520b3o104b2o2b2o11b
o$71bo2bo4b2o63b2o26b2o16bo442b3o4b2o71b3o103bobo$72b2o71bo26b2o15b2o
442b3o4bo72b3o100bo3bo$633b3o5b3o72b3o97b2o$630b3o10bo72b3o96b2obo3b2o
$630b3o83b3o95bo2b3o2bo$177b2o451b3o180bobobo5b3o$134b2o41b2o542bo90bo
bobo8bo$135bo9bo574bobo87b3o2bo$135bobo3bo3bo575b2o88bob2o$136b2o4bo2b
o538b2o31b2o93b2o$142b2ob2o16bobo517bo2bo4b2o23bobo55b2o37bo$143bobo
18b2o517bobo5b2o23bo5b2o50bo238b2o$144bo19bo519bo30b2o5b2o48bobo212b4o
22b2o$772b2o208b2o7bo$216b2o461b2o9b2o290b2o2b2o3bo$209b2o4bo2bo461bo
9b2obo292b2o2bo$209b2o5bobo458b3o13bo74b2o$217bo459bo15bo73bo2bo$171b
2o37bo479bo2bo73bobo$171bo37bobo9b2o327b2o139b2o75bo213bo$130b2o40b3o
33bo2bo9bo327bo2bo4b2o422bobo$130b2o42bo32bo2bo11b3o324bobo5b2o422bo2b
o13b2o$224bo325bo431b2o14b2o$207bo2bo561b2o$209b2o334b2o9b2o210b2obo2b
ob2o$135b2o409bo9b2obo208b2o2bo4bo208b2o$135b2o406b3o13bo213bo212bobo$
131b2o410bo15bo214bobo211bo$131b2o423bo2bo428b2o$172b2o383b2o$172b2o$
137b2o27b2o$137b2o27b2o850b2o$1018bo$749b2o268b3o$168b2o572b2o4bo2bo
269bo$161b2o5b2o572b2o5bobo$142b2o17b2o579b2o6bo$143bo599bo$140b3o599b
obo9b2o$140bo600b2obo9bo247b2o$755b3o245bo23b2o$757bo242b3o24bo$742b2o
256bo7b2o15bobo$742b2o264b2o15b2o10$4b2o$2obo2bob2o$2o2bo4bo997b2o$5bo
1000bobo$6bobo997bo$1005b2o2$9bo$8bobo$7bo2bo$8b2o$1023b2o$1023bo$4b2o
1018b3o$3bobo1020bo$3bo$2b2o4$1015b2o$1006b2o7b2o$1007bo$921b2o84bobo$
921b2o2b2o81b2o$925bobo$926bo$929b3o$923b2o3bo$924bo3bo3bo$921b3o4bo2b
obo$921bo8bobo2bo$931bo3bo$935bo150b2o$692bo239b3o151b2o$105b2o2bo580b
3o346b2o4b2o$101b2o2b2o3bo578bo348bo2bo3b2o$101b2o7bo578b2o348b2o$106b
4o$1013bo$162b2o848bobo$161bo2bo4b2o841bobo$110bo50bobo5b2o497b2o343bo
$109bobo50bo504bobo401b2o$108bo2bo57bo497bo376b2o25b2o$109b2o46b2o9bob
o495b2o353b2o21b2o$158bo9bo2bo840b2o7b2o$155b3o11bo2bo229b2o5b2o601b2o
33b2o$105b2o48bo247bo5b2o260b2o374b2o$104bobo62bo2bo230bobo264bobo384b
2o$104bo64b2o233b2o264bo386bo$103b2o303b2o259b2o384bobo$407bobo645b2o$
408bo$404bo686b2o$1091bo$402b3obo685b3o$401bob2o275b2o412bo$401b2obo
275b2o$399bob3o284b2o$688bo$401bo287b3o359b2o22b2o$691bo359bobo20bobo$
1053bo20bo25b2o$690bo362b2o18b2o25bo$689bobo389b2o15bobo$420b2o267bobo
