## A new way of constructing?

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
fch
Posts: 4
Joined: March 22nd, 2011, 2:07 pm

### A new way of constructing?

Here are the results of my life project I started 2 years ago. The original endgoal was to create a self replicating structure but since someone else was ahead of me I did not complete it (yet). I wanted to use an absolute minimum of structures. So I was interested if series of gliders fired at each other from 2 opposite guns (normal 30 generation) could be used for construction. It can as the attachment demonstrates.

Also my ideas of building a replicator this way would result in a replicator much bigger than the one found already. On the other hand It would result in a selfreplicator filling the univerce at a speed of c/16.

Multiple self made programs were used to create this. One for finding usefull patterns from collisions. One for creating timed glider path. and a construction application.

www.colaboy.nl/test.rle

dvgrn
Moderator
Posts: 6058
Joined: May 17th, 2009, 11:00 pm
Contact:

### Re: A new way of constructing?

fch wrote:Here are the results of my life project I started 2 years ago. The original endgoal was to create a self replicating structure but since someone else was ahead of me I did not complete it (yet). I wanted to use an absolute minimum of structures. So I was interested if series of gliders fired at each other from 2 opposite guns (normal 30 generation) could be used for construction. It can as the attachment demonstrates.
Wow! Sorry about the slow response; this is an ambitious research project! For anyone interested in the detailed workings of the new construction method, I've extracted some of the colliding-p30-glider-stream recipes from the large pattern in the original link. The output spaceships and gliders are used in various combinations to produce the sample construction.

In case anyone has trouble running the original large pattern, its end result is the incremental construction of two synchronized p30 guns identical to (but very far away from) the pairs of guns in the original pattern. The pattern is much too large to run efficiently in QuickLife, so be sure to switch over to HashLife and move the speed up to 8^5 or so before you run it.

Code: Select all

``````#C 61 gliders in two opposing intermittent p30 streams produce an LWSS
x = 1324, y = 1325, rule = B3/S23
1323bo\$1321b2o\$1322b2o6\$1314bobo\$1314b2o\$1315bo20\$1293bo\$1291b2o\$1292b
2o36\$1254bobo\$1254b2o\$1255bo5\$1248bo\$1246b2o\$1247b2o13\$1233bo\$1231b2o\$
1232b2o28\$1203bo\$1201b2o\$1202b2o13\$1188bo\$1186b2o\$1187b2o6\$1179bobo\$
1179b2o\$1180bo28\$1149bobo\$1149b2o\$1150bo43\$1104bobo\$1104b2o\$1105bo50\$
1053bo\$1051b2o\$1052b2o6\$1044bobo\$1044b2o\$1045bo20\$1023bo\$1021b2o\$1022b
2o43\$978bo\$976b2o\$977b2o6\$969bobo\$969b2o\$970bo13\$954bobo\$954b2o\$955bo
5\$948bo\$946b2o\$947b2o6\$939bobo\$939b2o\$940bo5\$933bo\$931b2o\$932b2o6\$924b
obo\$924b2o\$925bo5\$918bo\$916b2o\$917b2o6\$909bobo\$909b2o\$910bo5\$903bo\$
901b2o\$902b2o13\$888bo\$886b2o\$887b2o6\$879bobo\$879b2o\$880bo58\$819bobo\$
819b2o\$820bo28\$789bobo\$789b2o\$790bo20\$768bo\$766b2o\$767b2o13\$753bo\$751b
2o\$752b2o13\$738bo\$736b2o\$737b2o105\$631b2o\$630bobo\$632bo21\$608b3o\$610bo
\$609bo5\$601b2o\$600bobo\$602bo13\$586b2o\$585bobo\$587bo13\$571b2o\$570bobo\$
572bo28\$541b2o\$540bobo\$542bo21\$518b3o\$520bo\$519bo5\$511b2o\$510bobo\$512b
o6\$503b3o\$505bo\$504bo20\$481b2o\$480bobo\$482bo6\$473b3o\$475bo\$474bo80\$
391b2o\$390bobo\$392bo6\$383b3o\$385bo\$384bo5\$376b2o\$375bobo\$377bo13\$361b
2o\$360bobo\$362bo21\$338b3o\$340bo\$339bo13\$323b3o\$325bo\$324bo13\$308b3o\$
310bo\$309bo20\$286b2o\$285bobo\$287bo21\$263b3o\$265bo\$264bo50\$211b2o\$210bo
bo\$212bo6\$203b3o\$205bo\$204bo35\$166b2o\$165bobo\$167bo58\$106b2o\$105bobo\$
107bo21\$83b3o\$85bo\$84bo5\$76b2o\$75bobo\$77bo21\$53b3o\$55bo\$54bo20\$31b2o\$
30bobo\$32bo6\$23b3o\$25bo\$24bo20\$b2o\$obo\$2bo!``````

Code: Select all

``````#C 247 gliders produce a single 90-degree glider output on a particular
#C lane, with an exactly-timed delay relative to the final input glider.
x = 10431, y = 10432, rule = B3/S23
10428bo\$10428bobo\$10428b2o1220\$9206bo\$9205bo\$9205b3o13\$9191bo\$9190bo\$
9190b3o36\$9153bo\$9153bobo\$9153b2o13\$9138bo\$9138bobo\$9138b2o13\$9123bo\$
9123bobo\$9123b2o5\$9116bo\$9115bo\$9115b3o6\$9108bo\$9108bobo\$9108b2o5\$
9101bo\$9100bo\$9100b3o6\$9093bo\$9093bobo\$9093b2o13\$9078bo\$9078bobo\$9078b
2o28\$9048bo\$9048bobo\$9048b2o13\$9033bo\$9033bobo\$9033b2o620\$8411bo\$8410b
o\$8410b3o6\$8403bo\$8403bobo\$8403b2o5\$8396bo\$8395bo\$8395b3o21\$8373bo\$
8373bobo\$8373b2o5\$8366bo\$8365bo\$8365b3o21\$8343bo\$8343bobo\$8343b2o35\$
8306bo\$8305bo\$8305b3o13\$8291bo\$8290bo\$8290b3o28\$8261bo\$8260bo\$8260b3o
21\$8238bo\$8238bobo\$8238b2o5\$8231bo\$8230bo\$8230b3o6\$8223bo\$8223bobo\$
8223b2o5\$8216bo\$8215bo\$8215b3o6\$8208bo\$8208bobo\$8208b2o5\$8201bo\$8200bo
\$8200b3o73\$8435bo\$8434bo\$8434b3o21\$8412bo\$8412bobo\$8412b2o13\$8397bo\$
8397bobo\$8397b2o5\$8390bo\$8389bo\$8389b3o6\$8382bo\$8382bobo\$8382b2o5\$
8375bo\$8374bo\$8374b3o13\$8360bo\$8359bo\$8359b3o6\$8352bo\$8352bobo\$8352b2o
13\$8337bo\$8337bobo\$8337b2o43\$8292bo\$8292bobo\$8292b2o13\$8277bo\$8277bobo
\$8277b2o13\$8262bo\$8262bobo\$8262b2o5\$8255bo\$8254bo\$8254b3o13\$8240bo\$
8239bo\$8239b3o6\$8232bo\$8232bobo\$8232b2o635\$7595bo\$7594bo\$7594b3o6\$
7587bo\$7587bobo\$7587b2o13\$7572bo\$7572bobo\$7572b2o5\$7565bo\$7564bo\$7564b
3o21\$7542bo\$7542bobo\$7542b2o5\$7535bo\$7534bo\$7534b3o6\$7527bo\$7527bobo\$
7527b2o28\$7497bo\$7497bobo\$7497b2o5\$7490bo\$7489bo\$7489b3o6\$7482bo\$7482b
obo\$7482b2o13\$7467bo\$7467bobo\$7467b2o5\$7460bo\$7459bo\$7459b3o13\$7136bo\$
7135bo\$7135b3o6\$7128bo308bo\$7128bobo306bobo\$7128b2o307b2o5\$7121bo\$
7120bo\$7120b3o6\$7113bo\$7113bobo\$7113b2o13\$7407bo\$7407bobo\$7407b2o5\$
7091bo\$7090bo\$7090b3o6\$7083bo308bo\$7083bobo306bobo\$7083b2o307b2o20\$
7061bo\$7060bo\$7060b3o6\$7053bo\$7053bobo\$7053b2o5\$7046bo\$7045bo\$7045b3o
21\$7023bo\$7023bobo\$7023b2o20\$7001bo\$7000bo\$7000b3o36\$6963bo\$6963bobo\$
6963b2o13\$6948bo\$6948bobo\$6948b2o920\$6335bo\$6334bo\$6334b3o6\$6018bo\$
6018bobo\$6018b2o5\$6320bo\$6319bo\$6319b3o6\$6312bo\$6312bobo\$6312b2o5\$
5996bo308bo\$5995bo308bo\$5995b3o306b3o6\$5988bo\$5988bobo\$5988b2o13\$5973b
o308bo\$5973bobo306bobo\$5973b2o307b2o5\$5966bo308bo\$5965bo308bo\$5965b3o
306b3o6\$5958bo308bo\$5958bobo306bobo\$5958b2o307b2o5\$6260bo\$6259bo\$6259b
3o6\$6252bo\$6252bobo\$6252b2o20\$6230bo\$6229bo\$6229b3o21\$5898bo308bo\$
5898bobo306bobo\$5898b2o307b2o5\$5891bo308bo\$5890bo308bo\$5890b3o306b3o
13\$5876bo\$5875bo\$5875b3o6\$5868bo\$5868bobo\$5868b2o28\$6147bo\$6147bobo\$
6147b2o5\$6140bo\$6139bo\$6139b3o6\$6132bo\$6132bobo\$6132b2o830\$4991bo\$
4990bo\$4990b3o6\$4983bo\$4983bobo\$4983b2o13\$4968bo\$4968bobo\$4968b2o5\$
4961bo\$4960bo\$4960b3o21\$4938bo\$4938bobo\$4938b2o5\$4931bo\$4930bo\$4930b3o
6\$4923bo\$4923bobo\$4923b2o5\$5225bo\$5224bo\$5224b3o6\$4908bo\$4908bobo\$
4908b2o5\$5210bo\$5209bo\$5209b3o6\$4893bo\$4893bobo\$4893b2o20\$4871bo\$4870b
o\$4870b3o6\$4863bo\$4863bobo\$4863b2o5\$4856bo\$4855bo\$4855b3o13\$5150bo\$
5149bo\$5149b3o6\$4833bo\$4833bobo\$4833b2o5\$4826bo308bo\$4825bo308bo\$4825b
3o306b3o6\$4818bo\$4818bobo\$4818b2o5\$5120bo\$5119bo\$5119b3o6\$5112bo\$5112b
obo\$5112b2o5\$5105bo\$5104bo\$5104b3o13\$5090bo\$5089bo\$5089b3o6\$5082bo\$
5082bobo\$5082b2o13\$5067bo\$5067bobo\$5067b2o759\$3998bo\$3998b2o\$3997bobo
13\$3983bo\$3983b2o\$3982bobo13\$3968bo\$3968b2o\$3967bobo6\$3960b2o\$3961b2o\$
3960bo13\$3945b2o\$3946b2o\$3945bo5\$3938bo\$3938b2o\$3937bobo6\$3930b2o\$
3931b2o\$3930bo5\$3923bo\$3923b2o\$3922bobo13\$3908bo\$3908b2o\$3907bobo43\$
3863bo\$3863b2o\$3862bobo13\$4157bo\$4157b2o\$4156bobo6\$3840b2o\$3841b2o\$
3840bo5\$3833bo308bo\$3833b2o307b2o\$3832bobo306bobo6\$3825b2o307b2o\$3826b
2o307b2o\$3825bo308bo5\$3818bo\$3818b2o\$3817bobo13\$4112bo\$4112b2o\$4111bob
o28\$4082bo\$4082b2o\$4081bobo6\$4074b2o\$4075b2o\$4074bo5\$4067bo\$4067b2o\$
4066bobo6\$4059b2o\$4060b2o\$4059bo13\$4044b2o\$4045b2o\$4044bo28\$4014b2o\$
4015b2o\$4014bo5\$4007bo\$4007b2o\$4006bobo6\$3999b2o\$4000b2o\$3999bo5\$3992b
o\$3992b2o\$3991bobo13\$3977bo\$3977b2o\$3976bobo6\$3969b2o\$3970b2o\$3969bo
628\$3030b2o\$3031b2o\$3030bo20\$3008bo\$3008b2o\$3007bobo6\$3000b2o\$3001b2o\$
3000bo13\$2985b2o\$2986b2o\$2985bo13\$2970b2o\$2971b2o\$2970bo13\$2955b2o\$
2956b2o\$2955bo5\$2948bo\$2948b2o\$2947bobo6\$2940b2o\$2941b2o\$2940bo5\$2933b
o\$2933b2o\$2932bobo28\$2903bo\$2903b2o\$2902bobo6\$2895b2o307b2o\$2896b2o
307b2o\$2895bo308bo5\$3197bo\$3197b2o\$3196bobo6\$3189b2o\$3190b2o\$3189bo5\$
2873bo308bo\$2873b2o307b2o\$2872bobo306bobo6\$2865b2o307b2o\$2866b2o307b2o
\$2865bo308bo13\$2850b2o307b2o\$2851b2o307b2o\$2850bo308bo5\$3152bo\$3152b2o
\$3151bobo6\$3144b2o\$3145b2o\$3144bo13\$3129b2o\$3130b2o\$3129bo5\$3122bo\$
3122b2o\$3121bobo6\$3114b2o\$3115b2o\$3114bo13\$3099b2o\$3100b2o\$3099bo5\$
3092bo\$3092b2o\$3091bobo21\$3069b2o\$3070b2o\$3069bo13\$3054b2o\$3055b2o\$
3054bo5\$3047bo\$3047b2o\$3046bobo28\$3017bo\$3017b2o\$3016bobo6\$3009b2o\$
3010b2o\$3009bo620\$2078bo\$2078b2o\$2077bobo36\$2040b2o\$2041b2o\$2040bo5\$
2033bo\$2033b2o\$2032bobo6\$2025b2o\$2026b2o\$2025bo43\$1980b2o\$1981b2o\$
1980bo13\$1965b2o\$1966b2o\$1965bo13\$1950b2o\$1951b2o\$1950bo5\$1943bo\$1943b
2o\$1942bobo6\$2244b2o\$2245b2o\$2244bo5\$2237bo\$2237b2o\$2236bobo6\$1920b2o\$
1921b2o\$1920bo5\$1913bo308bo\$1913b2o307b2o\$1912bobo306bobo6\$1905b2o\$
1906b2o\$1905bo5\$1898bo\$1898b2o\$1897bobo6\$1890b2o307b2o\$1891b2o307b2o\$
1890bo308bo13\$2184b2o\$2185b2o\$2184bo5\$2177bo\$2177b2o\$2176bobo51\$2124b
2o\$2125b2o\$2124bo28\$2094b2o\$2095b2o\$2094bo13\$2079b2o\$2080b2o\$2079bo5\$
2072bo\$2072b2o\$2071bobo6\$2064b2o\$2065b2o\$2064bo5\$2057bo\$2057b2o\$2056bo
bo6\$2049b2o\$2050b2o\$2049bo613\$1125b2o\$1126b2o\$1125bo5\$1118bo\$1118b2o\$
1117bobo13\$1103bo\$1103b2o\$1102bobo51\$1050b2o\$1051b2o\$1050bo20\$1028bo\$
1028b2o\$1027bobo6\$1020b2o\$1021b2o\$1020bo5\$1013bo\$1013b2o\$1012bobo6\$
1005b2o\$1006b2o\$1005bo5\$998bo\$998b2o\$997bobo6\$990b2o\$991b2o\$990bo13\$
975b2o307b2o\$976b2o307b2o\$975bo308bo5\$1277bo\$1277b2o\$1276bobo6\$1269b2o
\$1270b2o\$1269bo5\$1262bo\$1262b2o\$1261bobo6\$945b2o307b2o\$946b2o307b2o\$
945bo308bo13\$930b2o\$931b2o\$930bo28\$1209b2o\$1210b2o\$1209bo13\$1194b2o\$
1195b2o\$1194bo20\$1172bo\$1172b2o\$1171bobo6\$1164b2o\$1165b2o\$1164bo43\$
1119b2o\$1120b2o\$1119bo5\$1112bo\$1112b2o\$1111bobo6\$1104b2o\$1105b2o\$1104b
o5\$1097bo\$1097b2o\$1096bobo6\$1089b2o\$1090b2o\$1089bo605\$173bo\$173b2o\$
172bobo28\$143bo\$143b2o\$142bobo13\$128bo\$128b2o\$127bobo6\$120b2o\$121b2o\$
120bo5\$113bo\$113b2o\$112bobo36\$75b2o\$76b2o\$75bo13\$60b2o\$61b2o\$60bo5\$53b
o\$53b2o\$52bobo6\$45b2o\$46b2o\$45bo20\$23bo\$23b2o\$22bobo6\$15b2o\$16b2o\$15bo
13\$2o\$b2o\$o!``````
The other constraints are totally different, but the single-file glider salvos are reminiscent of Paul Chapman's work last year designing a better construction arm for next-generation Geminoid spaceships. It turned out that an elbow block can be manipulated successfully by gliders coming in on just one lane:

