## Blockic splitters

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

### Blockic splitters

Post any blockic splitters you find here, especially if you find some that can produce more gliders than the number of blocks in the initial pattern. The initial pattern should be just one glider and a small number of blocks, say a dozen or less. The end result should be only gliders with no debris left over.

The best one I have found so far is this one with a ratio of 5:7 (blocks to gliders):
`x = 41, y = 30, rule = B3/S2312b2o\$12b2o9\$18b2o\$18b2o7\$2o\$2o4\$24b2o\$24b2o\$39b2o\$39b2o\$31b3o\$31bo\$32bo!`

These blockic patterns can usually be cascaded to make larger splitters. In this case you get six more gliders by adding five more blocks resulting in a 10:13 ratio if two of these patterns are cascaded. Continuing to do so will result in a pattern that gives you 1.2 times as many gliders as initial blocks as the cascading continues to infinity. I am wondering how high this multiplier can be for a blockic splitter in Conway's game of life. The best I have been able to do in this area is 1.5 gliders per block.

I will post a collection of some of the better blockic splitters here (ratio 1:1 or better):
Latest update: 2013 Sep 05
Updated blockic splitter table with dvgrn 4:5 and others:
`x = 2477, y = 955, rule = 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180.2A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A50.3D328.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A206.2A167.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.4A2.4A2.4A20.4A10.4A2.4A2.4A568.4A2.4A2.4A20.4A16.4A50.D330.4A2.4A2.4A20.4A10.4A2.4A2.4A61.D144.2A167.4A2.4A2.4A20.4A10.4A2.4A2.4A\$1453.2A434.D.D\$1453.2A19.2A413.3D\$689.4A8.4A8.4A8.4A10.4A8.4A568.4A8.4A8.4A8.4A16.4A91.2A288.4A8.4A8.4A8.4A22.4A59.D315.4A8.4A8.4A8.4A22.4A\$689.A2.A8.A2.A8.A2.A8.A2.A10.A2.A8.A2.A568.A2.A8.A2.A8.A2.A8.A2.A16.A2.A381.A2.A8.A2.A8.A2.A8.A2.A22.A2.A79.2A294.A2.A8.A2.A8.A2.A8.A2.A22.A2.A\$689.A2.A8.A2.A8.A2.A8.A2.A10.A2.A8.A2.A97.2A469.A2.A8.A2.A8.A2.A8.A2.A16.A2.A381.A2.A8.A2.A8.A2.A8.A2.A22.A2.A79.2A19.2A273.A2.A8.A2.A8.A2.A8.A2.A22.A2.A\$689.4A8.4A8.4A8.4A10.4A8.4A97.2A469.4A8.4A8.4A8.4A16.4A46.2A333.4A8.4A8.4A8.4A22.4A100.2A273.4A8.4A8.4A8.4A22.4A\$822.2A605.2A\$822.2A1225.2A\$689.4A2.4A2.4A20.4A10.4A8.4A568.4A2.4A2.4A20.4A16.4A381.4A2.4A2.4A20.4A10.4A2.4A2.4A55.2A162.2A154.4A2.4A2.4A20.4A10.4A2.4A2.4A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A8.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A381.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A55.2A318.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A8.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A61.2A318.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A375.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.4A2.4A2.4A20.4A10.4A8.4A568.4A2.4A2.4A20.4A16.4A61.2A25.2A291.4A2.4A2.4A20.4A10.4A2.4A2.4A375.4A2.4A2.4A20.4A10.4A2.4A2.4A\$834.2A635.2A832.2A19.D\$834.2A1469.2A19.D.D36.2A64.D\$701.4A8.4A8.4A10.4A8.4A63.2A515.4A8.4A8.4A16.4A393.4A8.4A8.4A10.4A109.2A288.4A8.4A8.4A22.4A55.3D36.2A40.A23.D.D36.2A\$701.A2.A8.A2.A8.A2.A10.A2.A8.A2.A63.2A515.A2.A8.A2.A8.A2.A16.A2.A393.A2.A8.A2.A8.A2.A10.A2.A109.2A288.A2.A8.A2.A8.A2.A22.A2.A57.D68.2A9.A22.3D36.2A\$701.A2.A8.A2.A8.A2.A10.A2.A8.A2.A580.A2.A8.A2.A8.A2.A16.A2.A393.A2.A8.A2.A8.A2.A10.A2.A399.A2.A8.A2.A8.A2.A22.A2.A126.2A7.3A24.D\$701.4A8.4A8.4A10.4A8.4A103.2A475.4A8.4A8.4A16.4A393.4A8.4A8.4A10.4A399.4A8.4A8.4A22.4A141.2A\$858.2A1488.D63.2A\$838.D34.2A578.2A855.2A36.3D102.D\$689.4A2.4A2.4A20.4A10.4A2.4A2.4A83.3D32.2A448.4A2.4A2.4A20.4A16.4A70.2A309.4A2.4A2.4A20.4A10.4A2.4A2.4A375.4A2.4A2.4A20.4A10.4A2.4A2.4A39.2A36.D.D19.2A81.3D\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A83.D.D24.3A455.A2.A2.A2.A2.A2.A20.A2.A16.A2.A381.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A375.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A79.D19.2A81.D.D19.2A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A85.D24.A457.A2.A2.A2.A2.A2.A20.A2.A16.A2.A381.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A79.2A140.2A152.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A184.D19.2A\$689.4A2.4A2.4A20.4A10.4A2.4A2.4A111.A456.4A2.4A2.4A20.4A16.4A381.4A2.4A2.4A20.4A10.4A2.4A2.4A79.2A140.2A152.4A2.4A2.4A20.4A10.4A2.4A2.4A\$1477.2A\$1477.2A\$1457.D34.2A\$1457.3D32.2A439.2A\$1457.D.D24.3A446.2A129.2A\$1459.D24.A428.D34.2A114.2A\$1485.A427.3D32.2A\$1913.D.D24.3A\$1915.D24.A\$1941.A\$2074.2A\$2074.2A6\$2047.3D\$2049.D\$2048.3D\$2318.D19.2A\$2316.D.D19.2A83.D19.2A\$2056.2A258.3D102.D.D19.2A\$2056.2A258.D104.3D\$2421.D3\$2333.2A\$2333.2A103.2A\$2312.2A124.2A\$2312.2A103.2A\$2417.2A51\$829.2A\$829.2A10\$1694.2A668.2A\$1462.2A230.2A668.2A\$1462.2A101.2A332.2A199.2A\$844.2A719.2A332.2A199.2A\$828.2A14.2A840.3D667.3D\$828.2A22.2A615.3D215.D669.D\$852.2A616.D86.3D68.A16.2A19.D18.3D404.3D260.3D\$1470.3D85.D70.A15.2A19.D.D424.D\$1437.2A117.3D68.3A36.3D422.3D\$1425.2A10.2A229.D684.2A\$684.4A10.4A2.4A2.4A20.4A16.4A557.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A30.2A152.2A175.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A361.4A10.4A2.4A2.4A20.4A10.4A8.4A76.2A\$684.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A557.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A159.2A23.2A175.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A361.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A8.A2.A\$684.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A557.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A159.2A200.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A69.2A290.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A8.A2.A105.2A\$684.4A10.4A2.4A2.4A20.4A16.4A557.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A255.2A104.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A69.2A290.4A10.4A2.4A2.4A20.4A10.4A8.4A105.2A\$1650.2A375.2A\$1533.2A136.2A354.2A\$684.4A10.4A8.4A8.4A8.4A16.4A557.4A10.4A8.4A8.4A8.4A22.4A34.D103.2A57.D78.2A83.4A10.4A8.4A8.4A8.4A22.4A361.4A10.4A8.4A8.4A8.4A10.4A8.4A\$684.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A557.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A34.3D160.D.D161.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A361.A2.A10.A2.A8.A2.A8.A2.A8.A2.A10.A2.A8.A2.A\$684.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A98.2A457.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A34.D.D160.3D161.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A198.3D160.A2.A10.A2.A8.A2.A8.A2.A8.A2.A10.A2.A8.A2.A95.2A\$684.4A10.4A8.4A8.4A8.4A16.4A98.2A457.4A10.4A8.4A8.4A8.4A22.4A36.D22.2A138.D161.4A10.4A8.4A8.4A8.4A22.4A199.D161.4A10.4A8.4A8.4A8.4A10.4A8.4A95.2A\$826.2A626.2A19.2A96.2A312.2A146.3D\$826.2A647.2A61.3D32.2A122.2A188.2A\$684.4A10.4A8.4A20.4A16.4A557.4A10.4A8.4A20.4A10.4A2.4A2.4A49.2A92.D4.2A152.2A57.4A10.4A8.4A20.4A10.4A2.4A2.4A361.4A10.4A8.4A20.4A10.4A2.4A2.4A72.D\$684.A2.A10.A2.A8.A2.A20.A2.A16.A2.A557.A2.A10.A2.A8.A2.A20.A2.A10.A2.A2.A2.A2.A2.A49.2A92.3D2.2A211.A2.A10.A2.A8.A2.A20.A2.A10.A2.A2.A2.A2.A2.A225.2A134.A2.A10.A2.A8.A2.A20.A2.A10.A2.A2.A2.A2.A2.A48.A23.D.D\$684.A2.A10.A2.A8.A2.A20.A2.A16.A2.A557.A2.A10.A2.A8.A2.A20.A2.A10.A2.A2.A2.A2.A2.A155.D205.A2.A10.A2.A8.A2.A20.A2.A10.A2.A2.A2.A2.A2.A225.2A134.A2.A10.A2.A8.A2.A20.A2.A10.A2.A2.A2.A2.A2.A38.2A9.A22.3D\$684.4A10.4A8.4A20.4A16.4A557.4A10.4A8.4A20.4A10.4A2.4A2.4A155.D.D44.2A73.D83.4A10.4A8.4A20.4A10.4A2.4A2.4A75.2A163.2A119.4A10.4A8.4A20.4A10.4A2.4A2.4A38.2A7.3A24.D\$838.2A710.3D44.2A73.D.D236.2A163.2A17.2A233.2A\$838.2A712.D85.2A32.3D216.D34.2A167.2A233.2A\$684.4A10.4A8.4A8.4A8.4A16.4A64.2A491.4A10.4A8.4A8.4A8.4A10.4A255.2A34.D81.4A10.4A8.4A8.4A8.4A22.4A55.3D32.2A269.4A10.4A8.4A8.4A8.4A22.4A\$684.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A64.2A491.A2.A10.A2.A8.A2.A8.A2.A8.A2.A10.A2.A270.2A26.2A73.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A55.D.D303.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A\$684.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A557.A2.A10.A2.A8.A2.A8.A2.A8.A2.A10.A2.A89.2A57.2A120.2A26.2A73.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A57.D27.2A274.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A83.2A\$684.4A10.4A8.4A8.4A8.4A16.4A104.2A451.4A10.4A8.4A8.4A8.4A10.4A89.2A56.A.A223.4A10.4A8.4A8.4A8.4A22.4A85.2A274.4A10.4A8.4A8.4A8.4A22.4A83.2A\$862.2A668.A28.2A\$877.2A662.2A18.2A\$684.4A10.4A2.4A2.4A20.4A16.4A119.2A436.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A146.2A213.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A241.2A118.4A10.4A2.4A2.4A20.4A22.4A\$684.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A111.3A443.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A361.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A193.2A46.2A118.A2.A10.A2.A2.A2.A2.A2.A20.A2.A22.A2.A\$684.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A111.A445.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A361.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A193.2A166.A2.A10.A2.A2.A2.A2.A2.A20.A2.A22.A2.A\$684.4A10.4A2.4A2.4A20.4A16.4A112.A444.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A361.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A361.4A10.4A2.4A2.4A20.4A22.4A\$1454.2A\$1454.2A645.2A233.2A19.2A\$1927.2A107.2A63.2A233.2A19.2A\$1558.2A367.2A107.2A43.D34.2A\$1558.2A99.2A420.3D32.2A\$1478.2A179.2A420.D.D24.3A\$1478.2A603.D24.A\$1458.D34.2A614.A\$1458.3D32.2A\$1458.D.D24.3A\$1460.D24.A423.2A\$1486.A422.2A431.2A\$2342.2A2\$1665.2A\$1665.2A266.2A\$1933.2A\$1913.D34.2A\$1913.3D32.2A\$1913.D.D24.3A\$1915.D24.A\$1941.A!`