389b2o15b2o$420b2o2b2o262b2ob3o$424bobo267bo$425bo262b2ob3o$428b3o257b
2obo344b2o$422b2o3bo608b2o$423bo3bo3bo248b2o362b2o$420b3o4bo2bobo238b
2o7b2o362bo$420bo8bobo2bo237bo372b3o$430bo3bo237bobo372bo$434bo238b2o$
431b3o612bo$1045bobo32b2o$1045bobo31bobo$693b2o349b2ob3o29bo$693b2o
355bo27b2o$74b2o968b2ob3o$74b2o968b2obo2$1036b2o63b2o5b2o$678bo348b2o
7b2o63b2o5bo$677bobo348bo77bobo$677bobo348bobo75b2o$678bo350b2o71b2o$
675b3o412b2o10bobo$675bo414b2o11bo3bo$1106b2o$1049b2o54bob2o$1049b2o
53b3o2bo35b2o$1106bobobo34b2o$25b2o1080bobobo$25b2o1052b2o27bo2b3o$
1080bo19b2o7b2obo$1034bo45bobo17bo9b2o$1033bobo45b2o15bobo9bo$1033bobo
57bo4b2o$1034bo57bobo$1031b3o58bobo$33b2o996bo49b2o10bo36b2o$33b2o
1045bobo47b2o$1080bo$1079b2o$710bo383b2o$708b3o383bo$707bo387b3o$707b
2o388bo4$1150b2o$686b2o462bo$685bobo463b3o$685bo467bo$684b2o3$574bo
114b2o$574b3o111bobo443b2o$577bo110bo446bo23b2o$576bobo108b2o443b3o24b
o$576bobo553bo24bobo$577bo579b2o2$2o$2o$698b2o$592b2o62bo41b2o442b2o$
592b2o62b3o47b2o434b2o7b2o$659bo46bo444bo$658bobo46b3o439bobo$658bobo
48bo439b2o$572b2o85bo472b2o$571bobo134bo423b2o$571bo135bobo412b2o$570b
2o7b2o126bobo413bo$579b2o125b2ob3o411bobo$674b2o36bo411b2o$587b2obo83b
2o30b2ob3o$587b2ob3o113b2obo$593bo$587b2ob3o105b2o$588bobo63b2o33b2o7b
2o$588bobo62bobo34bo$589bo63bo36bobo$652b2o7b2o28b2o$590bo70b2o465b2o$
588b3o536bobo$587bo81b2obo454bo$587b2o80b2ob3o36b2o413b2o$579b2o94bo
35b2o$579b2o88b2ob3o$670bobo$670bobo$671bo$696bo446b2o$672bo22bobo445b
2o$568b2o100b3o22bobo437b2o$569bo99bo26bo439bo$569bobo97b2o22b3o437b3o
$570b2o89b2o30bo439bo$661b2o$1134bo$565b2o566bobo$566bo566bobo$566bobo
562b3ob2o$567b2o561bo$650b2o479b3ob2o$651bo481bob2o$651bobo$652b2o489b
2o$588b2o553b2o7b2o72b2o$588bo563bo73b2o$589b3o55b2o501bobo$591bo56bo
501b2o$648bobo$649b2o2$1130b2o$1130b2o2$670b2o539b2o$670bo540b2o$671b
3o$673bo472bo$1145bobo$1145bobo$1146bo$1147b3o$502bo646bo$502b3o$505bo
$504bobo724b2o$504bobo724bo$505bo726b3o$1234bo$1134b2o11bo$1134b2o10bo
bo$1146bobo31b2o21b2o5b2o$520b2o62bo560b2ob3o2b2o25bo23bo5b2o$520b2o
62b3o564bo2bo23bobo23bobo$587bo557b2ob3o3bobo21b2o25b2o$586bobo556b2ob
o6b2o52b2o$586bobo619bobo10b2o$500b2o85bo621bo11b2o$499bobo$499bo704b