Code: Select all

``````#C pairs of synchronized gliders on a single lane produce all
#C necessary operations on a construction-arm elbow block:
#C several INCs and DECs, and output gliders of both colors.
x = 2149, y = 247, rule = LifeHistory
F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F
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59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F2\$4.F
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59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F2\$6.F
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59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F2\$8.F
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59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F59.F2\$18.
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fch wrote:Also my ideas of building a replicator this way would result in a replicator much bigger than the one found already. On the other hand It would result in a selfreplicator filling the univerce at a speed of c/16.
If you're referring to Andrew Wade's Gemini spaceship, I don't think the size comparison is fair -- Geminoids are self-constructing oblique spaceships, but not technically replicators because even if you disable the destructor arm, there's never more than one active copy of the original pattern.

It looks as if you're far enough along in your research that you might yet complete a true replicator pattern before anyone manages to modify the Gemini design to produce one (full disclosure: I'm working on this, or would be if I had more spare time!).

A replicator following along the general lines of the Gemini's construction methods will likely be quite a bit smaller than one based on the p30 reactions shown here -- but with Golly to run the simulation, an order of magnitude or three doesn't really mean very much any more! Reaching the goal _first_ (of constructing a working Conway's Life replicator, where the number of copies of the original pattern increases without bounds) seems like the important thing.
fch wrote: Multiple self made programs were used to create this. One for finding usefull patterns from collisions. One for creating timed glider path. and a construction application.
Do you have a stamp collection of the full set of "useful patterns" that your search program has found? Are the path calculator and construction app in a form that someone else might be able to figure out how to use?

Keep the cheer,

DaveG

fch
Posts: 4
Joined: March 22nd, 2011, 2:07 pm

### Re: A new way of constructing?

Anyone interested in the code of the programs can contact me.
A bit more detail:
Findig the b-hives:
- A miniature life on a 64*64 grid was made in C. This code was made superfast by performing bitwise operations to calculate 64 celss at a time.
- gliders were inserted at the corners and then perform 30 generations and stop when a b-hive was found or the pattern already existed.
Finding a timer path:
- In order to have full control over the gliders, gliders must be available on all 30 lines (any other line can be reached by delay in the streams). And in all 30 timings. (Any other timing can by reached by delay in the streams) So together there are 900 distict path's. I rerouted the gliders by b-hives to achieve the required path-length. This gives only an even number of delay. Using the glider from the other direction (for 1 glider there are 4 streams) solves the fase problem.
Construction (so far):
- Construction is based on building with 2 gliders.
- Construction is done with in mind the idea of buildig a replicator. 1 head, 1 tail and an enormous stream of gliders between them. The idea is to build 2 children both 90 degrees from the parent. The glider streams crossing (but not interacting) the glider stream of the parent.
- In order to buils something patterns (.rle) must be offered that can contain at most 2 existing patterns and 2 gliders. The app recognizes the pattrens calculated the new pattern and the cycle time of that pattren.
- The program then genereates the glidersteam needed to build that pattern.

I have included some of the circuits I want to use for futher development. My problem is that all of them are quite big. (I know how to make guns with gliders. So everything is made of guns). Any help in here will be very much appreciated.

I have attached a gif demonstrating where I visualize how these replicators should populate the life-universe.

Code: Select all

``````#CXRLE Pos=-40,0 Gen=499164
x = 750, y = 931, rule = B3/S23
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396b2o6\$403bobo\$404b2o\$404bo5\$411bo\$412b2o\$288b3o120b2o\$288bo\$289bo4\$
418bobo\$419b2o\$419bo5\$426bo\$427b2o\$426b2o6\$433bobo\$434b2o\$434bo5\$441bo
\$442b2o\$441b2o6\$448bobo\$449b2o\$449bo5\$456bo\$457b2o\$456b2o6\$463bobo\$
464b2o\$464bo5\$471bo\$472b2o\$471b2o6\$478bobo\$479b2o\$479bo4\$484b2o\$484bo\$
485b3o\$487bo22\$386b2o\$386bobo\$386bo\$379b2o\$380b2o\$379bo5\$372bo\$372b2o\$
371bobo90\$476bo\$476b2o\$475bobo\$491b2o\$491bobo\$491bo3\$468b2o\$469b2o\$
468bo\$498b3o\$498bo\$499bo2\$461bo\$461b2o\$460bobo\$506b2o\$506bobo\$506bo3\$
453b2o\$454b2o\$453bo\$513b3o\$513bo\$514bo2\$446bo80b2o\$446b2o74bo4b2o\$445b
obo68b2ob5o6b2o\$515bo4b2o2bo5b3o5b2o\$504b2o8bo8b2o5b2o6b2o\$504b2o8bo7b
o4b2o\$514bo12b2o\$515bo\$438b2o76b2o\$439b2o\$438bo5\$431bo\$431b2o\$430bobo
6\$423b2o\$424b2o\$423bo5\$416bo\$416b2o\$415bobo6\$408b2o\$409b2o\$408bo3\$394b
o\$391b4o3bob2o\$390b4o4bobob2o2b2o\$383b2o5bo2bo3b2obob2o2bobo\$383b2o5b
4o3b2o8b3o7b2o\$391b4o3b2o8b3o6b2o\$394bo12b3o\$406bobo\$406b2o40\$580bo\$
581bo\$579b3o104\$725b2o\$724bobo\$723b3o12bo\$714b2o6b3o8b2o3b4o\$714b2o7b
3o8b2o3b4o5b2o\$724bobo2b2obob2o3bo2bo5b2o\$725b2o2b2obobo4b4o\$731b2obo
3b4o\$738bo3\$724bo\$722b2o\$723b2o6\$715bobo\$715b2o\$716bo5\$709bo\$707b2o\$
708b2o6\$700bobo\$700b2o\$701bo5\$694bo\$692b2o\$693b2o6\$685bobo\$685b2o\$686b
o4\$649b2o\$649bobo27bo\$649bo27b2o\$678b2o6\$670bobo\$670b2o\$671bo5\$664bo\$
662b2o\$663b2o6\$655bobo\$655b2o\$656bo2\$652b2o\$653bo\$650b3o\$650bo!
``````
Duplicate signal to identical and inverted signal

Code: Select all