The left column of splitters are 1:1 ratio, with more efficient splitters in the columns to the right.
The best ratio is at the top of the last column, 7:11 block-to-glider ratio, so far.
Last edited by knightlife on September 5th, 2013, 5:13 am, edited 2 times in total.
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Blockic splitters

A search utility I wrote for finding self-destruct circuitry for Herschel tracks turns out to be mildly useful at helping to place blocks to make Blockic splitters. Here's a random 9:10 variation on the leftmost 7:7 splitter. It looks to me like there's room for significant improvement in the upper left corner -- there are actually 11 output gliders already, but for now I'm using up one glider and adding an extra block to do some sub-optimal cleanup.

`#C 11 gliders from 10 blocks -- room for improvement in NW corner#C (used up a glider to get rid of an awkward B-heptomino block)x = 57, y = 49, rule = LifeHistory7.2A\$7.2A13\$22.2A\$6.2A14.2A\$6.2A22.2A\$30.2A12\$34.2A\$34.2A\$4.2A\$4.2A5\$16.2A\$16.2A\$2A\$2A2\$40.2A\$40.2A\$55.2A\$55.2A\$47.3A\$47.A\$48.A!`

I have some more testing and cleaning up to do on the SOD-finder script, but sometime soon I'll post it somewhere here on the forums, probably on the Geminoid Challenge thread, in case anyone else wants to try it out.

dvgrn
Moderator

Posts: 5746
Joined: May 17th, 2009, 11:00 pm

### Re: Blockic splitters

I was able to find a 9:11 splitter by using a block to re-position a Herschel:
`x = 65, y = 49, rule = LifeHistory32.2A\$32.2A3\$39.3D\$40.D\$40.3D8\$6.D\$4.D.D\$4.3D\$4.D\$24.2A\$24.2A19.2A\$45.2A3\$2A\$2A4\$15.2A\$15.2A25.2A\$42.2A7\$24.2A\$24.2A4\$48.2A\$48.2A\$28.D34.2A\$28.3D32.2A\$28.D.D24.3A\$30.D24.A\$56.A!`

There is plenty of sub-optimal cleanup and one block used to re-position a Herschel, but the potential return of 3 gliders per Herschel makes up for the waste.