3o$498b2o7b2o695b3o$507b2o695b3o$602b2o538b2o13b2o42b3o$515b2obo83b2o
538b2o13b2o42b3o28b2o$515b2ob3o606b2o72b3o7b2o19bo$521bo604bo2bo82bo
17bobo$515b2ob3o604bob2o83bobo15b2o$516bobo63b2o541bo87b2o4bo$516bobo
62bobo540b2o92bobo$517bo63bo557b2o77bobo$580b2o7b2o548bo79bo10b2o$518b
o70b2o549b3o23b2o62bobo$516b3o623bo24bo64bo$515bo81b2obo563b3o4b2o59b
2o$515b2o80b2ob3o561bo6b2o44b2o$507b2o94bo614bo$507b2o88b2ob3o612b3o$
598bobo614bo$598bobo$599bo2$600bo$496b2o100b3o$497bo99bo$497bobo97b2o$
498b2o89b2o$589b2o$893bo$493b2o398b3o$494bo401bo364b2o$494bobo398bobo
363b3o$495b2o398bobo357b2o2bo2bobo$578b2o316bo358b2o2b2o2b2o$579bo679b
2o56b2o$579bobo735b2o$580b2o$516b2o$516bo394b2o342bo$517b3o55b2o334b2o
341bobo$519bo56bo677bo2bo$576bobo676b2o$577b2o$891b2o$890bobo366b2o$
890bo368bobo$889b2o7b2o361bo$598b2o298b2o361b2o$598bo$599b3o304b2obo$
601bo304b2ob3o$912bo$906b2ob3o$907bobo$907bobo$908bo2$909bo$907b3o$
906bo$906b2o$898b2o$898b2o6$887b2o$888bo$888bobo$889b2o4$887b2o$887b2o
6$907b2o$907bo$908b3o$910bo32$737bo$737b3o$740bo$739bobo$739bobo$740bo
5$755b2o$755b2o4$735b2o$734bobo$734bo$733b2o7b2o$742b2o2$750b2obo$750b
2ob3o$756bo$750b2ob3o$751bobo$751bobo$752bo2$753bo$751b3o$750bo$750b2o
$742b2o$742b2o6$731b2o$732bo$732bobo$733b2o4$731b2o$731b2o6$751b2o$
751bo$752b3o$754bo21$887bo$887b3o$890bo$889bobo$889bobo$890bo5$905b2o$
905b2o4$885b2o$884bobo$884bo$883b2o7b2o$892b2o2$900b2obo$900b2ob3o$
906bo$900b2ob3o$901bobo$901bobo$902bo2$903bo$901b3o$686b2o212bo$686b2o
2b2o208b2o$690bobo199b2o$691bo200b2o$695bo$688b2o4bobo$689bo3bo3bo$
686b3o5bo3bo$686bo8bo3bo$696bo3bo180b2o$697bobo182bo$698bo183bobo$883b
2o4$881b2o$881b2o5$1046b2o$901b2o142bo2bo4b2o$901bo143bobo4bo2bo$902b
3o141bo5bo$904bo147bo$1041b2o9bob2o$1042bo11b2o$1039b3o$1039bo$1053b2o
$1053b2o46$836b2o$836b2o2b2o$840bobo$841bo$845bo$838b2o4bobo$839bo3bo
3bo$836b3o5bo3bo$836bo8bo3bo$846bo3bo$847bobo$848bo654$1300b3o11$1280b
o$1279bobo$1278bo3bo$1277bo3bo$1276bo3bo$1275bo3bo$1276bobo$1277bo$
1273bo$1272bobo$1272b2o$1276b2o$1276bobo$1271b2o5bo$1271b2o5b2o23$
1250b2o$1248bob2o$1247bo$1250bo$1246b2obo$1246b2o2$1243bo$1242bobo$
1242b2o$1246b2o$1246bobo$1241b2o5bo$1241b2o5b2o360$874bo2$871b3o$873bo
$872bo39$824b2o$823bobo$825bo!