``````#CXRLE Pos=-16,0 Gen=70216
x = 1692, y = 1520, rule = B3/S23
1035bo\$1033bobo\$1024bo7bobo\$1023b2o6bo2bo11b2o\$1012b2o8b2o4b2o2bobo11b
2o\$1012b2o7b3o4b2o3bobo\$1022b2o4b2o5bo\$1023b2o\$1024bo\$1036bo\$1037bo\$
1035b3o6\$1044bo\$1042bobo\$1043b2o5\$1051bo\$1052bo\$1050b3o6\$1059bo\$1057bo
bo\$1058b2o10\$1057b2o\$1056bobo\$1058bo6\$1049b3o\$1051bo\$1050bo5\$1042b2o\$
1041bobo\$1043bo6\$1034b3o\$1036bo\$1035bo5\$1027b2o\$1026bobo\$1028bo6\$1019b
3o\$1021bo\$1020bo5\$1012b2o\$1011bobo\$1013bo2\$1118b2o\$1118bo\$1119b3o\$
1121bo\$1004b3o\$1006bo\$1005bo5\$997b2o\$996bobo\$998bo6\$989b3o\$991bo\$990bo
5\$982b2o\$981bobo\$983bo6\$974b3o\$976bo\$975bo5\$967b2o\$966bobo\$968bo13\$
952b2o\$951bobo\$953bo21\$929b3o\$931bo\$930bo5\$922b2o\$921bobo\$923bo6\$914b
3o\$916bo\$915bo5\$907b2o\$906bobo\$908bo6\$899b3o\$901bo\$900bo5\$892b2o\$891bo
bo\$893bo6\$884b3o\$886bo\$885bo5\$877b2o\$876bobo\$878bo6\$869b3o\$871bo\$870bo
5\$862b2o\$861bobo\$863bo6\$854b3o\$856bo\$855bo5\$847b2o\$846bobo\$848bo6\$839b
3o\$841bo\$840bo5\$832b2o\$831bobo\$833bo6\$824b3o\$826bo\$825bo5\$817b2o\$816bo
bo\$818bo6\$809b3o\$811bo\$810bo5\$802b2o\$801bobo\$803bo6\$794b3o\$796bo\$795bo
5\$787b2o\$786bobo\$788bo6\$779b3o\$781bo\$780bo569b2o\$1350b2o4\$772b2o\$771bo
bo576b3o\$773bo576b3o\$1349bo3bo2\$1348b2o3b2o3\$764b3o\$766bo\$765bo582b3o\$
1352b2o\$1352b2o\$1353b2o\$1351bobo\$757b2o592b2o\$756bobo616bo\$758bo616bob
o\$1346b2o3b2o25b2o6b2o\$1346b2o3b2o11b2o12b2o4bo3bo\$1358bo5b2o12b2o3bo
5bo8b2o\$1348b3o8b2o14bobo4b2obo3bo8b2o\$1348b3o7b2o15bo7bo5bo\$749b3o
597bo34bo3bo\$751bo634b2o\$750bo625bo\$1374b2o\$1375b2o\$1365bobo\$1349b2o
15b2o\$742b2o605b2o15bo\$741bobo\$743bo625b2o\$1369b2o5\$734b3o\$736bo\$735bo
625bo\$1359b2o\$1360b2o3\$727b2o\$726bobo\$728bo6\$719b3o\$721bo\$720bo625bo\$
1344b2o\$1345b2o3\$712b2o\$711bobo\$713bo6\$704b3o\$706bo\$705bo625bo\$1329b2o
\$1330b2o3\$697b2o\$696bobo\$698bo6\$689b3o\$691bo\$690bo625bo\$1314b2o\$1315b
2o3\$682b2o\$681bobo\$683bo6\$674b3o\$676bo\$675bo625bo\$1299b2o\$1300b2o3\$
667b2o\$666bobo\$668bo6\$659b3o\$661bo\$660bo625bo\$1284b2o\$1285b2o3\$652b2o\$
651bobo\$653bo3\$630b2o\$630b2o\$1642b2o\$644b3o995b2o\$646bo\$645bo625bo\$
1269b2o\$1270b2o371bo\$1642b3o\$1641bo3bo\$637b2o1001bob3obo\$636bobo1002b
5o\$627b2o3b2o4bo\$629b3o\$628bo3bo\$629bobo340b2o\$630bo341b2o\$1640b2o2bo\$
631b3o1008bobo\$631b3o1010b2o\$1256bo388b2o\$1254b2o387bob2o\$1255b2o386b
3o\$629b2o3b2o1033bo\$630b5o1033bobo\$631b3o1004b2o3b2o23b2obo7b2o\$632bo
1008bo14b2o10b2ob2o6bobo\$971b5o662bo5bo11b2o10b2obob3o6bo7b2o\$970bob3o
bo662b2ob2o6bobo15bobo2bo2bo2bo2bo7b2o\$971bo3bo664bobo8b2o16bo4b2o6bo\$
972b3o666bo9bo27bobo\$973bo667bo37b2o2\$1666bobo\$631b2o1033b2o\$631b2o
338bo269bo416bo8bo\$971bo22bo244b2o400b2o16b2o\$970bobo5bo14bobo244b2o
399b2o15b2o\$969b2ob2o2bobo13bob2o15b2o\$968bo5bo2b2o7b2o3b2ob2o14bobo
648b2o\$971bo14b2o4bob2o13bo6b2o2b2o639b2o\$968b2o3b2o18bobo13bo2bo2bo2b
ob2o\$994bo5bo8bo6b2o\$1000bobo7bobo\$970bo14bo14b2o9b2o\$970bo15bo\$969bo
14b3o2\$1494b2o155bobo\$971b2o494b2o24b2o156b2o\$971b2o253bo241b2o25bo
156bo\$1224b2o241bo\$991b2o232b2o\$991b2o2\$1501b2o\$1501b2o\$985bo\$985bobo
493b2o\$985b2o494b2o\$1496bo\$1496b2o\$1495bobo\$1509b2o125bobo\$1452b2o54b
2o10bobo113b2o\$1211bo241b2o55bo8bo2bo4bo109bo\$1209b2o241bo52b2o11b2o5b
2o\$1210b2o293bobo8b2o3bo8b2o\$1488b2o6b2o2b2o6bo9b2o10b2o\$1489b2o5b2obo
2bo2bo2bo10bo2bo\$1479b5o4bo11b2o6bo11bobo\$1478bob3obo20bobo\$970bo508bo
3bo21b2o\$970bobo507b3o\$970b2o509bo\$1482b2o\$1482bobo\$1482bobo\$1483bo
137bobo\$1437b2o182b2o\$1196bo241b2o182bo\$1194b2o241bo42b2obob2o\$1195b2o
283bo5bo\$1481bo3bo\$1482b3o3\$955bo\$955bobo\$955b2o3\$1482b2o\$1482b2o122bo
bo\$1422b2o182b2o\$1423b2o182bo\$1196b2o224bo\$1195b2o\$1197bo3\$1197b2o\$
940bo238b2o17b2o\$940bobo236b2o16bo6bo\$940b2o261b2o\$1203bobo2\$1179bo\$
1178bobo9bo26b2o372bobo\$1177bo3bo8b2o18bob2o3b3o187b2o182b2o\$1178b3o8b
obo14bo2bo3bo5b2obo185b2o182bo\$1176b2o3b2o22b2o2bo4bo4bo2bo5b2o177bo\$
1194b2o8b2o5b4o4b2obo5b2o\$1194b2o7b3o7bo3b3o\$1204b2o11b2o\$1205b2o\$
1182b2o22bo\$925bo257b2o\$925bobo254bo\$925b2o4\$1576bobo\$1392b2o182b2o\$
1181bo211b2o182bo\$1180b3o209bo\$1179b5o\$1178b2o3b2o4\$910bo269b3o\$910bob
o267b3o\$910b2o2\$1180b2o\$1180b2o\$1561bobo\$1377b2o182b2o\$1378b2o182bo\$
1377bo4\$597b2o\$597b2o128b2o\$518bobo206b2o166bo\$513bo4bo2bo373bobo\$514b
2o5b2o8bo363b2o\$509b2o8bo3b2o5bobo66b2o\$509b2o10b2o6bob2o10b2o\$518bo2b
o6b2ob2o10b2o\$518bobo8bob2o1013bobo\$530bobo829b2o182b2o\$521bo9bo63b2o
3b2o761b2o182bo\$520bo75b5o123b2obob2o631bo\$520b3o73b2ob2o\$596b2ob2o
123bo5bo\$597b3o\$725b2ob2o\$727bo\$880bo\$513bo366bobo\$513bobo364b2o\$513b
2o\$602bo\$596bo3bobo121bo\$595b3o3b2o119b2o4b3o800bobo\$594b5o124b2o2bo3b
o615b2o182b2o\$506bo4b3o79bobobobo748b2o182bo\$505bo5bo81b2o3b2o126bo5bo
614bo\$505b3o4bo213b2o3b2o2\$596bo12b2o\$595bobo11b2o104b2o12bo\$595bobo
117b2o11bobo\$596bo131bobo134bo\$596b2o132bo134bobo\$596b2o5b3o115bo8bo
134b2o\$596b2o7bo114b2o5bo2bo\$604bo12bo102bobo5b2o\$615bobo91bo\$616b2o
89b2o807bobo\$708b2o622b2o182b2o\$491bo34b3o804b2o182bo\$490bo35bo69b2o
734bo\$490b3o34bo67bobo130b2o\$597bo129b2o\$729bo\$583b2o\$582bobo156b2o\$
581b3o4b2o4bo146bo2bo105bo\$572b2o6b3o4bo2b2obobo135bo3b3o7bo104bobo\$
572b2o7b3o4b3obo3bo9b2o122b5o3bo6bo6b2o96b2o\$582bobo4b2obo3bo9b2o110b
2o9b2ob2o3bo7bo6b2o\$583b2o6b2o3bo35bo85b2o8b3ob2o3bo3bo2bo\$593bobo34bo
bo61bo34b2ob4o5b2o\$594bo36b2o59b2o36b4o767bobo\$693b2o36bo585b2o182b2o\$
476bo64b3o774b2o182bo\$475bo65bo775bo\$475b3o64bo5\$835bo\$835bobo\$835b2o
2\$647bo\$645bobo31bo\$646b2o29b2o807bobo\$678b2o622b2o182b2o\$461bo94b3o
744b2o182bo\$460bo95bo745bo\$460b3o94bo5\$820bo\$820bobo\$820b2o3\$660bo2bo\$
660bo4bo805bobo\$661bo3bo621b2o182b2o\$446bo124b3o714b2o182bo\$445bo125bo
715bo\$445b3o124bo5\$805bo\$805bobo\$805b2o4\$1456bobo\$1272b2o182b2o\$431bo
154b3o684b2o182bo\$430bo155bo685bo\$430b3o154bo5\$790bo\$790bobo\$790b2o4\$
1441bobo\$1257b2o182b2o\$416bo184b3o654b2o182bo\$415bo185bo655bo\$415b3o
184bo5\$775bo\$775bobo\$775b2o4\$1426bobo\$1242b2o182b2o\$401bo214b3o624b2o
182bo\$400bo215bo625bo\$400b3o214bo5\$760bo\$760bobo\$760b2o4\$1411bobo\$
1227b2o182b2o\$386bo244b3o594b2o182bo\$385bo245bo595bo\$385b3o244bo5\$745b
o\$745bobo\$745b2o4\$1396bobo\$1212b2o182b2o\$371bo274b3o316bo247b2o182bo\$
370bo275bo318b2o245bo\$370b3o274bo316bobo2\$746b2o228b2o\$746bobo227bobo\$
746bo229bo228bo\$1205b2o20bo\$1204bobo19b2o\$1226bobo4\$755b2o228b2o394bob
o\$755b2o228b2o210b2o182b2o\$356bo304b3o286bo247b2o182bo\$355bo305bo73b2o
213b2o13b2o230bo\$355b3o304bo72b2o14b3o195bobo13b2o14b3o252b2o\$753bo
229bo252b2o\$752bo8b2o219bo8b2o\$761bobo227bobo222b2o15b2o\$761bo229bo
198bo25b2o16b2o\$669b2o101bo229bo187b2o41bo8bo\$669b2o99b4o226b4o185bobo
49b2o\$734b3o7b2o14bobo6bobob2o189b3o7b2o14bobo6bobob2o236bobo\$649b2o
82bo3bo5bobo14bo3bo3bo2bob3o8b2o177bo3bo5bobo14bo3bo3bo2bob3o8b2o\$649b
2o94bo4b2o12bo4bobob2o9b2o189bo4b2o12bo4bobob2o9b2o200bo37b2o\$664b2o
66bo5bo11b2o8bo4bo4b4o188bo5bo11b2o8bo4bo4b4o212bo9bo27bobo\$663bobo66b
2o3b2o25bo7bo189b2o3b2o25bo7bo212bobo8b2o16bo4b2o6bo108bobo\$665bo94bo
3bo225bo3bo187b2o30b2ob2o6bobo15bobo2bo2bo2bo2bo7b2o99b2o\$676b3o81bobo
172bo54bobo190b2o28bo5bo11b2o10b2obob3o6bo7b2o100bo\$676bo12bo47b2o196b
2o30b2o213bo33bo14b2o10b2ob2o6bobo\$677bo8b4o4bo42bobo194bobo30bobo243b
2o3b2o23b2obo7b2o\$673b2o10b4o5bo44bo229bo273bobo\$673bobo9bo2bo9b2o38b
2o228b2o274bo\$656b3o5b3ob2o4b3o8b4o9b2o35bo229bo252b3o\$648b3o7bo5b4o2b
o4b3o8b4o45bo2bo226bo2bo206bo42bob2o\$647bo3bo5bo10b2o4b3o12bo45bo229bo
209b2o43b2o\$646bo5bo20bobo498bobo42b2o\$647bo3bo21b2o542bobo\$359bo288b
3o83b2obob2o223b2obob2o244b2o2bo\$358b2o288bo2bo\$358bobo288b3o82bo5bo
223bo5bo\$649b2obo698bobo\$650bobo82b2ob2o225b2ob2o197b2o182b2o\$651bo85b
o182bo46bo200b2o182bo\$920b2o245bo48b5o\$919bobo293bob3obo\$648b2o3b2o
561bo3bo\$648bobobobo562b3o\$649b5o82b2o228b2o250bo\$650b3o83b2o228b2o
192bo\$651bo508b2o\$1159bobo\$1217b2o\$374bo842b2o\$373b2o\$373bobo\$1336bobo
\$650b2o500b2o182b2o\$650b2o253bo247b2o182bo\$905b2o245bo\$904bobo4\$1145bo
\$1145b2o\$1144bobo2\$389bo\$388b2o\$388bobo\$1321bobo\$1137b2o182b2o\$890bo
247b2o182bo\$890b2o245bo\$889bobo4\$1130bo\$1130b2o\$1129bobo2\$404bo\$403b2o
\$403bobo1026bo\$1306bobo120b4o4bo\$1122b2o182b2o112bo7b4o5bo\$281bo593bo
247b2o182bo111bobo6bo2bo9b2o\$280bo594b2o245bo284b2o9bo3b2o4b4o9b2o\$
280b3o591bobo530b2o9bo3b2o5b4o\$1418bo3b2o8bo\$1419bobo\$1420bo\$1115bo
313bobo\$1115b2o313b2o\$273bo840bobo313bo\$273bobo\$273b2o144bo\$418b2o\$
418bobo\$1291bobo143bo\$1107b2o182b2o145b2o\$860bo247b2o182bo144b2o\$860b
2o245bo\$859bobo4\$1100bo343bobo\$1100b2o343b2o\$258bo840bobo343bo\$258bobo
\$258b2o174bo644b2o\$433b2o642bo2bo\$433bobo\$1076bo199bobo173bo\$1092b2o
182b2o175b2o\$845bo231b2o14b2o182bo174b2o\$845b2o232bo12bo\$844bobo2\$
1076b2o3b2o\$1076b2o3b2o\$1077b5o3bo\$1078bobo4b2o\$1084bobo\$1078b3o\$449bo
\$448b2o\$448bobo\$1261bobo203bo\$1081bo179b2o205b2o\$553b2o275bo249bobo
179bo204b2o\$553b2o128b2o145b2o247bo3bo\$553b2o127bo2bo143bobo248b3o\$
554bo127bo395b2o3b2o\$553bobo126bo761bo\$553bobo126bobo759b2o\$554bo127bo
bo758bobo\$683bo2\$551b2o3b2o\$464bo86bobobobo122b2o3b2o\$463b2o87b5o123bo