Note that cascading the 5:7 gives 10:13 but I am going to limit the table of patterns to 12 output gliders. I have updated the collection and included the 10:11 splitter from the post above:
`x = 1493, y = 935, rule = 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2.A2.A2.A2.A\$4A2.4A2.4A20.4A2.4A2.4A2\$212.D21.2A\$4A20.4A8.4A172.3D19.2A\$A2.A20.A2.A8.A2.A172.D.D\$A2.A20.A2.A8.A2.A174.D120.2A\$4A20.4A8.4A76.2A113.2A102.2A\$116.2A16.2A95.2A\$134.2A134.2A\$4A2.4A2.4A20.4A2.4A2.4A218.2A\$A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A307.2A\$A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A307.2A\$4A2.4A2.4A20.4A2.4A2.4A287.D34.2A\$339.3D32.2A\$129.2A208.D.D24.3A\$4A8.4A8.4A8.4A8.4A77.2A134.2A74.D24.A\$A2.A8.A2.A8.A2.A8.A2.A8.A2.A213.2A100.A\$A2.A8.A2.A8.A2.A8.A2.A8.A2.A\$4A8.4A8.4A8.4A8.4A3\$4A2.4A2.4A20.4A2.4A2.4A64.2A15.2A\$A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A64.2A15.2A\$A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A\$4A2.4A2.4A20.4A2.4A2.4A6\$112.2A\$112.2A50\$1042.A\$1043.A\$1041.3A5\$703.4A2.4A2.4A18.4A2.4A2.4A\$703.A2.A2.A2.A2.A2.A18.A2.A2.A2.A2.A2.A\$703.A2.A2.A2.A2.A2.A18.A2.A2.A2.A2.A2.A\$703.4A2.4A2.4A18.4A2.4A2.4A417.2A\$820.2A348.2A\$820.2A110.2A112.2A\$715.4A7.4A7.4A8.4A75.2A102.2A112.2A\$715.A2.A7.A2.A7.A2.A8.A2.A75.2A110.2A235.3D\$715.A2.A7.A2.A7.A2.A8.A2.A187.2A236.D\$715.4A7.4A7.4A8.4A425.3D3\$715.4A18.4A2.4A2.4A\$715.A2.A18.A2.A2.A2.A2.A2.A\$715.A2.A18.A2.A2.A2.A2.A2.A\$715.4A18.4A2.4A2.4A171.2A243.2A\$924.2A243.2A2\$715.4A7.4A7.4A8.4A46.2A250.2A\$715.A2.A7.A2.A7.A2.A8.A2.A46.2A31.2A217.2A\$715.A2.A7.A2.A7.A2.A8.A2.A79.2A110.2A\$715.4A7.4A7.4A8.4A191.2A\$1183.2A\$1183.2A\$4A2.4A2.4A20.4A2.4A2.4A663.4A18.4A2.4A2.4A\$A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A663.A2.A18.A2.A2.A2.A2.A2.A\$A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A663.A2.A18.A2.A2.A2.A2.A2.A280.2A\$4A2.4A2.4A20.4A2.4A2.4A162.2A499.4A18.4A2.4A2.4A61.2A217.2A\$214.2A598.2A110.2A\$229.2A695.2A\$12.4A9.4A19.4A177.2A\$12.A2.A9.A2.A19.A2.A\$12.A2.A9.A2.A19.A2.A53.2A731.2A340.2A\$12.4A9.4A19.4A53.2A138.D592.2A110.2A85.D21.2A119.2A\$100.2A11.2A94.2A32.3D572.D34.2A95.2A85.3D19.2A\$100.2A11.2A94.2A32.D.D572.3D32.2A75.D34.2A70.D.D\$12.4A32.4A191.D574.D.D24.3A82.3D32.2A72.D\$12.A2.A32.A2.A202.2A564.D24.A84.D.D24.3A96.2A\$12.A2.A32.A2.A202.2A590.A85.D24.A98.2A\$12.4A32.4A906.A116.D19.2A\$1073.D.D19.2A65.2A\$1073.3D86.2A\$12.4A9.4A19.4A1021.D\$12.A2.A9.A2.A19.A2.A\$12.A2.A9.A2.A19.A2.A\$12.4A9.4A19.4A183.2A3.2A944.2A\$235.2A3.2A848.2A94.2A\$117.2A971.2A74.D34.2A\$12.4A32.4A65.2A1047.3D32.2A\$12.A2.A32.A2.A1114.D.D24.3A\$12.A2.A32.A2.A202.2A912.D24.A\$12.4A32.4A202.2A938.A4\$99.2A\$99.2A3\$242.3A\$123.2A117.A\$123.2A118.A\$103.D34.2A\$103.3D32.2A\$103.D.D24.3A\$105.D24.A\$131.A56\$701.4A2.4A2.4A20.4A2.4A2.4A68.2A\$701.A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A68.2A\$701.A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A\$701.4A2.4A2.4A20.4A2.4A2.4A3\$701.4A8.4A8.4A8.4A8.4A\$701.A2.A8.A2.A8.A2.A8.A2.A8.A2.A74.2A\$701.A2.A8.A2.A8.A2.A8.A2.A8.A2.A74.2A\$701.4A8.4A8.4A8.4A8.4A82.2A\$835.2A2\$701.4A2.4A2.4A20.4A2.4A2.4A\$701.A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A\$701.A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A\$701.4A2.4A2.4A20.4A2.4A2.4A3\$701.4A8.4A8.4A20.4A\$701.A2.A8.A2.A8.A2.A20.A2.A\$701.A2.A8.A2.A8.A2.A20.A2.A\$701.4A8.4A8.4A20.4A55.2A\$808.2A29.2A\$839.2A\$701.4A2.4A2.4A20.4A2.4A2.4A\$701.A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A\$701.A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A\$701.4A2.4A2.4A20.4A2.4A2.4A3\$821.2A\$821.2A4\$845.2A\$845.2A\$825.D34.2A\$825.3D32.2A\$825.D.D24.3A\$827.D24.A\$853.A75\$1459.2A\$1459.2A3\$1466.3D\$1467.D\$1467.3D\$812.2A24.2A\$812.2A24.2A\$846.2A\$846.2A4\$687.4A2.4A2.4A20.4A10.4A2.4A2.4A568.4A2.4A2.4A20.4A16.4A52.D\$687.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A50.D.D\$687.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A50.3D\$687.4A2.4A2.4A20.4A10.4A2.4A2.4A568.4A2.4A2.4A20.4A16.4A50.D\$1451.2A\$1451.2A19.2A\$687.4A8.4A8.4A8.4A10.4A8.4A568.4A8.4A8.4A8.4A16.4A91.2A\$687.A2.A8.A2.A8.A2.A8.A2.A10.A2.A8.A2.A568.A2.A8.A2.A8.A2.A8.A2.A16.A2.A\$687.A2.A8.A2.A8.A2.A8.A2.A10.A2.A8.A2.A97.2A469.A2.A8.A2.A8.A2.A8.A2.A16.A2.A\$687.4A8.4A8.4A8.4A10.4A8.4A97.2A469.4A8.4A8.4A8.4A16.4A46.2A\$820.2A605.2A\$820.2A\$687.4A2.4A2.4A20.4A10.4A8.4A568.4A2.4A2.4A20.4A16.4A\$687.A2.A2.A2.A2.A2.A20.A2.A10.A2.A8.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A\$687.A2.A2.A2.A2.A2.A20.A2.A10.A2.A8.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A61.2A\$687.4A2.4A2.4A20.4A10.4A8.4A568.4A2.4A2.4A20.4A16.4A61.2A25.2A\$832.2A635.2A\$832.2A\$699.4A8.4A8.4A10.4A8.4A63.2A515.4A8.4A8.4A16.4A\$699.A2.A8.A2.A8.A2.A10.A2.A8.A2.A63.2A515.A2.A8.A2.A8.A2.A16.A2.A\$699.A2.A8.A2.A8.A2.A10.A2.A8.A2.A580.A2.A8.A2.A8.A2.A16.A2.A\$699.4A8.4A8.4A10.4A8.4A103.2A475.4A8.4A8.4A16.4A\$856.2A\$836.D34.2A578.2A\$687.4A2.4A2.4A20.4A10.4A2.4A2.4A83.3D32.2A448.4A2.4A2.4A20.4A16.4A70.2A\$687.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A83.D.D24.3A455.A2.A2.A2.A2.A2.A20.A2.A16.A2.A\$687.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A85.D24.A457.A2.A2.A2.A2.A2.A20.A2.A16.A2.A\$687.4A2.4A2.4A20.4A10.4A2.4A2.4A111.A456.4A2.4A2.4A20.4A16.4A\$1475.2A\$1475.2A\$1455.D34.2A\$1455.3D32.2A\$1455.D.D24.3A\$1457.D24.A\$1483.A76\$827.2A\$827.2A11\$1460.2A\$1460.2A\$842.2A\$826.2A14.2A\$826.2A22.2A615.3D\$850.2A616.D\$1468.3D\$1435.2A\$1423.2A10.2A\$682.4A10.4A2.4A2.4A20.4A16.4A557.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A30.2A\$682.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A557.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$682.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A557.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$682.4A10.4A2.4A2.4A20.4A16.4A557.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A3\$682.4A10.4A8.4A8.4A8.4A16.4A557.4A10.4A8.4A8.4A8.4A22.4A34.D\$682.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A557.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A34.3D\$682.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A98.2A457.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A34.D.D\$682.4A10.4A8.4A8.4A8.4A16.4A98.2A457.4A10.4A8.4A8.4A8.4A22.4A36.D22.2A\$824.2A626.2A19.2A\$824.2A647.2A\$682.4A10.4A8.4A20.4A16.4A557.4A10.4A8.4A20.4A10.4A2.4A2.4A49.2A\$682.A2.A10.A2.A8.A2.A20.A2.A16.A2.A557.A2.A10.A2.A8.A2.A20.A2.A10.A2.A2.A2.A2.A2.A49.2A\$682.A2.A10.A2.A8.A2.A20.A2.A16.A2.A557.A2.A10.A2.A8.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$682.4A10.4A8.4A20.4A16.4A557.4A10.4A8.4A20.4A10.4A2.4A2.4A\$836.2A\$836.2A\$682.4A10.4A8.4A8.4A8.4A16.4A64.2A491.4A10.4A8.4A8.4A8.4A10.4A\$682.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A64.2A491.A2.A10.A2.A8.A2.A8.A2.A8.A2.A10.A2.A\$682.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A557.A2.A10.A2.A8.A2.A8.A2.A8.A2.A10.A2.A89.2A\$682.4A10.4A8.4A8.4A8.4A16.4A104.2A451.4A10.4A8.4A8.4A8.4A10.4A89.2A\$860.2A\$875.2A\$682.4A10.4A2.4A2.4A20.4A16.4A119.2A436.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A\$682.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A111.3A443.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$682.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A111.A445.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$682.4A10.4A2.4A2.4A20.4A16.4A112.A444.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A\$1452.2A\$1452.2A4\$1476.2A\$1476.2A\$1456.D34.2A\$1456.3D32.2A\$1456.D.D24.3A\$1458.D24.A\$1484.A!`

I am still hoping to find improved splitters with ratio n:n+3 but with n<10. I want to add another column to the collection.
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Blockic splitters