#C [[ THEME Blues STEP 16 X 0 Y -200 Z -4 ]]
#C [[ LABELANGLE 45 ]]
#C [[ LABEL 300 500 2 "FIRE_CC_ODD_DEC1" ]]
#C [[ LABEL 336 464 2 "FIRE_CP_EVEN_DEC1" ]]
#C [[ LABEL 372 428 2 "FIRE_CC_EVEN_DEC1" ]]
#C [[ LABEL 408 392 2 "FIRE_CP_ODD_DEC1" ]]
#C [[ LABEL 444 356 2 "INC16" ]]
#C [[ LABEL 480 320 2 "DEC8" ]]
#C [[ LABEL 516 284 2 "INC4" ]]
#C [[ LABEL 552 248 2 "DEC2" ]]
#C [[ LABEL 588 212 2 "INC1" ]]
#C [[ PASTET 1024 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]
#C [[ PASTET 2048 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]
#C [[ PASTET 3072 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]
#C [[ PASTET 4096 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]
#C [[ PASTET 12288 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]
#C [[ PASTET 16384 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]
#C [[ PASTET 18432 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]
#C [[ PASTET 20480 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]
#C [[ STOP 33000 ]]


With a combination of some subset of these nine operations, the DBCA can generally fire exactly the right next glider in its recipe, at a standard cost of just nine bits on the tape (one "codon"). In any bit position, two incoming gliders will suppress the output and nothing will happen; one incoming glider will allow that operation to happen.

Slow And Steady Wins The Race

Notice what happens when the unary decoder in the northwest reaches the ninth output position, and the entire bistable switch stack has to be reset to return to zero position. Feeding the final bistable switch output back into one of its inputs does a great job of resetting the entire stack -- eventually. It's all done in 35,000 ticks or so -- see below.

Code: Select all

x = 636, y = 595, rule = LifeHistory
583.2A$583.2A$569.A13.2A$569.3A12.A$572.A10.A.A$571.2A9.2A.A2$576.A$
575.A.A5.2A$575.A2.A4.2A$576.2A10$547.A.A$550.A$546.A4.A2.2A30.A.A$
546.2A.A2.A.2A31.2A$550.2A35.A4$555.A$554.A.A$553.A2.A$554.2A3$550.2A
$549.A.A$549.A$548.2A5$598.2A$591.2A5.2A15.F$591.2A22.F$615.F$615.F$
593.2A27.2A$593.2A27.2A$587.2A$587.2A$628.2A$628.2A$624.2A$624.2A$
550.2A$549.A2.A$536.A15.A$536.3A13.A66.3A7.2A$539.A9.2A.A34.2A30.A2.A
6.2A$538.2A9.2A35.2A30.A3.A$588.A34.A$619.3A.2A$543.A.2A3.2A71.A$541.
3A.3A2.2A66.A3.2A$542.A.A.2A74.A$543.3A$543.3A$615.A.A$615.2A18.F$
616.A18.F$635.F$626.F8.F$582.2A42.F$582.2A42.F$626.F3$587.2A$587.2A$
583.2A$583.2A$624.2A$624.2A$589.2A27.2A$589.2A27.2A3$620.2A$613.2A5.
2A$613.2A24$533.2A$533.A$531.A.A$516.2A13.2A$516.2A3$496.2A$496.2A3$
495.A$494.A.A$495.A$480.2A10.3A$481.2A9.A$480.A3$535.2A$535.2A7$532.
2A$532.A$533.3A$535.A6$503.2A$503.2A2$480.2A$480.2A$502.2A$502.A$460.
2A38.A.A$460.2A38.2A3$459.A$458.A.A$459.A$456.3A$456.A29.2A$485.A.A$
486.A10$496.2A$496.A$497.3A$499.A6$467.2A$467.2A2$444.2A$444.2A$466.