5bo\$463bobo87b3o\$554bo126bo3bo560bobo233bo\$682b3o395b2o164b2o235b2o\$
815bo264b2o165bo234b2o\$815b2o\$814bobo2\$1429bo\$555bobo871b2o\$556b2o122b
o747bobo\$556bo123bobo\$680b2o2\$479bo71b3o131bo\$478b2o70bo3bo129b3o\$478b
obo68bo5bo7bo119b5o\$550bo3bo9b2o107bo8b2o3b2o542bobo263bo\$551b3o9b2o
107bo10b5o543b2o265b2o\$551b3o118b3o8bo3bo112bo431bo264b2o\$684bobo113b
2o\$685bo113bobo2\$552b2o860bo\$552b2o4b2o124b2o728b2o\$559b2o116b3o4b2o
727bobo\$558bo118bo\$678bo2\$494bo\$493b2o\$493bobo55bo26bo\$551b2o26b2o77bo
26b2o529bobo\$550bobo25b2o77bo27bobo528b2o\$541bo115b3o25bo99bo431bo295b
2o\$540bobo153bo88b2o726bo\$539bo3b2o8bo140b4o86bobo727b3o\$528b2o9bo3b2o
5b4o130bobo6bobob2o817bo\$528b2o9bo3b2o4b4o9b2o120bo3bo3bo2bob3o8b2o
689bo\$540bobo6bo2bo9b2o110b2o12bo4bobob2o9b2o689b2o\$541bo7b4o5bo115b2o
8bo4bo4b4o700bobo\$550b4o4bo129bo7bo\$553bo130bo3bo\$684bobo\$509bo265b2o\$
508b2o265b2o\$508bobo82bo\$594b2o47bo134b2o15b2o404bobo\$593b2o47bo134b2o
16b2o404b2o\$642b3o125bo8bo422bo\$770b2o\$769bobo2\$757b2o37bo587bo\$756bob
o27bo9bo587b2o\$755bo6b2o4bo16b2o8bobo585bobo\$746b2o7bo2bo2bo2bo2bobo
15bobo6b2ob2o\$746b2o7bo6b3obob2o10b2o11bo5bo\$756bobo6b2ob2o10b2o14bo\$
524bo232b2o7bob2o23b2o3b2o\$523b2o242bobo\$523bobo82bo159bo\$609b2o17bo
163b3o391bobo\$608b2o17bo163b2obo391b2o\$627b3o161b2o394bo\$792b2o\$793bob
o\$793bo2b2o\$1369bo\$983bo385b2o\$983bobo382bobo\$986b2o6b2o\$972b2o12b2o4b
o3bo\$792b5o175b2o12b2o3bo5bo8b2o\$539bo251bob3obo185bobo4b2obo3bo8b2o\$
538b2o252bo3bo186bo7bo5bo\$538bobo252b3o196bo3bo\$794bo199b2o175bobo\$
984bo186b2o\$982b2o188bo\$983b2o\$794b2o\$794b2o\$1354bo\$1354b2o\$1353bobo\$
975bobo\$975b2o\$976bo\$554bo\$553b2o\$553bobo\$1156bobo\$969bo186b2o\$967b2o
188bo\$968b2o3\$1339bo\$1339b2o\$1338bobo\$960bobo\$960b2o\$961bo\$569bo\$568b
2o\$568bobo\$1141bobo\$954bo186b2o\$952b2o188bo\$953b2o2\$o\$3o1321bo\$3bo
1320b2o\$2b2o1319bobo\$945bobo\$945b2o\$946bo\$584bo\$583b2o\$583bobo\$9b3o
1114bobo\$9bo929bo186b2o\$10bo926b2o188bo\$938b2o\$590b2o\$590b2o\$1309bo\$
17b2o551b2o737b2o\$17bobo550b2o736bobo\$17bo912bobo\$584b2o344b2o\$585b2o
344bo\$584bo14bo\$598b2o10b2o\$598bobo9b2o4b3o\$24b3o566b2o12b2o6b5o491bob
o\$24bo566bo3bo10b3o5bo3bobo303bo186b2o\$25bo551bo7b2o3bo5bo10b2o6bo3b2o
301b2o188bo\$567b2o3b2o3b2o6b2o2b2obo3bo13b2o311b2o\$576bobo11bo5bo13b2o
\$568bo3bo18bo3bo\$569b3o21b2o699bo\$32b2o535b3o722b2o\$32bobo1258bobo\$32b
o\$572bo123b2o\$571b3o121b2o\$570bo3bo94b2o26bo\$572bo97b2o\$569bo5bo93bo\$
39b3o527bo5bo123b2o395bobo\$39bo530bo3bo125b2o207bo19bo166b2o\$40bo530b
3o106b2o17bo4bo202b2o19b2o167bo310bo\$680b2o21b2o203b2o18bobo477bobo\$
703bobo705b2o6b2o\$1397b2o12b2o4bo3bo\$680bo598bo117b2o12b2o3bo5bo8b2o\$
47b2o630b3o10bo586b2o127bobo4b2obo3bo8b2o\$47bobo628bo3bo9b2o18bo7bo
557bobo127bo7bo5bo\$47bo632bo10bobo17b4o5bobo694bo3bo\$677bo5bo22b2o2bo
2b2o8b2o694b2o\$571b2o104bo5bo22b2o2b2o11b2o4b2o207b2o469bo\$571b2o81b2o
22bo3bo12b2o6b2o10bo7b2o4b2o207b2o467b2o\$655b2o22b3o13b2o5b3o10bo4bobo
685b2o\$654bo48b2o10bo4bo197b2o15b2o\$54b3o627b2o20b2o210b2o16b2o143bobo
\$54bo630b2o19b2o186bo40bo8bo136b2o\$55bo628bo207b2o49b2o137bo\$893b2o48b
obo\$1400bobo\$918bo37b2o442b2o\$918bo9bo27bobo305bo136bo\$62b2o853bobo8b
2o16bo4b2o6bo304b2o\$62bobo617bo233b2ob2o6bobo15bobo2bo2bo2bo2bo7b2o
294bobo\$62bo618b3o231bo5bo11b2o10b2obob3o6bo7b2o\$681b3o234bo14b2o10b2o
b2o6bobo\$915b2o3b2o23b2obo7b2o436bo\$639b2o38b2o3b2o259bobo444b2o\$640b
2o37b2o3b2o260bo446b2o\$639bo280b3o\$69b3o848bob2o142bobo\$69bo612bo196bo
42b2o142b2o\$70bo610bobo193b2o42b2o144bo\$683b2o193b2o39bobo\$683b2o232b
2o2bo463bobo\$682b3o700b2o\$681bobo565bo136bo\$77b2o602b2o566b2o\$77bobo
1168bobo\$77bo\$918b5o\$917bob3obo455bo\$624b2o292bo3bo454b2o\$625b2o292b3o
456b2o\$624bo295bo\$84b3o964bobo\$84bo779bo186b2o\$85bo776b2o188bo\$97bo
765b2o54b2o\$97b2o820b2o449bobo\$86bo5b2o4b2o1270b2o\$86bobo3b2o4b3o7b2o
1124bo136bo\$74b2o11bobo2b2o4b2o8b2o1124b2o\$74b2o11bo2bo6b2o1134bobo\$
87bobo7bo\$86bobo\$86bo1277bo\$609b2o751b2o\$610b2o751b2o\$609bo\$1036bobo\$
849bo186b2o\$847b2o188bo\$848b2o\$1355bobo\$1355b2o\$1219bo136bo\$1219b2o\$
1218bobo3\$1349bo\$594b2o751b2o\$595b2o751b2o\$594bo\$1021bobo\$834bo186b2o\$
832b2o188bo\$833b2o3\$1204bo\$1204b2o\$1203bobo3\$1334bo22bo\$579b2o751b2o
22b2o\$580b2o751b2o21bobo\$579bo\$1006bobo\$819bo186b2o\$817b2o188bo\$818b2o
3\$1189bo\$1189b2o\$1188bobo3\$1319bo52bo\$564b2o751b2o52b2o\$565b2o751b2o
51bobo\$564bo\$991bobo\$804bo186b2o377bo\$802b2o188bo377b2o\$803b2o564bobo\$
1379b2o\$1378b2o\$1174bo205bo\$1174b2o\$1173bobo\$1362b2o\$1363b2o\$1304bo57b
o24bo\$549b2o751b2o82b2o\$550b2o751b2o81bobo\$549bo\$976bobo\$789bo186b2o
377bo\$787b2o188bo377b2o\$788b2o564bobo49bo\$1393b2o2b2o6b4o\$1388bobo2bob
4o5b2obobo\$540b2o617bo226bo3bo3bob2o5b3obo2bo2b2o\$540b2o617b2o218b2o5b
o12bo4b2obobo3b2o\$1158bobo218b2o4bo4bo14b4o\$544bo15b2o785b2o37bo19bo\$
543b2o15b2o786b2o36bo3bo\$543bobo743bo57bo40bobo\$534b2o751b2o\$535b2o
751b2o\$534bo\$523b2o436bobo365bo9b2o\$522bo3bo34bo212bo186b2o365bobo7b4o
\$521bo5bo7bo15b2o7b3o209b2o188bo364bob2o5b3o2bo2bobo\$511b2o8bo3bob2o4b
obo14b2o8b3o210b2o546b2o3b2ob2o9b2o2bo2bo\$511b2o8bo5bo3b2o12b2o5bo768b
2o4bob2o6bo9b2o6b2o\$522bo3bo4b2o12b2o11b2o3b2o763bobo5bo8bo3b2o4b2o\$
523b2o6b2o25b2o3b2o579bo184bo6bo10b2o\$533bobo608b2o198bo2bo\$535bo607bo
bo198bobo\$558b2o\$557bobo\$556b2o716bo\$557b2o713b2o\$557b2o714b2o\$560b3o\$
946bobo\$759bo186b2o\$757b2o188bo\$758b2o\$556b2o3b2o2\$557bo3bo567bo\$558b
3o568b2o\$558b3o567bobo3\$1259bo\$1257b2o\$559b2o697b2o\$559b2o\$931bobo\$
744bo186b2o\$742b2o188bo\$743b2o3\$1114bo\$1114b2o\$1113bobo3\$1244bo\$1242b
2o\$1243b2o2\$916bobo\$729bo186b2o\$727b2o188bo\$728b2o3\$1099bo\$1099b2o\$
1098bobo7\$901bobo\$714bo186b2o338b2o\$712b2o188bo337b2o\$713b2o527bo3\$
1084bo\$1084b2o\$1083bobo7\$886bobo\$699bo186b2o186b2o180b2o\$697b2o188bo
186b2o179b2o\$698b2o557bo\$1077b2o15b2o\$1076b2o16b2o\$1069bo8bo178b2o\$
1069b2o187b2o\$1068bobo186bo6bo\$1263b2o\$1056b2o37bo167bobo\$1055bobo27bo
9bo\$1054bo6b2o4bo16b2o8bobo\$1045b2o7bo2bo2bo2bo2bobo15bobo6b2ob2o152bo
\$1045b2o7bo6b3obob2o10b2o11bo5bo151b2o\$871bobo181bobo6b2ob2o10b2o14bo
153bobo\$684bo186b2o183b2o7bob2o23b2o3b2o172b2o\$682b2o188bo193bobo201b
2o\$683b2o382bo204bo\$1091b3o\$1090b2obo\$1090b2o150b2o\$1091b2o150b2o\$
1092bobo147bo36bo\$1092bo2b2o181b2o10b2o\$1278bobo9b2o4b3o\$1273b2o12b2o
6b5o\$1271bo3bo10b3o5bo3bobo\$684b2o549bo29b2o3bo5bo10b2o6bo3b2o\$683b2o
550b2o28b2o2b2obo3bo13b2o\$685bo170bobo232b5o138bobo33bo5bo13b2o\$856b2o
232bob3obo174bo3bo\$857bo233bo3bo177b2o\$1092b3o\$1093bo2\$1216b2o9b2o\$
693b2o521bobo9b2o\$693b2o398b2o116b2o4b3o7bo6bo\$1093b2o112b4o2bo4b3o12b
obo\$673b2o15bo516b3ob2o4b3o12bo3b2o3b2o\$673b2o15b2o524bobo13bo3b2o3b2o
\$689bobo524b2o14bo3b2o\$699b2o532bobo\$698b2o534bo\$700bo140bobo\$710b2o
129b2o\$673bo34bo3bo129bo\$672b3o7b2o15bo7bo5bo\$672b3o8b2o14bobo4b2obo3b
o8b2o\$682bo5b2o12b2o3bo5bo8b2o\$670b2o3b2o11b2o12b2o4bo3bo\$670b2o3b2o
25b2o6b2o\$699bobo\$699bo\$675b2o\$675bobo\$677b2o\$676b2o\$676b2o\$672b3o151b
obo\$826b2o\$827bo3\$672b2o3b2o2\$673bo3bo\$674b3o\$674b3o5\$674b2o\$674b2o
135bobo\$811b2o\$812bo13\$796bobo\$796b2o\$797bo13\$781bobo\$781b2o\$782bo13\$
766bobo\$766b2o\$767bo13\$751bobo\$751b2o\$752bo13\$736bobo\$736b2o\$737bo4\$
652bo\$651bobo\$641b2o7bob2o\$640bobo6b2ob2o10b2o\$630b2o7bo6b3obob2o10b2o
\$630b2o7bo2bo2bo2bo2bobo\$639bo6b2o4bo\$640bobo\$641b2o\$721bobo\$653bobo
65b2o\$654b2o66bo\$654bo5\$661bo\$662b2o\$661b2o5\$706bobo\$668bobo35b2o\$669b
2o36bo\$669bo5\$676bo\$677b2o\$676b2o5\$691bobo\$683bobo5b2o\$684b2o6bo\$684bo
5\$691bo\$692b2o\$691b2o13\$706bo\$707b2o\$706b2o13\$721bo\$722b2o\$721b2o14\$
736b2o\$736bo\$737b3o\$739bo!
``````
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dvgrn
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### Re: A new way of constructing?

fch wrote:Finding a timer path:
- In order to have full control over the gliders, gliders must be available on all 30 lines (any other line can be reached by delay in the streams). And in all 30 timings. (Any other timing can by reached by delay in the streams) So together there are 900 distict path's. I rerouted the gliders by b-hives to achieve the required path-length...
[Just to clear up a detail: "boat" is the standard term for the 5-cell "b-hive" that you're using as one-time glider turners. Beehives have six cells and rectangular symmetry.]
fch wrote:I have attached a gif demonstrating where I visualize how these replicators should populate the life-universe.
This starts out looking like a standard staggered replication spiral, very similar to the pattern produced by, e.g., Langton's Loops. How will the replication process be suppressed along the southwest edge, so that only half the plane is filled instead of the whole universe? Is this to prevent collisions between the fringe of active replicators and the discarded shells of old replicators, after one revolution?
fch wrote:Duplicate signal to identical and inverted signal
Here's the same pattern backed up by 6000 ticks to show where the input signal came from (many nearby lanes and timings would also work, of course):

Code: Select all