It is possible to extend a blockic splitter by cascading smaller patterns to make a bigger one, but there is another way to extend a splitter if there is a Herschel involved. If a Herschel plus blocks combination produces another Herschel plus gliders, then you have essentially a one-time Herschel track that hopefully produces gliders and nothing else. Then tracks can be used to extend the splitter by repeating a track and/or its mirror image:
`x = 128, y = 117, rule = LifeHistory12.2A\$12.2A9\$18.2A17.2A\$18.2A17.2A3\$44.3D\$45.D\$45.3D2\$2A\$2A6\$4.D\$4.3D\$4.D.D\$6.D22.2A\$29.2A19.2A\$50.2A\$19.2A\$19.2A7\$47.2A17.2A\$47.2A17.2A3\$73.3D\$74.D\$74.3D2\$29.2A\$29.2A6\$33.D\$33.3D\$33.D.D\$35.D22.2A\$58.2A19.2A\$79.2A\$48.2A\$48.2A7\$76.2A17.2A\$76.2A17.2A3\$102.3D\$103.D\$103.3D2\$58.2A\$58.2A6\$62.D\$62.3D\$62.D.D\$64.D22.2A\$87.2A19.2A\$108.2A\$77.2A\$77.2A7\$105.2A\$105.2A7\$87.2A\$87.2A4\$111.2A\$111.2A\$91.D34.2A\$91.3D32.2A\$91.D.D24.3A\$93.D24.A\$119.A!`

Adding six blocks to the middle repeating section will produce eight more gliders (two more Herschels). This means you are getting 1.333 gliders per block as you approach infinite size. The example above is producing 31 gliders with 23 blocks giving 23/31 = 1.348 gliders per block. This number is slightly higher due to the efficiency of the endpoints overall. This splitter is an extension of the 9:11 pattern.

Here is the one that approaches 1.25 gliders per block:
`x = 172, y = 75, rule = LifeHistory117.A\$118.A\$116.3A13\$48.2A70.2A\$48.2A70.2A9\$54.2A70.2A\$54.2A70.2A14\$40.D21.2A48.D21.2A\$40.3D19.2A48.3D19.2A\$40.D.D69.D.D\$42.D71.D\$23.2A34.2A34.2A34.2A\$23.2A34.2A34.2A34.2A\$6.D71.D71.D19.2A\$4.D.D69.D.D69.D.D19.2A\$4.3D19.2A48.3D19.2A48.3D\$4.D21.2A48.D21.2A48.D4\$165.2A\$165.2A\$2A\$2A7\$18.2A70.2A\$18.2A70.2A9\$12.2A70.2A\$12.2A70.2A!`

This one is an extension of the third pattern in the 7:8 section of the collection. Adding four blocks gives you five more gliders. EDIT: actually the 7:8 has been improved to 7:9, see update below.

I thought I had an example for 1.5 gliders per block but I can't find it.

There is a way to get 2 gliders per block, but it requires some engineering to do the final cleanup. Here is the basic reaction:
`x = 140, y = 55, rule = LifeHistory85.A\$86.A\$84.3A38\$2A29.2A29.2A29.2A\$2A29.2A29.2A29.2A5\$138.2A\$138.2A6\$133.2A\$133.2A!`

There are two new gliders for each block added. There are leftover blocks but they are in a straight orthoghonal line. A final stage can then cleanup by producing two heavyweight spaceships to do the cleanup job. When done with the cleanup, the spaceships could crash into blocks and be destroyed cleanly. I suppose this is cheating a little and not entirely satisfying, but it is possible to achieve 2 gliders per block in the limit.

Updated collection with an 8:8 entry, corrected the 8:9, and added a 7:9 entry:
`x = 1495, y = 945, rule = 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knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Blockic splitters

knightlife wrote:I was able to find a 9:11 splitter by using a block to re-position a Herschel...
I am still hoping to find improved splitters with ratio n:n+3 but with n<10. I want to add another column to the collection.

Here's one for your new column:

`#C Moving one block in the 9:11 makes a 9:12.x = 65, y = 49, rule = LifeHistory32.2A\$32.2A3\$39.3D\$40.D\$40.3D2\$18.2A\$18.2A5\$6.D\$4.D.D\$4.3D\$4.D\$24.2A\$24.2A19.2A\$45.2A3\$2A\$2A5\$42.2A\$42.2A7\$24.2A\$24.2A4\$48.2A\$48.2A\$28.D34.2A\$28.3D32.2A\$28.D.D24.3A\$30.D24.A\$56.A!`

I thought at first that there was some hope for 9:13, if the reaction could have suppressed the B-heptomino block directly instead of via a glider collision -- or an alternate 9:12 using two blocks in that location. But I see that cleanup glider is doomed anyway, since it would interfere with the first natural glider from the final Herschel -- would have to really luck out to drop one or two blocks there and get a clean one-time turner in just the right place. I think I tried all the possible singleton block positions, anyway.

dvgrn
Moderator

Posts: 5746
Joined: May 17th, 2009, 11:00 pm

### Re: Blockic splitters

Nice move, pun intended! Offhand I would guess 9:12 is the clear winner but 5:7 is still doing OK at 1.4 gliders per block. Here is the updated table with the new column:
`x = 1950, y = 945, rule = 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Suddenly a fifth column is not so far fetched
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Blockic splitters

knightlife wrote:I thought I had an example for 1.5 gliders per block but I can't find it.

There is a way to get 2 gliders per block, but it requires some engineering to do the final cleanup.

I found the file for 1.5 gliders per block:
`x = 204, y = 35, rule = LifeHistory169.A\$170.A\$168.3A18\$D21.2A48.D21.2A48.D21.2A\$3D19.2A48.3D19.2A48.3D19.2A\$D.D69.D.D69.D.D\$2.D71.D71.D\$19.2A34.2A34.2A34.2A34.2A\$19.2A34.2A34.2A34.2A34.2A\$38.D71.D71.D19.2A\$36.D.D69.D.D69.D.D19.2A\$36.3D19.2A48.3D19.2A48.3D\$36.D21.2A48.D21.2A48.D4\$197.2A\$197.2A!`

Cleanup will be needed, same as in the following example:

Here is a proof-of-concept for approaching 2 gliders per block:
`x = 279, y = 111, rule = LifeHistory224.A\$225.A\$223.3A15\$18.2A\$18.2A4\$8.2A\$8.2A6\$22.2A\$22.2A2\$2.2A\$2.2A3\$53.2A\$53.2A\$267.2A\$267.2A\$2A106.2A29.2A29.2A29.2A29.2A\$2A41.2A63.2A29.2A29.2A29.2A29.2A\$43.2A2\$9.2A13.2A\$9.2A13.2A\$277.2A\$277.2A\$57.2A\$57.2A2\$37.2A\$37.2A\$272.2A\$272.2A\$96.2A\$96.2A\$258.2A\$258.2A\$35.2A\$35.2A2\$119.2A\$44.2A13.2A58.2A\$44.2A13.2A3\$115.2A\$115.2A2\$119.2A\$119.2A4\$115.2A\$115.2A17\$80.2A\$80.2A3\$85.2A\$85.2A7\$76.2A\$76.2A3\$81.2A\$81.2A!`

The middle section is expandable, gaining 2 gliders for every block added. However, the pattern will be very large before the total pattern gets near 2 gliders per block due to the overhead required for cleanup. The example uses 32 blocks to get 12 gliders which means there is a 26 block overhead for cleanup. The overhead can be reduced a little with some optimization.

(26+n) : 2n --------blocks to gliders ratio
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Blockic splitters

knightlife wrote:I found the file for 1.5 gliders per block...

I like this one! Thought of a couple of things, probably not useful:

1) You can get a clean 1-glider-per-block delta by running two copies of this side by side, with just a little cleanup at the end and splitting the input glider into two at the beginning -- I didn't bother to wire up a splitter, since 1:1 deltas for long chains are a dime a dozen these days! Still, it's fun to watch it work:

`x = 388, y = 135, rule = B3/S23351bo\$352bo\$69b2o70b2o207b3o\$69b2o70b2o3\$75b2o70b2o\$75b2o70b2o8\$36b2o\$36b2o6\$62b2o70b2o70b2o70b2o70b2o\$62b2o70b2o70b2o70b2o70b2o3\$59b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o\$59b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o\$386b2o\$386b2o\$98b2o70b2o70b2o70b2o\$98b2o70b2o70b2o70b2o4\$381b2o\$381b2o10\$111b2o\$111b2o3\$105b2o\$105b2o2\$69b2o\$69b2o3\$75b2o\$75b2o10\$345b2o\$345b2o4\$62b2o70b2o70b2o70b2o\$62b2o70b2o70b2o70b2o\$350b2o\$350b2o\$23b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o\$23b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o34b2o3\$26b2o70b2o70b2o70b2o70b2o\$26b2o70b2o70b2o70b2o70b2o6\$2o\$2o8\$39b2o70b2o\$39b2o70b2o3\$33b2o70b2o\$33b2o70b2o30\$284b3o\$286bo\$285bo!`

2) Watching the chains work, with a Herschel basically eating a pattern of blocks and leaving behind another pattern of blocks with the same spacing, gave me another crackpot idea: do you know any chainable reactions that use one block and leave one block, with at least one output glider per link?