2A$416.2A48.A$417.2A5.2A38.A.A$416.A7.2A38.2A3$423.A$422.A.A$423.A$
420.3A$420.A29.2A$449.A.A$450.A10$460.2A$460.A45.4B$461.3A43.4B$463.A
44.4B$509.4B$510.4B$511.4B$512.4B$513.4B$431.2A$431.2A2$408.2A$408.2A
$430.2A$430.A$388.2A38.A.A$388.2A38.2A3$387.A$386.A.A$387.A$384.3A$
384.A29.2A$413.A.A$414.A10$424.2A43.4B$424.A45.4B$425.3A43.4B$427.A
44.4B$473.4B$474.4B$475.4B$352.2A122.4B$353.2A122.4B$352.A42.2A81.4B$
395.2A82.3B$480.2B$372.2A107.B$372.2A$394.2A$394.A$352.2A38.A.A$352.
2A38.2A3$351.A$350.A.A$351.A$348.3A$348.A29.2A$377.A.A$378.A7$433.B$
433.2B$433.3B$388.2A43.4B$388.A45.4B$389.3A43.4B$391.A44.4B$437.4B$
438.4B$439.4B$440.4B$441.4B$359.2A81.4B$359.2A82.4B$444.4B$336.2A107.
4B$336.2A108.4B$358.2A87.4B$358.A89.4B$316.2A38.A.A90.4B$316.2A38.2A
92.4B$451.4B$452.4B$315.A137.4B$314.A.A137.4B$315.A139.4B$312.3A141.
4B$312.A29.2A113.4B$341.A.A114.4B$342.A116.4B$460.4B$461.4B2$394.B$
394.2B$394.3B$394.4B$395.4B$288.2A106.4B$289.2A61.2A43.4B$288.A63.A
45.4B$353.3A43.4B$355.A44.4B$401.4B$402.4B$403.4B$404.4B$405.4B$323.
2A81.4B$323.2A82.4B$408.4B$300.2A107.4B$300.2A108.4B$322.2A87.4B$322.
A89.4B$280.2A38.A.A90.4B$280.2A38.2A92.4B$415.4B$416.4B$279.A137.4B$
278.A.A137.4B$279.A139.4B$276.3A141.4B$276.A29.2A113.4B$305.A.A114.4B
$306.A116.4B$424.4B$425.4B$426.4B$427.4B6$316.2A43.4B$316.A45.4B$317.
3A43.4B$319.A44.4B$365.4B$366.4B$367.4B$368.4B$369.4B$287.2A81.4B$
287.2A82.4B$372.4B$264.2A107.4B$264.2A108.4B$286.2A87.4B$286.A89.4B$
244.2A38.A.A90.4B$244.2A38.2A92.4B$379.4B$380.4B$243.A137.4B$242.A.A
137.4B$243.A139.4B$240.3A141.4B$240.A29.2A113.4B$269.A.A114.4B$270.A
116.4B$224.2A162.4B$225.2A162.4B$224.A165.4B$391.4B$392.4B$393.4B$
394.4B$395.4B$396.4B$280.2A115.4B$280.A117.4B$281.3A43.4B68.4B$283.A
44.4B$329.4B$330.4B$331.4B$332.4B$333.4B$251.2A81.4B$251.2A82.4B$336.
4B$228.2A107.4B$228.2A108.4B$250.2A87.4B$250.A89.4B$208.2A38.A.A90.4B
$208.2A38.2A92.4B$343.4B$344.4B$207.A137.4B$206.A.A137.4B$207.A139.4B
$204.3A141.4B$204.A29.2A113.4B$233.A.A114.4B$234.A116.4B$352.4B$353.
4B$354.4B$355.4B$356.4B$357.4B$358.4B$359.4B$360.4B$244.2A43.4B68.4B$
244.A45.4B68.4B$245.3A43.4B68.4B$247.A44.4B68.4B$293.4B68.4B$294.4B
68.4B$295.4B68.4B$296.4B68.4B$297.4B68.4B$215.2A81.4B68.4B$215.2A82.
4B68.4B$191.A108.4B68.4B$187.2A2.2A.3A104.4B68.4B$187.2A4.4A105.4B68.