``````x = 1692, y = 1520, rule = B3/S23
1035bo\$1033bobo\$1024bo7bobo\$1023b2o6bo2bo11b2o\$1012b2o8b2o4b2o2bobo11b
2o\$1012b2o7b3o4b2o3bobo\$1022b2o4b2o5bo\$1023b2o\$1024bo\$1036bo\$1037bo\$
1035b3o6\$1044bo\$1042bobo\$1043b2o5\$1051bo\$1052bo\$1050b3o6\$1059bo\$1057bo
bo\$1058b2o10\$1057b2o\$1056bobo\$1058bo6\$1049b3o\$1051bo\$1050bo5\$1042b2o\$
1041bobo\$1043bo6\$1034b3o\$1036bo\$1035bo5\$1027b2o\$1026bobo\$1028bo6\$1019b
3o\$1021bo\$1020bo5\$1012b2o\$1011bobo\$1013bo2\$1118b2o\$1118bo\$1119b3o\$
1121bo\$1004b3o\$1006bo\$1005bo5\$997b2o\$996bobo\$998bo6\$989b3o\$991bo\$990bo
5\$982b2o\$981bobo\$983bo6\$974b3o\$976bo\$975bo5\$967b2o\$966bobo\$968bo6\$959b
3o\$961bo\$960bo5\$952b2o\$951bobo\$953bo6\$944b3o\$946bo\$945bo5\$937b2o\$936bo
bo\$938bo6\$929b3o\$931bo\$930bo5\$922b2o\$921bobo\$923bo6\$914b3o\$916bo\$915bo
5\$907b2o\$906bobo\$908bo6\$899b3o\$901bo\$900bo5\$892b2o\$891bobo\$893bo6\$884b
3o\$886bo\$885bo5\$877b2o\$876bobo\$878bo6\$869b3o\$871bo\$870bo5\$862b2o\$861bo
bo\$863bo6\$854b3o\$856bo\$855bo5\$847b2o\$846bobo\$848bo6\$839b3o\$841bo\$840bo
5\$832b2o\$831bobo\$833bo6\$824b3o\$826bo\$825bo5\$817b2o\$816bobo\$818bo6\$809b
3o\$811bo\$810bo5\$802b2o\$801bobo\$803bo6\$794b3o\$796bo\$795bo5\$787b2o\$786bo
bo\$788bo6\$779b3o\$781bo\$780bo569b2o\$1350b2o4\$772b2o\$771bobo576b3o\$773bo
576b3o\$1349bo3bo2\$1348b2o3b2o3\$764b3o\$766bo\$765bo582b3o\$1352b2o\$1352b
2o\$1353b2o\$1351bobo\$757b2o592b2o\$756bobo616bo\$758bo616bobo\$1346b2o3b2o
25b2o6b2o\$1346b2o3b2o11b2o12b2o4bo3bo\$1358bo5b2o12b2o3bo5bo8b2o\$1348b
3o8b2o14bobo4b2obo3bo8b2o\$1348b3o7b2o15bo7bo5bo\$749b3o597bo34bo3bo\$
751bo634b2o\$750bo625bo\$1374b2o\$1375b2o\$1365bobo\$1349b2o15b2o\$742b2o
605b2o15bo\$741bobo\$743bo625b2o\$1369b2o5\$734b3o\$736bo\$735bo625bo\$1359b
2o\$1360b2o3\$727b2o\$726bobo\$728bo6\$719b3o\$721bo\$720bo625bo\$1344b2o\$
1345b2o3\$712b2o\$711bobo\$713bo6\$704b3o\$706bo\$705bo625bo\$1329b2o\$1330b2o
3\$697b2o\$696bobo\$698bo6\$689b3o\$691bo\$690bo625bo\$1314b2o\$1315b2o3\$682b
2o\$681bobo\$683bo6\$674b3o\$676bo\$675bo625bo\$1299b2o\$1300b2o3\$667b2o\$666b
obo\$668bo6\$659b3o\$661bo\$660bo625bo\$1284b2o\$1285b2o3\$652b2o\$651bobo\$
653bo3\$630b2o\$630b2o\$1642b2o\$644b3o995b2o\$646bo\$645bo625bo\$1269b2o\$
1270b2o371bo\$1642b3o\$1641bo3bo\$637b2o1001bob3obo\$636bobo1002b5o\$627b2o
3b2o4bo\$629b3o\$628bo3bo\$629bobo340b2o\$630bo341b2o\$1640b2o2bo\$631b3o
1008bobo\$631b3o1010b2o\$1256bo388b2o\$1254b2o387bob2o\$1255b2o386b3o\$629b
2o3b2o1033bo\$630b5o1033bobo\$631b3o1004b2o3b2o23b2obo7b2o\$632bo1008bo
14b2o10b2ob2o6bobo\$971b5o662bo5bo11b2o10b2obob3o6bo7b2o\$970bob3obo662b
2ob2o6bobo15bobo2bo2bo2bo2bo7b2o\$971bo3bo664bobo8b2o16bo4b2o6bo\$972b3o
666bo9bo27bobo\$973bo667bo37b2o2\$1666bobo\$631b2o1033b2o\$631b2o338bo269b
o416bo8bo\$971bo22bo244b2o400b2o16b2o\$970bobo5bo14bobo244b2o399b2o15b2o
\$969b2ob2o2bobo13bob2o15b2o\$968bo5bo2b2o7b2o3b2ob2o14bobo648b2o\$971bo
14b2o4bob2o13bo6b2o2b2o639b2o\$968b2o3b2o18bobo13bo2bo2bo2bob2o\$994bo5b
o8bo6b2o\$1000bobo7bobo\$970bo14bo14b2o9b2o\$970bo15bo\$969bo14b3o2\$1494b
2o155bobo\$971b2o494b2o24b2o156b2o\$971b2o253bo241b2o25bo156bo\$1224b2o
241bo\$991b2o232b2o\$991b2o2\$1501b2o\$1501b2o\$985bo\$985bobo493b2o\$985b2o
494b2o\$1496bo\$1496b2o\$1495bobo\$1509b2o125bobo\$1452b2o54b2o10bobo113b2o
\$1211bo241b2o55bo8bo2bo4bo109bo\$1209b2o241bo52b2o11b2o5b2o\$1210b2o293b
obo8b2o3bo8b2o\$1488b2o6b2o2b2o6bo9b2o10b2o\$1489b2o5b2obo2bo2bo2bo10bo
2bo\$1479b5o4bo11b2o6bo11bobo\$1478bob3obo20bobo\$970bo508bo3bo21b2o\$970b
obo507b3o\$970b2o509bo\$1482b2o\$1482bobo\$1482bobo\$1483bo137bobo\$1437b2o
182b2o\$1196bo241b2o182bo\$1194b2o241bo42b2obob2o\$1195b2o283bo5bo\$1481bo
3bo\$1482b3o3\$955bo\$955bobo\$955b2o3\$1482b2o\$1482b2o122bobo\$1422b2o182b
2o\$1423b2o182bo\$1196b2o224bo\$1195b2o\$1197bo3\$1197b2o\$940bo238b2o17b2o\$
940bobo236b2o16bo6bo\$940b2o261b2o\$1203bobo2\$1179bo\$1178bobo9bo26b2o
372bobo\$1177bo3bo8b2o18bob2o3b3o187b2o182b2o\$1178b3o8bobo14bo2bo3bo5b
2obo185b2o182bo\$1176b2o3b2o22b2o2bo4bo4bo2bo5b2o177bo\$1194b2o8b2o5b4o
4b2obo5b2o\$1194b2o7b3o7bo3b3o\$1204b2o11b2o\$1205b2o\$1182b2o22bo\$925bo
257b2o\$925bobo254bo\$925b2o4\$1576bobo\$1392b2o182b2o\$1181bo211b2o182bo\$
1180b3o209bo\$1179b5o\$1178b2o3b2o4\$910bo269b3o\$910bobo267b3o\$910b2o2\$
1180b2o\$1180b2o\$1561bobo\$1377b2o182b2o\$1378b2o182bo\$1377bo4\$597b2o\$
597b2o128b2o\$518bobo206b2o166bo\$513bo4bo2bo373bobo\$514b2o5b2o8bo363b2o
\$509b2o8bo3b2o5bobo66b2o\$509b2o10b2o6bob2o10b2o\$518bo2bo6b2ob2o10b2o\$
518bobo8bob2o1013bobo\$530bobo829b2o182b2o\$521bo9bo63b2o3b2o761b2o182bo
\$520bo75b5o123b2obob2o631bo\$520b3o73b2ob2o\$596b2ob2o123bo5bo\$597b3o\$
725b2ob2o\$727bo\$880bo\$513bo366bobo\$513bobo364b2o\$513b2o\$602bo\$596bo3bo
bo121bo\$595b3o3b2o119b2o4b3o800bobo\$594b5o124b2o2bo3bo615b2o182b2o\$
506bo4b3o79bobobobo748b2o182bo\$505bo5bo81b2o3b2o126bo5bo614bo\$505b3o4b
o213b2o3b2o2\$596bo12b2o\$595bobo11b2o104b2o12bo\$595bobo117b2o11bobo\$
596bo131bobo134bo\$596b2o132bo134bobo\$596b2o5b3o115bo8bo134b2o\$596b2o7b
o114b2o5bo2bo\$604bo12bo102bobo5b2o\$615bobo91bo\$616b2o89b2o807bobo\$708b
2o622b2o182b2o\$491bo34b3o804b2o182bo\$490bo35bo69b2o734bo\$490b3o34bo67b
obo130b2o\$597bo129b2o\$729bo\$583b2o\$582bobo156b2o\$581b3o4b2o4bo146bo2bo
105bo\$572b2o6b3o4bo2b2obobo135bo3b3o7bo104bobo\$572b2o7b3o4b3obo3bo9b2o
122b5o3bo6bo6b2o96b2o\$582bobo4b2obo3bo9b2o110b2o9b2ob2o3bo7bo6b2o\$583b
2o6b2o3bo35bo85b2o8b3ob2o3bo3bo2bo\$593bobo34bobo61bo34b2ob4o5b2o\$594bo
36b2o59b2o36b4o767bobo\$693b2o36bo585b2o182b2o\$476bo64b3o774b2o182bo\$
475bo65bo775bo\$475b3o64bo5\$835bo\$835bobo\$835b2o2\$647bo\$645bobo31bo\$
646b2o29b2o807bobo\$678b2o622b2o182b2o\$461bo94b3o744b2o182bo\$460bo95bo
745bo\$460b3o94bo5\$820bo\$820bobo\$820b2o3\$660bo2bo\$660bo4bo805bobo\$661bo
3bo621b2o182b2o\$446bo124b3o714b2o182bo\$445bo125bo715bo\$445b3o124bo5\$
805bo\$805bobo\$805b2o4\$1456bobo\$1272b2o182b2o\$431bo154b3o684b2o182bo\$
430bo155bo685bo\$430b3o154bo5\$790bo\$790bobo\$790b2o4\$1441bobo\$1257b2o
182b2o\$416bo184b3o654b2o182bo\$415bo185bo655bo\$415b3o184bo5\$775bo\$775bo
bo\$775b2o4\$1426bobo\$1242b2o182b2o\$401bo214b3o624b2o182bo\$400bo215bo
625bo\$400b3o214bo5\$760bo\$760bobo\$760b2o4\$1411bobo\$1227b2o182b2o\$386bo
244b3o594b2o182bo\$385bo245bo595bo\$385b3o244bo5\$745bo\$745bobo\$745b2o4\$
1396bobo\$1212b2o182b2o\$371bo274b3o316bo247b2o182bo\$370bo275bo318b2o
245bo\$370b3o274bo316bobo2\$746b2o228b2o\$746bobo227bobo\$746bo229bo228bo\$
1205b2o20bo\$1204bobo19b2o\$1226bobo4\$755b2o228b2o394bobo\$755b2o228b2o
210b2o182b2o\$356bo304b3o286bo247b2o182bo\$355bo305bo73b2o213b2o13b2o
230bo\$355b3o304bo72b2o14b3o195bobo13b2o14b3o252b2o\$753bo229bo252b2o\$
752bo8b2o219bo8b2o\$761bobo227bobo222b2o15b2o\$761bo229bo198bo25b2o16b2o
\$669b2o101bo229bo187b2o41bo8bo\$669b2o99b4o226b4o185bobo49b2o\$734b3o7b
2o14bobo6bobob2o189b3o7b2o14bobo6bobob2o236bobo\$649b2o82bo3bo5bobo14bo
3bo3bo2bob3o8b2o177bo3bo5bobo14bo3bo3bo2bob3o8b2o\$649b2o94bo4b2o12bo4b
obob2o9b2o189bo4b2o12bo4bobob2o9b2o200bo37b2o\$664b2o66bo5bo11b2o8bo4bo
4b4o188bo5bo11b2o8bo4bo4b4o212bo9bo27bobo\$663bobo66b2o3b2o25bo7bo189b
2o3b2o25bo7bo212bobo8b2o16bo4b2o6bo108bobo\$665bo94bo3bo225bo3bo187b2o
30b2ob2o6bobo15bobo2bo2bo2bo2bo7b2o99b2o\$676b3o81bobo172bo54bobo190b2o
28bo5bo11b2o10b2obob3o6bo7b2o100bo\$676bo12bo47b2o196b2o30b2o213bo33bo
14b2o10b2ob2o6bobo\$677bo8b4o4bo42bobo194bobo30bobo243b2o3b2o23b2obo7b
2o\$673b2o10b4o5bo44bo229bo273bobo\$673bobo9bo2bo9b2o38b2o228b2o274bo\$
656b3o5b3ob2o4b3o8b4o9b2o35bo229bo252b3o\$648b3o7bo5b4o2bo4b3o8b4o45bo
2bo226bo2bo206bo42bob2o\$647bo3bo5bo10b2o4b3o12bo45bo229bo209b2o43b2o\$
646bo5bo20bobo498bobo42b2o\$647bo3bo21b2o542bobo\$359bo288b3o83b2obob2o
223b2obob2o244b2o2bo\$358b2o288bo2bo\$358bobo288b3o82bo5bo223bo5bo\$649b
2obo698bobo\$650bobo82b2ob2o225b2ob2o197b2o182b2o\$651bo85bo182bo46bo
200b2o182bo\$920b2o245bo48b5o\$919bobo293bob3obo\$648b2o3b2o561bo3bo\$648b
obobobo562b3o\$649b5o82b2o228b2o250bo\$650b3o83b2o228b2o192bo\$651bo508b
2o\$1159bobo\$1217b2o\$374bo842b2o\$373b2o\$373bobo\$1336bobo\$650b2o500b2o
182b2o\$650b2o253bo247b2o182bo\$905b2o245bo\$904bobo4\$1145bo\$1145b2o\$
1144bobo2\$389bo\$388b2o\$388bobo\$1321bobo\$1137b2o182b2o\$890bo247b2o182bo
\$890b2o245bo\$889bobo4\$1130bo\$1130b2o\$1129bobo2\$404bo\$403b2o\$403bobo
1026bo\$1306bobo120b4o4bo\$1122b2o182b2o112bo7b4o5bo\$875bo247b2o182bo
111bobo6bo2bo9b2o\$875b2o245bo284b2o9bo3b2o4b4o9b2o\$874bobo530b2o9bo3b
2o5b4o\$1418bo3b2o8bo\$1419bobo\$1420bo\$1115bo313bobo\$1115b2o313b2o\$1114b
obo313bo2\$419bo\$418b2o\$418bobo\$1291bobo143bo\$1107b2o182b2o145b2o\$860bo
247b2o182bo144b2o\$860b2o245bo\$859bobo4\$1100bo343bobo\$1100b2o343b2o\$
1099bobo343bo2\$434bo644b2o\$433b2o642bo2bo\$433bobo\$1076bo199bobo173bo\$
1092b2o182b2o175b2o\$845bo231b2o14b2o182bo174b2o\$845b2o232bo12bo\$844bob
o2\$1076b2o3b2o\$1076b2o3b2o\$1077b5o3bo\$1078bobo4b2o\$1084bobo\$1078b3o\$
449bo\$448b2o\$448bobo\$1261bobo203bo\$1081bo179b2o205b2o\$553b2o275bo249bo
bo179bo204b2o\$553b2o128b2o145b2o247bo3bo\$553b2o127bo2bo143bobo248b3o\$
554bo127bo395b2o3b2o\$553bobo126bo761bo\$553bobo126bobo759b2o\$554bo127bo
bo758bobo\$683bo2\$551b2o3b2o\$464bo86bobobobo122b2o3b2o\$463b2o87b5o123bo
5bo\$463bobo87b3o\$554bo126bo3bo560bobo233bo\$682b3o395b2o164b2o235b2o\$
815bo264b2o165bo234b2o\$815b2o\$814bobo2\$1429bo\$555bobo871b2o\$556b2o122b
o747bobo\$556bo123bobo\$680b2o2\$479bo71b3o131bo\$478b2o70bo3bo129b3o\$478b
obo68bo5bo7bo119b5o\$550bo3bo9b2o107bo8b2o3b2o542bobo263bo\$551b3o9b2o
107bo10b5o543b2o265b2o\$551b3o118b3o8bo3bo112bo431bo264b2o\$684bobo113b
2o\$685bo113bobo2\$552b2o860bo\$552b2o4b2o124b2o728b2o\$559b2o116b3o4b2o
727bobo\$558bo118bo\$678bo2\$494bo\$493b2o\$493bobo55bo26bo\$551b2o26b2o77bo
26b2o529bobo\$550bobo25b2o77bo27bobo528b2o\$541bo115b3o25bo99bo431bo295b
2o\$540bobo153bo88b2o726bo\$539bo3b2o8bo140b4o86bobo727b3o\$528b2o9bo3b2o
5b4o130bobo6bobob2o817bo\$528b2o9bo3b2o4b4o9b2o120bo3bo3bo2bob3o8b2o
689bo\$540bobo6bo2bo9b2o110b2o12bo4bobob2o9b2o689b2o\$541bo7b4o5bo115b2o
8bo4bo4b4o700bobo\$550b4o4bo129bo7bo\$553bo130bo3bo\$684bobo\$509bo265b2o\$
508b2o265b2o\$508bobo82bo\$594b2o47bo134b2o15b2o404bobo\$593b2o47bo134b2o
16b2o404b2o\$642b3o125bo8bo422bo\$770b2o\$769bobo2\$757b2o37bo587bo\$756bob
o27bo9bo587b2o\$755bo6b2o4bo16b2o8bobo585bobo\$746b2o7bo2bo2bo2bo2bobo
15bobo6b2ob2o\$746b2o7bo6b3obob2o10b2o11bo5bo\$756bobo6b2ob2o10b2o14bo\$
524bo232b2o7bob2o23b2o3b2o\$523b2o242bobo\$523bobo82bo159bo\$609b2o17bo
163b3o391bobo\$608b2o17bo163b2obo391b2o\$627b3o161b2o394bo\$792b2o\$793bob
o\$793bo2b2o\$1369bo\$983bo385b2o\$983bobo382bobo\$986b2o6b2o\$972b2o12b2o4b
o3bo\$792b5o175b2o12b2o3bo5bo8b2o\$539bo251bob3obo185bobo4b2obo3bo8b2o\$
538b2o252bo3bo186bo7bo5bo\$538bobo252b3o196bo3bo\$794bo199b2o175bobo\$
984bo186b2o\$982b2o188bo\$983b2o\$794b2o\$794b2o\$1354bo\$1354b2o\$1353bobo\$
975bobo\$975b2o\$976bo\$554bo\$553b2o\$553bobo\$1156bobo\$969bo186b2o\$967b2o
188bo\$968b2o3\$1339bo\$1339b2o\$1338bobo\$960bobo\$960b2o\$961bo\$569bo\$568b
2o\$568bobo\$1141bobo\$954bo186b2o\$952b2o188bo\$953b2o2\$o\$3o1321bo\$3bo
1320b2o\$2b2o1319bobo\$945bobo\$945b2o\$946bo\$584bo\$583b2o\$583bobo\$9b3o
1114bobo\$9bo929bo186b2o\$10bo926b2o188bo\$938b2o\$590b2o\$590b2o\$1309bo\$
17b2o551b2o737b2o\$17bobo550b2o736bobo\$17bo912bobo\$584b2o344b2o\$585b2o
344bo\$584bo14bo\$598b2o10b2o\$598bobo9b2o4b3o\$24b3o566b2o12b2o6b5o491bob
o\$24bo566bo3bo10b3o5bo3bobo303bo186b2o\$25bo551bo7b2o3bo5bo10b2o6bo3b2o
301b2o188bo\$567b2o3b2o3b2o6b2o2b2obo3bo13b2o311b2o\$576bobo11bo5bo13b2o
\$568bo3bo18bo3bo\$569b3o21b2o699bo\$32b2o535b3o722b2o\$32bobo1258bobo\$32b
o\$572bo123b2o\$571b3o121b2o\$570bo3bo94b2o26bo\$572bo97b2o\$569bo5bo93bo\$
39b3o527bo5bo123b2o395bobo\$39bo530bo3bo125b2o207bo19bo166b2o\$40bo530b
3o106b2o17bo4bo202b2o19b2o167bo310bo\$680b2o21b2o203b2o18bobo477bobo\$
703bobo705b2o6b2o\$1397b2o12b2o4bo3bo\$680bo598bo117b2o12b2o3bo5bo8b2o\$
47b2o630b3o10bo586b2o127bobo4b2obo3bo8b2o\$47bobo628bo3bo9b2o18bo7bo
557bobo127bo7bo5bo\$47bo632bo10bobo17b4o5bobo694bo3bo\$677bo5bo22b2o2bo
2b2o8b2o694b2o\$571b2o104bo5bo22b2o2b2o11b2o4b2o207b2o469bo\$571b2o81b2o
22bo3bo12b2o6b2o10bo7b2o4b2o207b2o467b2o\$655b2o22b3o13b2o5b3o10bo4bobo
685b2o\$654bo48b2o10bo4bo197b2o15b2o\$54b3o627b2o20b2o210b2o16b2o143bobo
\$54bo630b2o19b2o186bo40bo8bo136b2o\$55bo628bo207b2o49b2o137bo\$893b2o48b
obo\$1400bobo\$918bo37b2o442b2o\$918bo9bo27bobo305bo136bo\$62b2o853bobo8b
2o16bo4b2o6bo304b2o\$62bobo617bo233b2ob2o6bobo15bobo2bo2bo2bo2bo7b2o
294bobo\$62bo618b3o231bo5bo11b2o10b2obob3o6bo7b2o\$681b3o234bo14b2o10b2o
b2o6bobo\$915b2o3b2o23b2obo7b2o436bo\$639b2o38b2o3b2o259bobo444b2o\$640b
2o37b2o3b2o260bo446b2o\$639bo280b3o\$69b3o848bob2o142bobo\$69bo612bo196bo
42b2o142b2o\$70bo610bobo193b2o42b2o144bo\$683b2o193b2o39bobo\$683b2o232b
2o2bo463bobo\$682b3o700b2o\$681bobo565bo136bo\$77b2o602b2o566b2o\$77bobo
1168bobo\$77bo\$918b5o\$917bob3obo455bo\$624b2o292bo3bo454b2o\$625b2o292b3o
456b2o\$624bo295bo\$84b3o964bobo\$84bo779bo186b2o\$85bo776b2o188bo\$97bo
765b2o54b2o\$97b2o820b2o449bobo\$86bo5b2o4b2o1270b2o\$86bobo3b2o4b3o7b2o
1124bo136bo\$74b2o11bobo2b2o4b2o8b2o1124b2o\$74b2o11bo2bo6b2o1134bobo\$
87bobo7bo\$86bobo\$86bo1277bo\$609b2o751b2o\$610b2o751b2o\$609bo\$1036bobo\$
849bo186b2o\$847b2o188bo\$848b2o\$1355bobo\$1355b2o\$1219bo136bo\$1219b2o\$
1218bobo3\$1349bo\$594b2o751b2o\$595b2o751b2o\$594bo\$1021bobo\$834bo186b2o\$
832b2o188bo\$833b2o3\$1204bo\$1204b2o\$1203bobo3\$1334bo22bo\$579b2o751b2o
22b2o\$580b2o751b2o21bobo\$579bo\$1006bobo\$819bo186b2o\$817b2o188bo\$818b2o
3\$1189bo\$1189b2o\$1188bobo3\$1319bo52bo\$564b2o751b2o52b2o\$565b2o751b2o
51bobo\$564bo\$991bobo\$804bo186b2o377bo\$802b2o188bo377b2o\$803b2o564bobo\$
1379b2o\$1378b2o\$1174bo205bo\$1174b2o\$1173bobo\$1362b2o\$1363b2o\$1304bo57b
o24bo\$549b2o751b2o82b2o\$550b2o751b2o81bobo\$549bo\$976bobo\$789bo186b2o
377bo\$787b2o188bo377b2o\$788b2o564bobo49bo\$1393b2o2b2o6b4o\$1388bobo2bob
4o5b2obobo\$540b2o617bo226bo3bo3bob2o5b3obo2bo2b2o\$540b2o617b2o218b2o5b
o12bo4b2obobo3b2o\$1158bobo218b2o4bo4bo14b4o\$544bo15b2o785b2o37bo19bo\$
543b2o15b2o786b2o36bo3bo\$543bobo743bo57bo40bobo\$534b2o751b2o\$535b2o
751b2o\$534bo\$523b2o436bobo365bo9b2o\$522bo3bo34bo212bo186b2o365bobo7b4o
\$521bo5bo7bo15b2o7b3o209b2o188bo364bob2o5b3o2bo2bobo\$511b2o8bo3bob2o4b
obo14b2o8b3o210b2o546b2o3b2ob2o9b2o2bo2bo\$511b2o8bo5bo3b2o12b2o5bo768b
2o4bob2o6bo9b2o6b2o\$522bo3bo4b2o12b2o11b2o3b2o763bobo5bo8bo3b2o4b2o\$
523b2o6b2o25b2o3b2o579bo184bo6bo10b2o\$533bobo608b2o198bo2bo\$535bo607bo
bo198bobo\$558b2o\$557bobo\$556b2o716bo\$557b2o713b2o\$557b2o714b2o\$560b3o\$
946bobo\$759bo186b2o\$757b2o188bo\$758b2o\$556b2o3b2o2\$557bo3bo567bo\$558b
3o568b2o\$558b3o567bobo\$1503b3o\$1503bo\$1259bo244bo\$1257b2o\$559b2o697b2o
\$559b2o\$931bobo\$744bo186b2o\$742b2o188bo\$743b2o3\$1114bo\$1114b2o\$1113bob
o\$1518b3o\$1518bo\$1244bo274bo\$1242b2o\$1243b2o2\$916bobo\$729bo186b2o608b
2o\$727b2o188bo608bobo\$728b2o796bo3\$1099bo\$1099b2o\$1098bobo7\$901bobo\$
714bo186b2o338b2o\$712b2o188bo337b2o\$713b2o527bo3\$1084bo\$1084b2o\$1083bo
bo7\$886bobo\$699bo186b2o186b2o180b2o\$697b2o188bo186b2o179b2o\$698b2o557b
o\$1077b2o15b2o\$1076b2o16b2o\$1069bo8bo178b2o\$1069b2o187b2o\$1068bobo186b
o6bo\$1263b2o\$1056b2o37bo167bobo\$1055bobo27bo9bo\$1054bo6b2o4bo16b2o8bob
o\$1045b2o7bo2bo2bo2bo2bobo15bobo6b2ob2o152bo\$1045b2o7bo6b3obob2o10b2o
11bo5bo151b2o\$871bobo181bobo6b2ob2o10b2o14bo153bobo\$684bo186b2o183b2o
7bob2o23b2o3b2o172b2o\$682b2o188bo193bobo201b2o\$683b2o382bo204bo\$1091b
3o\$1090b2obo\$1090b2o150b2o\$1091b2o150b2o\$1092bobo147bo36bo\$1092bo2b2o
181b2o10b2o\$1278bobo9b2o4b3o\$1273b2o12b2o6b5o\$1271bo3bo10b3o5bo3bobo\$
684b2o549bo29b2o3bo5bo10b2o6bo3b2o\$683b2o550b2o28b2o2b2obo3bo13b2o\$
685bo170bobo232b5o138bobo33bo5bo13b2o\$856b2o232bob3obo174bo3bo\$857bo
233bo3bo177b2o\$1092b3o\$1093bo2\$1216b2o9b2o\$693b2o521bobo9b2o\$693b2o
398b2o116b2o4b3o7bo6bo\$1093b2o112b4o2bo4b3o12bobo\$673b2o15bo516b3ob2o
4b3o12bo3b2o3b2o\$673b2o15b2o524bobo13bo3b2o3b2o\$689bobo524b2o14bo3b2o\$
699b2o532bobo\$698b2o534bo\$700bo140bobo\$710b2o129b2o\$673bo34bo3bo129bo\$
672b3o7b2o15bo7bo5bo\$672b3o8b2o14bobo4b2obo3bo8b2o\$682bo5b2o12b2o3bo5b
o8b2o\$670b2o3b2o11b2o12b2o4bo3bo\$670b2o3b2o25b2o6b2o\$699bobo\$699bo\$
675b2o\$675bobo\$677b2o\$676b2o\$676b2o\$672b3o151bobo\$826b2o\$827bo3\$672b2o
3b2o2\$673bo3bo\$674b3o\$674b3o5\$674b2o\$674b2o135bobo\$811b2o\$812bo13\$796b
obo\$796b2o\$797bo13\$781bobo\$781b2o\$782bo13\$766bobo\$766b2o\$767bo13\$751bo
bo\$751b2o\$752bo13\$736bobo\$736b2o\$737bo4\$652bo\$651bobo\$641b2o7bob2o\$
640bobo6b2ob2o10b2o\$630b2o7bo6b3obob2o10b2o\$630b2o7bo2bo2bo2bo2bobo\$
639bo6b2o4bo\$640bobo\$641b2o\$721bobo\$653bobo65b2o\$654b2o66bo\$654bo5\$
661bo\$662b2o\$661b2o5\$706bobo\$668bobo35b2o\$669b2o36bo\$669bo5\$676bo\$677b
2o\$676b2o5\$691bobo\$683bobo5b2o\$684b2o6bo\$684bo5\$691bo\$692b2o\$691b2o13\$
706bo\$707b2o\$706b2o13\$721bo\$722b2o\$721b2o14\$736b2o\$736bo\$737b3o\$739bo!
``````
But what is the timing or phasing problem that's solved by all this p30 signal splitting and recombining? For some reason I've never paid much attention to p30 logic circuitry, so I don't know all the pitfalls. But it seems as if a minimal p30 signal duplicator ought to be easier to construct, and equally able to produce identical or inverted signals. What am I missing here?

Code: Select all