Doesn't have to be Herschel-based, though Herschels, B's and R's are maybe the most likely to leave a block behind. It might be possible to use the output blocks as input for another chain, if the offset was right (i.e., another set of "ignition" blocks at that offset wouldn't get in the way of the first chain reaction). Probably this would only work for chains with no glide-reflection, though. A long enough chain, with the wick reburned enough times, could produce a fairly impressive B:G ratio.

dvgrn
Moderator

Posts: 5746
Joined: May 17th, 2009, 11:00 pm

### Re: Blockic splitters

Here's a 5:6 with (I think) some potential for improvement:

`#C H+3B4 -> 5Gx = 51, y = 39, rule = LifeHistory38.A\$37.A\$37.3A3\$43.2A\$43.2A3\$35.3D\$36.D\$34.3D15\$49.2A\$49.2A3\$2A19.D\$2A19.D.D\$21.3D\$23.D\$30.2A\$30.2A2\$5.2A\$5.2A!`

Along the same lines, I haven't found a convenient cleanup for the leftover block in this reaction yet, but even using two blocks and a glider for the cleanup, it's _still_ a 6:6 --

` #C H + 2B4 -> 6G + B4x = 43, y = 57, rule = LifeHistory38.A\$37.A\$37.3A6\$5.2A\$5.2A4\$41.2A\$41.2A16\$2A19.D\$2A19.D.D\$21.3D\$23.D4\$5.2A\$5.2A13\$20.2A\$20.2A3\$15.2A\$15.2A!`

Or here it is as a 7:8 --

`x = 43, y = 66, rule = LifeHistory5.2A\$5.2A4\$41.2A\$41.2A6\$18.A\$17.A\$17.3A8\$2A19.D\$2A19.D.D\$21.3D\$23.D4\$5.2A\$5.2A9\$19.2A\$19.2A14\$21.2A\$21.2A9\$15.2A\$15.2A!`

Or a 9:12, for another entry in the n:n+3 column --

`x = 45, y = 79, rule = LifeHistory5.2A\$5.2A4\$41.2A\$41.2A6\$18.A\$17.A\$17.3A8\$2A19.D\$2A19.D.D\$21.3D\$23.D4\$5.2A\$5.2A8\$18.2A\$18.2A14\$20.2A\$20.2A5\$33.2A\$33.2A5\$43.2A\$43.2A6\$16.3D\$18.D\$17.3D3\$25.2A\$25.2A!`

I'm hoping there's some way of combining these with previously-known reactions to get an n:n+4 ... but I think I'm out of inspiration (and time) for the moment.

Edit: No, not quite! Here's the obvious 9:13 --

`x = 67, y = 73, rule = LifeHistory38.A\$37.A\$37.3A6\$5.2A\$5.2A4\$41.2A\$41.2A16\$2A19.D\$2A19.D.D36.2A\$21.3D36.2A\$23.D3\$43.D\$5.2A36.3D\$5.2A36.D.D19.2A\$45.D19.2A23\$13.D19.2A\$11.D.D19.2A\$11.3D\$11.D4\$28.2A\$28.2A\$7.2A\$7.2A!`

dvgrn
Moderator

Posts: 5746
Joined: May 17th, 2009, 11:00 pm

### Re: Blockic splitters

The real question is: can the 1:2 ratio be passed? Or, for that matter, met with a finite number of blocks.
137ben

Posts: 343
Joined: June 18th, 2010, 8:18 pm

### Re: Blockic splitters

137ben wrote:The real question is: can the 1:2 ratio be passed? Or, for that matter, met with a finite number of blocks.

No reason why not -- the search space is enormous, and we don't even know for sure that some three-block constellation isn't a pure 6-glider generator. But one step at a time -- I'd like to crack the 1:1.5 ratio before tackling 1:2...!

Here's a 10B:14G based on a new H+B4->3G+pi reaction:

`x = 69, y = 51, rule = LifeHistory49.2A\$49.2A3\$41.3D\$42.D\$40.3D3\$38.2A\$38.2A2\$67.2A\$67.2A5\$57.2A\$57.2A3\$34.D\$10.A23.D.D\$2A9.A22.3D\$2A7.3A24.D\$15.2A\$15.2A3\$45.2A\$45.2A8\$21.2A19.2A\$21.2A19.2A9\$27.2A\$27.2A!`

There's a subtle variant that's very nearly an 8B:12G, but the last block seems intractable -- could also be a 6B:9G, but then there's trouble with the input glider as well as the block:

`x = 125, y = 57, rule = LifeHistory33.2A88.2A\$33.2A88.2A3\$25.3D87.3D\$26.D89.D\$24.3D87.3D10\$24.2A88.2A\$24.2A88.2A11\$2A19.D89.D\$2A19.D.D63.A23.D.D\$6.A14.3D53.2A9.A22.3D\$5.A17.D53.2A7.3A24.D\$5.3A84.2A\$92.2A2\$5.2A\$5.2A25.2A88.2A\$32.2A88.2A8\$29.2A67.2A19.2A\$29.2A67.2A19.2A9\$104.2A\$104.2A!`

dvgrn
Moderator

Posts: 5746
Joined: May 17th, 2009, 11:00 pm

### Re: Blockic splitters

No reason why not -- the search space is enormous, and we don't even know for sure that some three-block constellation isn't a pure 6-glider generator. But one step at a time -- I'd like to crack the 1:1.5 ratio before tackling 1:2...!

But...but we already have a (26+n):n splitter Why doesn't that mean that we have already cracked every ratio less than 2?
137ben

Posts: 343
Joined: June 18th, 2010, 8:18 pm

### Re: Blockic splitters

137ben wrote:
But one step at a time -- I'd like to crack the 1:1.5 ratio before tackling 1:2...!

But...but we already have a (26+n):n splitter Why doesn't that mean that we have already cracked every ratio less than 2?

The (26+n):2n proof-of-concept, as knightlife says, is maybe "cheating a little and not entirely satisfying". I don't think it's cheating exactly, but it's not a good solution for the original problem, which really needs as-few-as-possible blocks producing as-many-as-possible gliders.

So it's knightlife's table of splitters that I'm trying to push up to 1:1.5, and then hopefully to 1:2 or above. I found an "n:n+3 but with n<10". After that came an n:n+4, but I can't quite get that into the table because the limit is 12 output gliders and the 8:12 version isn't quite clean.

-- I'm playing by knightlife's rules for now, but really for my purposes limiting the number of input blocks would be better -- I wouldn't object at all to n:n+10, myself... but even a 3:13 would be excluded by the current criteria. In self-destruct circuitry the 8:12 would really be quite usable in practice -- just have to be sure to line up the extra output block with a spare glider that needs to be absorbed anyway.

Anyway, I think there are some ideas floating around that should be able to get us well above 1:2 in limit -- all we need is a reburnable fuse with a big enough offset that it can be touched off multiple times. That's the trouble with this "in limit" stuff, it encourages Rube Goldbergian "solutions": a reburnable fuse will easily beat 1:2 even if it needs huge one-time seed patterns at the beginning and end to rebuild triggers and suppress final output.

Just now I'm hunting for known reburnable reactions. Can't resist posting a couple of eminently non-Blockic fuses from Nicolay Beluchenko, as a placeholder -- just imagine all blocks, one block input per Herschel and one block output per Herschel, along with the glider...

`#C (1, 13)c/31 clean and (10,10)c/140 dirty fuse#C Nicolay Beluchenko, 15 Sep 2006x = 213, y = 71, rule = B3/S2315b2o11bo\$15b2o10bobo12bo\$4bo3bo19bo12bobo9b2o\$3b2o3b2o31b2o10bobo11bo12b2o\$2obo5b2o43bo11bobo12bo14bo\$2obo5bo57b2o11bo13b3o8b2o12b2o59b2o\$b2o5bo71b2o11bo11bo13b2o39b2o18b2o\$93b2o12bo35bo16bo2bo\$106b2o11b2o22b3o15b3o\$119b2o11b2ob2o9bo\$132b2ob2o8bobo11b3o\$145b2o11bo2bo\$158b2o3\$190b2o\$190b2o\$171b2o\$171b2o4\$153b2o\$154bo20b2o\$151b3o21b2o\$151bo48b2o\$155bo44b2o\$154bobo24b2o\$155bo25b2o2\$157b2o\$157b2o\$163b2o\$163b2o20b2o\$185b2o\$210b2o\$210b2o\$191b2o\$191b2o4\$173b2o\$173b2o20b2o\$195b2o3\$201b2o\$201b2o4\$183b2o\$183b2o20b2o\$205b2o3\$211b2o\$211b2o11\$206b2o\$206b2o!`

dvgrn
Moderator

Posts: 5746
Joined: May 17th, 2009, 11:00 pm

### Re: Blockic splitters

dvgrn wrote:Just now I'm hunting for known reburnable reactions...