4B$191.2A110.4B$146.2A156.4B$139.2A5.2A157.4B$79.2A58.2A165.4B$78.B2A
2B113.A110.4B$65.A13.2A2B77.2A33.A.A110.4B$65.3A11.BA2B58.2A18.2A7.2A
22.A2.A111.4B$68.A9.BABA59.2A17.A9.2A23.2A113.4B$67.2A9.2ABA53.2A174.
4B$77.4B54.2A175.4B$72.A4.4B95.2A13.2A120.4B$71.A.A3.2B2AB94.2A12.A.A
121.4B$71.A2.A4.2A91.2A16.A124.4B$72.2A98.2A15.2A125.4B$317.4B$318.4B
$319.4B$177.2A141.4B$134.2A41.2A142.4B$135.A186.4B$135.A.A185.4B$136.
2A186.4B$325.4B$326.4B$327.4B$328.4B$216.2A42.B68.4B$209.2A4.A2.A41.
2B68.4B$209.A2.A3.A.A41.3B68.4B$217.A42.4B68.4B$171.2A36.A2.A48.4B68.
4B$171.A36.A2.A9.2A39.4B68.4B$130.2A40.3A33.A.A10.A41.4B68.4B$130.2A
19.A22.A34.A12.3A39.4B68.4B$150.2A72.A40.4B68.4B$150.A.A56.2A55.4B68.
4B$209.2A56.4B68.4B$135.2A23.3A105.4B68.4B$135.2A20.A.A.A.A105.4B68.
4B$131.2A23.2A.A3.A106.4B68.4B$131.2A24.A.A2.2A107.4B68.4B$155.A5.A
10.2A98.4B68.4B$155.2A.A2.A10.2A99.4B$137.2A18.2A.A5.2A106.4B$137.2A
27.2A107.4B$276.4B$277.4B$168.2A108.4B$161.2A5.2A109.4B$142.2A17.2A
117.4B$143.A137.4B$140.3A139.4B$140.A142.4B$284.4B$285.4B$286.4B$287.
4B$288.4B$289.4B$290.4B$291.4B$292.4B$293.4B$294.4B$295.4B$.ABA292.4B
$.3BAB2.B288.4B$A4BA2B2A288.4B$2ABA2BAB2A289.4B$.B2.2A3B291.4B$6.3B
292.4B$302.4B$303.4B$9.A294.4B$8.A.A294.4B$7.A2.A295.4B$8.2A297.4B$
308.4B$309.4B$4.2A304.4B$3.A.A$3.A$2.2A19$102.4A$101.A7.2A$101.A3.2A
2.2A$102.A2.2A2$162.2A$161.A2.A4.2A$110.A50.A.A3.A2.A$109.A.A50.A$
108.A2.A55.A2.A$109.2A46.2A9.A2.A$158.A10.A.A$155.3A12.A$105.2A48.A$
104.A.A62.2A$104.A64.2A$103.2A32$153.A$152.2A$152.A.A!
#C [[ THEME Blues ]]


Compared to the amount of time between successive bits coming in from the RCT mechanism, 35,000 ticks is practically instantaneous. This is a case where the simplicity of the mechanism is paramount (because we're trying to minimize the total number of bits that have to be stored in the RCT mechanism). The length of time that the mechanism takes to recover doesn't matter at all, compared to how much it costs to build it -- and Paul Callahan's bistable switch is made out of just a few Spartan still lifes, and is very cheap to construct.

What Comes Next

Current RCT plans call for a second optional bootstrap stage, further improving the encoding efficiency of the system. The ECCA (Extreme Compression Construction Arm) uses 4-bit and 7-bit codons instead of 9-bit codons, and will be constructed with its own integrated self-destruct circuitry. As described in the next post, the ECCA will be responsible for several cleanup tasks, as well as for building the ATBC -- the Actual Thing Being Constructed, which we should be careful not to lose sight of because it's really supposed to be the whole point of this RCT exercise.