``````#C p30 signal duplicator from old p30 stream-crossing pattern
x = 49, y = 16, rule = B3/S23
5\$33b2o\$32bo3bo\$16b2o13bo5bo\$16b2o13bo3bob2o2b2o\$7b2o3bo6b2o10bo5bo3b
2o\$7bobo3bo5b3o10bo3bo\$8b5o6b2o12b2o\$9b3o4b2o9bobo\$16b2o10b2o\$28bo!
``````
I haven't figured out yet what the input signals are in this pattern, or the purpose of the switchable intermittent glider stream -- some kind of filter, it looks like? The two input gliders have very different fates: the first one changes the gap in the filter from short to long, and the second one is just absorbed by the filter before the first glider has any chance to affect that outcome. Can you rewind this pattern a few hundred ticks and explain a little more what is happening here?

Thanks --

DaveG

fch
Posts: 4
Joined: March 22nd, 2011, 2:07 pm

### Re: A new way of constructing?

I haven't figured out yet what the input signals are in this pattern, or the purpose of the switchable intermittent glider stream -- some kind of filter, it looks like? The two input gliders have very different fates: the first one changes the gap in the filter from short to long, and the second one is just absorbed by the filter before the first glider has any chance to affect that outcome. Can you rewind this pattern a few hundred ticks and explain a little more what is happening here?
The idea is to have a multiple series of gliders (100000+). Each serie starting with a vew gliders controlling the cicuitry. The first gliders should control the gates to open/close. (Similar to an opcode) The rest of the serie is outputed through the gates.
The pattern given shows a swich to the upper left. A single glider can turn the swith on or off.
A clock is shown to the bottom right producing a glider each n generations. (equal to the time of a serie to pass)
There are 2 gliders coming from the left bottom (duplicated signal) the first glider intercepts the glider coming from the clock. By doing so controling the switch to go on or off (opcode). The second one (data) intercepts a glider from the switch and so modulating the stream.
But what is the timing or phasing problem that's solved by all this p30 signal splitting and recombining? For some reason I've never paid much attention to p30 logic circuitry, so I don't know all the pitfalls. But it seems as if a minimal p30 signal duplicator ought to be easier to construct, and equally able to produce identical or inverted signals. What am I missing here?
You are not missing anything. I am looking for a small p30 signal duplicator (in terms of number of gliders needed for construction). This is what I have made myself.
This starts out looking like a standard staggered replication spiral, very similar to the pattern produced by, e.g., Langton's Loops. How will the replication process be suppressed along the southwest edge, so that only half the plane is filled instead of the whole universe? Is this to prevent collisions between the fringe of active replicators and the discarded shells of old replicators, after one revolution?
Yes it is to prevent collisions. The idea behind preventing collissions is to have a little knowledge of the parent being build to the left or to the right. just 2 bits are enough to decide if a child to the left and-or a child to the right must be build.

[Just to clear up a detail: "boat" is the standard term for the 5-cell "b-hive" that you're using as one-time glider turners. Beehives have six cells and rectangular symmetry.]
Thanks. I´ll use that term.

fch
Posts: 4
Joined: March 22nd, 2011, 2:07 pm

### Re: A new way of constructing?

I found parts to improve my design on this forum:

The signal duplicator (What an improvement over my design!)

Code: Select all