Haven't come up with any known reactions yet that burn a block, release a glider, and then leave a block behind at some offset. This is not too surprising, I suppose -- I would think such a reaction would have found its way into some kind of wickstretcher, spaceship, or Herschel conduit if it were known.

I didn't look too hard for known two-dimensional agars, though -- quite possibly someone has previously discovered some variant of the pattern below. What else am I missing? Can anyone point out some good prior art that I've forgotten about?

I did a few searches with my Seeds-Of-Destruction-Finder Python script, and so far I've come up with this experimental pattern. Can't think of any use for it in a Blockic-splitter context -- it makes lots of gliders, but also an extra block for each glider, so the net gain is zero:

`#C block field navigable by Herschelsx = 524, y = 364, rule = B3/S23258b2o\$258b2o\$280b2o\$280b2o\$302b2o\$302b2o\$324b2o\$324b2o\$346b2o\$346b2o\$368b2o\$368b2o\$246b2o142b2o\$246b2o142b2o\$268b2o142b2o\$268b2o142b2o\$290b2o142b2o\$290b2o142b2o\$312b2o142b2o\$312b2o142b2o\$334b2o142b2o\$334b2o142b2o\$356b2o142b2o\$356b2o142b2o\$234b2o142b2o142b2o\$234b2o142b2o142b2o\$256b2o142b2o\$256b2o142b2o\$278b2o142b2o\$278b2o142b2o\$300b2o142b2o\$300b2o142b2o\$322b2o142b2o\$322b2o142b2o\$344b2o142b2o\$344b2o142b2o\$366b2o\$366b2o\$388b2o\$388b2o\$410b2o\$410b2o\$432b2o\$432b2o\$454b2o\$454b2o7\$512b2o\$213b2o297b2o\$213b2o\$235b2o\$235b2o\$257b2o\$257b2o\$279b2o\$279b2o\$301b2o\$301b2o175b2o\$323b2o153b2o\$323b2o\$345b2o\$345b2o\$367b2o\$367b2o\$389b2o\$389b2o\$411b2o\$411b2o31b2o\$444b2o11\$480b2o\$181b2o297b2o\$181b2o\$203b2o\$203b2o\$225b2o\$225b2o\$247b2o\$247b2o\$269b2o\$269b2o175b2o\$291b2o153b2o\$291b2o\$313b2o\$313b2o\$335b2o\$335b2o\$357b2o\$357b2o\$379b2o\$379b2o31b2o\$412b2o11\$448b2o\$149b2o297b2o\$149b2o\$171b2o\$171b2o\$193b2o\$193b2o\$215b2o\$215b2o\$237b2o\$237b2o175b2o\$259b2o153b2o\$259b2o\$281b2o\$281b2o\$303b2o\$303b2o\$325b2o\$325b2o\$347b2o\$347b2o31b2o\$380b2o11\$416b2o\$117b2o297b2o\$117b2o\$139b2o\$139b2o\$161b2o\$161b2o\$183b2o\$183b2o\$205b2o\$205b2o175b2o\$227b2o153b2o\$227b2o\$249b2o\$249b2o\$271b2o\$271b2o\$293b2o\$293b2o\$315b2o\$315b2o31b2o\$348b2o11\$384b2o\$85b2o297b2o\$85b2o\$107b2o\$107b2o\$129b2o\$129b2o\$151b2o\$151b2o\$173b2o\$173b2o175b2o\$195b2o153b2o\$195b2o\$217b2o\$217b2o\$239b2o\$239b2o\$261b2o\$261b2o\$283b2o\$283b2o31b2o\$316b2o11\$352b2o\$53b2o297b2o\$53b2o\$75b2o\$75b2o\$97b2o\$97b2o\$119b2o\$119b2o\$141b2o\$141b2o175b2o\$163b2o153b2o\$163b2o\$185b2o\$185b2o\$207b2o\$207b2o\$229b2o\$229b2o\$251b2o\$251b2o31b2o\$284b2o8\$253b3o\$254bo\$254b3o\$320b2o\$21b2o297b2o\$21b2o\$43b2o\$43b2o\$65b2o\$65b2o\$87b2o\$87b2o\$109b2o142b2o\$109b2o132b2o8b2o31b2o\$131b2o110b2o41b2o\$131b2o\$153b2o\$153b2o\$67b3o105b2o\$68bo106b2o\$68b3o18b3o105b2o\$90bo106b2o31b2o\$90b3o18b3o116b2o\$112bo\$112b3o18b3o\$134bo\$134b3o18b3o\$156bo\$156b3o18b3o\$178bo\$67b2o109b3o18b3o\$57b2o8b2o131bo\$57b2o30b2o109b3o\$11bo67b2o8b2o\$11bobo65b2o30b2o\$2o9b3o19bo67b2o8b2o175b2o\$2o11bo19bobo65b2o30b2o153b2o\$22b2o9b3o87b2o8b2o\$22b2o11bo87b2o30b2o\$44b2o99b2o8b2o\$44b2o99b2o30b2o\$167b2o8b2o\$167b2o30b2o\$189b2o8b2o\$2o187b2o30b2o\$2o219b2o31b2o\$22b2o230b2o\$22b2o10\$35bo\$35bobo\$24b2o9b3o19bo\$24b2o11bo19bobo\$46b2o9b3o19bo\$46b2o11bo19bobo\$68b2o9b3o19bo\$68b2o11bo19bobo\$90b2o9b3o19bo\$90b2o11bo19bobo\$112b2o9b3o19bo110b2o\$24b2o86b2o11bo19bobo108b2o\$24b2o108b2o9b3o19bo\$46b2o86b2o11bo19bobo\$46b2o108b2o9b3o19bo\$156b2o11bo19bobo\$67b2o109b2o9b3o19bo\$67b2o109b2o11bo19bobo\$89b2o109b2o9b3o\$89b2o109b2o11bo\$111b2o109b2o\$111b2o109b2o\$133b2o\$133b2o\$155b2o\$15b2o138b2o\$15b2o160b2o\$37b2o138b2o\$37b2o160b2o\$59b2o138b2o\$59b2o\$81b2o\$81b2o\$103b2o\$103b2o\$17b3o105b2o\$18bo106b2o\$18b3o18b3o105b2o\$40bo106b2o\$40b3o18b3o105b2o\$62bo106b2o\$62b3o18b3o105b2o\$84bo106b2o31b2o\$84b3o18b3o116b2o\$106bo\$106b3o18b3o\$128bo\$17b2o109b3o18b3o\$7b2o8b2o131bo\$7b2o30b2o109b3o18b3o\$29b2o8b2o131bo\$29b2o30b2o109b3o18b3o\$51b2o8b2o131bo\$51b2o30b2o109b3o\$73b2o8b2o\$73b2o30b2o\$95b2o8b2o\$95b2o30b2o\$117b2o8b2o\$117b2o30b2o\$139b2o8b2o\$139b2o30b2o\$161b2o8b2o\$161b2o30b2o\$183b2o8b2o\$183b2o!`

There's no reason why the active pattern has to be a Herschel, R, or B-heptomino, though those do travel well. It would be equally interesting to have a LOM or century or pre-honeyfarm or what have you, interacting with a block to produce a glider, block and an offset LOM/century/pre-honeyfarm. [For that matter, a reburnable line of tubs or beehives or blinkers would also be very interesting -- just not relevant to this particular discussion!]

---------------------------

Also, I just realized yesterday that there's an obvious (so to speak) Rube-Goldberg way to get 1:2, or 1:3, or or 1:1000000, or any 1:X ratio of gliders to blocks you might want, with a finite number of blocks. You just need to make minor adjustments to the same ~250 blocks -- inside a fairly large bounding box, diameter proportional to X in limit.

I have some proof-of-concept patterns to post as soon as someone can guess the basic mechanism.

dvgrn
Moderator

Posts: 5746
Joined: May 17th, 2009, 11:00 pm

### Re: Blockic splitters

dvgrn wrote:I have some proof-of-concept patterns to post as soon as someone can guess the basic mechanism.

Would that be to create a glider gun and then destroy it after a long enough delay? It takes only 10 gliders to create a p30 stream of gliders of any length (I posted an example of this a while back). Then I'm guessing it would take around 250 blocks to produce the exact 10 gliders needed to do the job!