``````#CXRLE Pos=22,21 Gen=85
x = 102, y = 101, rule = B3/S23
o\$b2o\$2o6\$7bobo\$8b2o\$8bo13\$22bobo\$23b2o\$23bo5\$30bo\$31b2o\$30b2o21\$52bob
o\$53b2o\$53bo5\$60bo\$61b2o\$60b2o3\$94b2o\$94b2o2\$67bobo\$68b2o\$68bo7\$91b2o
3b2o\$93b3o\$92bo3bo\$93bobo\$94bo2\$82bobo\$83b2o\$83bo\$95b3o\$89bobo\$89b2o4b
obo\$81b2o7bo3b5o\$81b2o10b2o3b2o\$93b2o3b2o3\$90bo\$88bobo\$89b2o\$98b2o\$98b
o\$99b3o\$101bo!
``````
The signal inverter

Code: Select all

``````#CXRLE Pos=93,101 Gen=57
x = 20, y = 36, rule = B3/S23
2b2o\$2b2o6\$19bo\$17b2o\$18b2o2\$2b3o\$bo3bo\$o5bo\$bo3bo\$2b3o5bobo\$2b3o5b2o\$
11bo4\$4b3o\$3b2ob2o\$3b2ob2o\$3b5o\$2b2o3b2o5\$3b2o4\$5b2o\$5b2o!
``````
Not realy nessesary for my project but maybe for future extentions
P30-Gun cleanup

Code: Select all