Another implementation of this would be to construct a Herschel track in a loop and then destroy it later.

BTW, I really like your n:n+4 solution that simultaneously gets rid of an extra block and avoids adding an extra block to complete the final cascade stage!

Also, I considered removing the 12 glider limit as you mention. What if 7 blocks could produce 13 gliders? I never intended to limit how many gliders a small number of blocks could produce!

I didn't post this, but it is possible to turn corners while still producing more gliders, then burning through a square structure rather than a straight line. I realize the corners are not really necessary since any stray glider can initiate another chain at any distance, but this is where I discovered the H+b4 ---> 3G reaction!

`x = 112, y = 95, rule = LifeHistory19.2A\$19.2A3\$97.2A11.2A\$26.2A69.2A11.2A\$26.2A7\$14.2A\$13.A.A77.3D\$15.A78.D\$94.3D2\$105.2A\$105.2A\$24.2A\$19.3D2.2A\$21.D\$20.3D82.2A\$105.2A5\$89.2A\$89.2A3\$23.2A\$23.2A8\$88.2A\$88.2A3\$22.2A\$22.2A8\$87.2A\$87.2A4\$16.3D\$18.D\$17.3D4\$89.3D\$90.D\$25.2A59.2A2.3D\$25.2A11.2A46.2A\$18.2D18.2A11.2A\$18.D.D7.D22.2A11.2A\$2A18.D5.3D35.2A\$2A16.3D5.D.D\$9.2A15.D62.3D\$9.2A69.D7.D2.D\$78.3D7.2D.D\$78.D.D\$78.D\$13.2A\$13.2A82.2A\$97.2A3\$92.2A\$92.2A8\$90.2A\$90.2A!`

Maybe after traversing the square, a re-burnable pattern could traverse it again!

I have found corners that can maintain a 1:1 ratio, I believe. For chains, I like the following:
`x = 180, y = 31, rule = B3/S2319b2o36b2o36b2o36b2o\$19b2o36b2o36b2o36b2o\$40b2o36b2o36b2o36b2o\$40b2o36b2o36b2o36b2o\$3bo\$4bo\$2b3o3\$45b2o36b2o36b2o36b2o\$45b2o36b2o36b2o36b2o10\$26b2o36b2o36b2o36b2o36b2o\$26b2o36b2o36b2o36b2o36b2o6\$21b2o36b2o36b2o36b2o36b2o\$21b2o36b2o36b2o36b2o36b2o\$2o36b2o36b2o36b2o36b2o\$2o36b2o36b2o36b2o36b2o!`

I will update the table when I have more time.
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Blockic splitters

knightlife wrote:Also, I considered removing the 12 glider limit as you mention. What if 7 blocks could produce 13 gliders? I never intended to limit how many gliders a small number of blocks could produce!

There is a void in the table after 4:4 (there is no 4:5 that I know of) so I tried to see how many gliders 4 blocks can produce:
`x = 91, y = 39, rule = B3/S23bo\$2bo\$3o3\$23b2o\$23b2o17\$19b2o\$19b2o2\$26b2o\$26b2o10\$89b2o\$89b2o!`

Wow, 18 gliders! Surely some of those can be directed to clean up the mess!
To avoid using too many blocks, use efficient patterns to create more gliders, using "strays" to clean up the mess.

Hmmm, not very likely, right now it is just an idea.
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Blockic splitters

knightlife wrote:Wow, 18 gliders! Surely some of those can be directed to clean up the mess!
To avoid using too many blocks, use efficient patterns to create more gliders, using "strays" to clean up the mess.

Hmmm, not very likely, right now it is just an idea.

Yes, that's an awfully big mess for 18 gliders to clean up, and you don't get the last three until the very end (actually there's a 19th glider that might be saveable, too.) And when you're all done you still won't have a 4:5...!

knightlife wrote:It takes only 10 gliders to create a p30 stream of gliders of any length (I posted an example of this a while back)...Another implementation of this would be to construct a Herschel track in a loop and then destroy it later.

Close enough. There are lots of variations; I was thinking -- if you can call it thinking -- that lots of gliders on the same exact lanes would be less useful (going back to my original purpose for wanting Blockic super-splitters). So I thought maybe it would be better to build a spacerake, and then destroy it:

`x = 554, y = 99, rule = B3/S2343bobo\$44b2o\$44bo123bo\$167bo\$167b3o\$161bobo\$161b2o\$51bo110bo\$52b2o\$51b2o28\$26bobo\$27b2o\$27bo53bo\$80bo\$80b3o5\$27bo52bo\$28b2o50bobo\$27b2o51b2o\$68bo\$66b2o\$67b2o\$41bobo\$42b2o\$42bo2\$544b2o\$544b2o3\$539b2o\$539b2o2\$23bo\$24b2o\$23b2o8\$6bo\$4bobo545b2o\$5b2o545b2o\$540b2o\$540b2o5\$bo\$b2o\$obo2\$11bo\$10b2o\$10bobo4\$19b2o\$18bobo\$20bo2\$48b2o\$48bobo\$48bo!`

knightlife wrote:Then I'm guessing it would take around 250 blocks to produce the exact 10 gliders needed to do the job!

I was almost certainly being too pessimistic. If a spacerake takes only 16 synchronized gliders, and a Blockic seed for a loafer was 81 blocks producing 8 synchronized gliders -- and the splitters I used in the loafer seed were much less efficient than the ones that have been found since -- then a spacerake seed plus spacerake stopper should come in well under 250 blocks, and your glider-gun trick would be less than 100 blocks.

I don't like having to keep moving the stopper (or the final one-time turners, in the case of the glider gun) farther away to get more gliders, though. For 1:N ratios with very large N, it might be possible to pack everything into a relatively small initial bounding box by using a slow rake followed by a fast spaceship, or a slow spaceship followed by a fast rake:

`#C Clear the road, you loafer!x = 766, y = 189, rule = B3/S23742b2o4b2o\$742b2o4b2o2\$764b2o\$764b2o5\$751b2o11b2o\$713b2o36b2o11b2o\$713b2o\$755b2o\$755b2o\$64bobo651b2o\$65b2o651b2o\$65bo123bo503b2o\$188bo504b2o\$188b3o\$182bobo\$182b2o514b2o\$72bo110bo514b2o\$73b2o\$72b2o12\$643b2o\$643b2o\$698b2o41b2o\$698b2o41b2o\$645b2o\$645b2o\$703b2o\$703b2o32b2o\$646b2o89b2o\$646b2o\$723b2o\$723b2o2\$647b2o\$647b2o62b2o\$711b2o6b2o\$47bobo669b2o\$48b2o602b2o\$48bo53bo549b2o\$101bo605b2o\$101b3o527b2o74b2o\$627b2o2b2o\$627b2o\$623b2o\$623b2o\$48bo52bo\$49b2o50bobo559b2o\$48b2o51b2o560b2o\$89bo\$87b2o\$88b2o\$30bo31bobo586b2o11b2o\$30bobo30b2o582b2o2b2o11b2o18b2o\$30b2o31bo583b2o35b2o\$643b2o\$2bo640b2o\$obo\$b2o676b2o4b2o\$674b2o3b2o4b2o\$674b2o\$662b2o\$657b2o3b2o\$44bo607b2o3b2o\$45b2o605b2o46b2o\$44b2o649b2o3b2o\$626b2o67b2o\$626b2o55b2o\$678b2o3b2o\$617b2o48b2o4b2o3b2o26b2o\$617b2o48b2o4b2o31b2o\$650b2o\$650b2o\$27bo\$25bobo640b2o32b2o\$26b2o589b2o49b2o18b2o12b2o\$617b2o27b2o9b2o29b2o\$646b2o9b2o\$701b2o\$701b2o\$689b2o\$689b2o\$22bo\$22b2o681b2o\$21bobo681b2o\$5b2o653b2o4b2o\$6b2o24bo627b2o4b2o\$5bo25b2o\$31bobo4\$40b2o672b2o\$39bobo672b2o\$41bo\$654b2o\$69b2o583b2o\$69bobo638b2o\$69bo640b2o\$653b2o\$653b2o22b2o\$661b2o14b2o\$657b2o2b2o58b2o\$652b2o3b2o9b2o46b2o3b2o\$652b2o14b2o46b2o3\$695b2o\$695b2o3\$726b2o\$699b2o25b2o\$699b2o5\$635b2o75b2o\$635b2o75b2o2\$626b2o\$626b2o\$704b2o\$704b2o3\$626b2o75b2o\$626b2o75b2o2\$637b2o\$637b2o3\$642b2o\$642b2o37\$613bo\$613b2o\$612bobo!`

The only downside there is that to increase G, the total number of output gliders, you have to delay the rake construction. To get better than an O(G) delay and keep the limit size of the bounding box down, you'd have to put in a increasing number of one-time-turner delay blocks. Might just be logarithmically increasing, if you built let's say a p256-based period doubler and then destroyed it -- but that's getting expensive and no doubt there's a better way to get a long delay.