``````x = 209, y = 113, rule = B3/S23
2bo\$obo\$b2o18bo\$22bo\$20b3o74\$206bo\$206bobo\$206b2o\$57bo\$58b2o\$57b2o6\$
195bo\$193b2o\$194b2o\$70bo\$71bo\$69b3o5\$106bobo\$107b2o77bo\$107bo77bo\$185b
3o6\$148bo\$148bobo\$83bobo62b2o\$84b2o\$84bo!
``````
I am still looking for a pattern that can easily block/unblock a p30 steam of gliders.
I am thinking of a gun and an oscilotor near the gliderstream. Together with a single glider an eater should be build in stopping the glider stream. a second glider destroying the eater.
Does such a construction exist or does anyone know a tool that can search for it?

dvgrn
Moderator
Posts: 6058
Joined: May 17th, 2009, 11:00 pm
Contact:

### Re: A new way of constructing?

fch wrote:I am still looking for a pattern that can easily block/unblock a p30 steam of gliders.
I am thinking of a gun and an oscilotor near the gliderstream. Together with a single glider an eater should be build in stopping the glider stream. a second glider destroying the eater.
Does such a construction exist or does anyone know a tool that can search for it?
Going back through old posts, I was reminded of this fascinating project. Did you (assuming you're still reading the forums!) ever find the necessary technology to answer this question?

I was hoping someone else would dig up something for you, since I'm far from being an expert on p30 circuitry. But just as a first attempt: it doesn't seem as if building and destroying an eater would be necessary to produce a toggleable p30 glider stream. Here's a discovery from Dean Hickerson back in 1996:

Code: Select all

``````#C Single gliders block and unblock a toggleable glider gun
#C Dean Hickerson, 9/4/96
x = 180, y = 116, rule = B3/S23
37b2o\$37bo2bo\$41bo9bobo\$25bo15bo7bo3bo\$22b4o15bo7bo25b2o\$13bo7b4o12bo
2bo7bo4bo22bo\$12bobo6bo2bo12b2o10bo26bobo4bo\$11bo3b2o4b4o24bo3bo6b2o
15b2o3bobo\$2o9bo3b2o5b4o14bobo8bobo6bobo18bob2o15b2o\$2o9bo3b2o8bo14b2o
20bo17b2ob2o14bobo\$12bobo26bo20b2o17bob2o13bo\$13bo68bobo13bo2bo\$22bobo
58bo5bo8bo\$23b2o64bobo7bobo5b2o\$23bo65b2o9b2o5bobo\$34bo74bo\$32b2o75b2o
\$33b2o2\$30bo13bo2bo26bo2bo4bo30b2o\$31b2o15bo11b4o14bo2bo31b2o\$30b2o12b
o3bo10bo3bo10bo3bo2b3o\$34b3o8b4o14bo11b4o\$36bo22bo2bo\$25bo9bo\$24bobo\$
12b2o10b2obo8bobo\$12b2o10b2ob2o6bo2bo\$24b2obo6b2o10b2o\$24bobo5b2o3bo8b
2o\$25bo8b2o5b2o\$35bo2bo4bo\$36bobo6\$102b3o\$102bo\$103bo35\$140b2o\$140bobo
\$140bo36\$177b3o\$177bo\$178bo!``````
Very likely there's something simpler than this, using only gliders, but I haven't dug it up yet. Obviously if you want input and output gliders on different lanes or coming from different directions, it's easy to move the "toggle-ON" signal 90 degrees and kill one of the LWSSes from a different angle. But then the gun isn't failsafe any more -- two "toggle-ON" signals will destroy the gun, and a second "toggle-OFF" will still just toggle the gun back on, of course.

Making a failsafe two-input toggleable gun might be a bit more of a challenge -- or maybe it's already been done, I'm not sure. I have a vague recollection of a three-glider collision that saves some kind of internal state based on a glider input, but I could be remembering some Heisenburp reaction or other...!