A faintly ridiculous alternative is a constructible Cordership rake (two identical halves, 22 synchronized gliders each) followed by a glider. The great advantage is that a glider kickback reaction can be used on the rake itself to get longer and longer delays for each 180-degree one-time turner you add -- I think that's O(log G) increase in bounding box size for the seed blocks (did I get that right?) which seems pretty good.

`#C Cordership stopped by 31 following gliders.#C The initial glider is wrong -- it needs a synchronized companion glider#C   to get through the Cordership's output gliders -- so the search should#C be re-run... good enough for a proof-of-concept illustration, though.#C The search could also be optimized to produce many more output#C   gliders, as shown by the last boat cleanup.x = 2965, y = 2944, rule = B3/S23o\$b2o\$2o16\$66bo\$67b2o\$66b2o48\$98bo\$99b2o\$98b2o48\$139bo\$140b2o\$139b2o48\$197bo\$198b2o\$197b2o78\$245bo\$246bo\$244b3o98\$350bo\$351b2o\$350b2o48\$333bo\$334b2o\$333b2o48\$455bo\$456b2o\$455b2o48\$480bo\$481b2o\$480b2o48\$504bo\$505b2o\$504b2o48\$540bo\$541b2o\$540b2o48\$576bo\$577b2o\$576b2o48\$620bo\$621b2o\$620b2o48\$607bo\$608b2o\$607b2o45\$654bo\$655b2o\$654b2o48\$822bo\$823b2o\$822b2o48\$862bo\$863b2o\$862b2o48\$830bo\$831b2o\$830b2o48\$872bo\$873b2o\$872b2o48\$915bo\$916b2o\$915b2o48\$1064bo\$1065b2o\$1064b2o48\$1086bo\$1087b2o\$1086b2o48\$1128bo\$1129b2o\$1128b2o48\$1157bo\$1158b2o\$1157b2o48\$1177bo\$1178b2o\$1177b2o48\$1312bo\$1313b2o\$1312b2o48\$1397bo\$1398b2o\$1397b2o48\$1426bo\$1427b2o\$1426b2o444\$1885bo\$1886b2o\$1885b2o8\$1885bo\$1886b2o\$1885b2o885\$2837bobo\$2838b2o\$2838bo43\$2842bobo\$2843b2o\$2843bo\$2867bo\$2868b2o\$2867b2o2\$2963bo\$2962bo\$2962b3o2\$2923bo\$2923bobo\$2923b2o2\$2857bo\$2855bobo\$2856b2o4\$2951bo\$2951bobo\$2858bobo90b2o\$2859b2o\$2859bo16bo\$2877b2o\$2867bo8b2o\$2868b2o\$2867b2o2\$2924bo\$2923bo\$2923b3o\$2916bobo\$2916b2o\$2917bo2\$2848bobo\$2849b2o\$2834bo14bo\$2835bo\$2833b3o\$2885bo\$2884bo29bo\$2884b3o25b2o6bo\$2913b2o4bo\$2919b3o\$2865bo\$2866bo\$2844bo19b3o\$2845bo\$2843b3o\$2839b2o50bo\$2839b2o49bo16bo\$2890b3o14bobo\$2907b2o2\$2854bo\$2827b2o26b2o\$2828b2o24b2o\$2827b3o17b2o\$2828b3o16b2o\$2828b2o7bo\$2828b5o4bo\$2827b4obo\$2827bo2b2o\$2827b4o\$2828bo6\$2835b3o\$2849b2o\$2835bobo11bobo\$2837b2o4bo5bobob2o\$2838b5obo8b2o\$2836b2o2b2obo6b2ob2o\$2838bo2\$2826b2o\$2825b2ob2o\$2814b2o14b2o\$2813bo2bo11bo3bo\$2812b2ob3o11b3o\$2812bo3bo\$2804b2o6b4o\$2803b2obo6bo\$2803bo2b2o\$2802b2o2b2o9b2o\$2802bo14b2o\$2800b2o\$2796bobo2bo\$2789b2o4b2obo\$2789b2o3b2o2bo\$2795bo2bo\$2796b2o5\$2797b2o\$2797b2o6b3o\$2819b2o\$2805bobo11bobo\$2807b2o4bo5bobob2o\$2808b5obo8b2o\$2806b2o2b2obo6b2ob2o\$2808bo!`

I believe there's a way to get down to O(sqrt(log G)) in the size of the initial bounding box, and a fixed total number of blocks, but the way I'm thinking of doing it is so huge and horrible that I'm too embarrassed to describe it -- never mind whether it will fit in the margin or not...! I'm not sure O(sqrt(log G)) is the theoretical minimum in this case, anyway, because it's okay for the pattern to grow temporarily to any size as long as it cleans itself up and leaves nothing but gliders at the end.

dvgrn
Moderator

Posts: 5746
Joined: May 17th, 2009, 11:00 pm

### Re: Blockic splitters

dvgrn wrote:...your glider-gun trick would be less than 100 blocks

Here is a small optimization for making a smaller Blockic seed for a p30 glider stream, possibly reducing the seed to 90 blocks or less.

Instead of 10 gliders, use 9 gliders and 2 blocks:
`x = 188, y = 134, rule = B3/S23bo\$2bo\$3o73\$185bo\$185bobo\$185b2o\$36bo\$37b2o\$36b2o6\$174bo\$172b2o\$173b2o\$49bo\$50bo\$48b3o5\$85bobo\$86b2o77bo\$86bo77bo\$164b3o6\$127bo\$127bobo\$62bobo62b2o\$63b2o\$63bo18\$76b2o\$76b2o4\$78b2o\$78b2o!`

One of the blocks is stopping a stray glider, but the extra glider may actually be useful.
It is a lot cheaper to add two blocks than to add the tenth synchronized glider.

EDIT:
Here is the updated table of Blockic splitters with dvgrn additions including 9:13, the only n:n+4 example:
`x = 2372, y = 945, rule = 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.D24.A\$136.A60\$2036.2A\$2036.2A4\$2072.2A\$2072.2A6\$2049.A\$1461.2A585.A294.A\$1461.2A585.3A291.A\$2342.3A\$1917.2A\$1468.3D446.2A\$1469.D\$1469.3D\$814.2A24.2A1082.3D\$814.2A24.2A1083.D384.2A\$848.2A1075.3D103.2A19.D257.2A\$848.2A1181.2A19.D.D\$1903.2A147.3D\$1903.2A149.D\$2346.2A\$689.4A2.4A2.4A20.4A10.4A2.4A2.4A568.4A2.4A2.4A20.4A16.4A52.D328.4A2.4A2.4A20.4A10.4A2.4A2.4A375.4A2.4A2.4A20.4A10.4A2.4A2.4A75.2A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A50.D.D328.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A375.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A50.3D328.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A206.2A167.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.4A2.4A2.4A20.4A10.4A2.4A2.4A568.4A2.4A2.4A20.4A16.4A50.D330.4A2.4A2.4A20.4A10.4A2.4A2.4A61.D144.2A167.4A2.4A2.4A20.4A10.4A2.4A2.4A\$1453.2A434.D.D\$1453.2A19.2A413.3D\$689.4A8.4A8.4A8.4A10.4A8.4A568.4A8.4A8.4A8.4A16.4A91.2A288.4A8.4A8.4A8.4A22.4A59.D315.4A8.4A8.4A8.4A22.4A\$689.A2.A8.A2.A8.A2.A8.A2.A10.A2.A8.A2.A568.A2.A8.A2.A8.A2.A8.A2.A16.A2.A381.A2.A8.A2.A8.A2.A8.A2.A22.A2.A79.2A294.A2.A8.A2.A8.A2.A8.A2.A22.A2.A\$689.A2.A8.A2.A8.A2.A8.A2.A10.A2.A8.A2.A97.2A469.A2.A8.A2.A8.A2.A8.A2.A16.A2.A381.A2.A8.A2.A8.A2.A8.A2.A22.A2.A79.2A19.2A273.A2.A8.A2.A8.A2.A8.A2.A22.A2.A\$689.4A8.4A8.4A8.4A10.4A8.4A97.2A469.4A8.4A8.4A8.4A16.4A46.2A333.4A8.4A8.4A8.4A22.4A100.2A273.4A8.4A8.4A8.4A22.4A\$822.2A605.2A\$822.2A1225.2A\$689.4A2.4A2.4A20.4A10.4A8.4A568.4A2.4A2.4A20.4A16.4A381.4A2.4A2.4A20.4A10.4A2.4A2.4A55.2A162.2A154.4A2.4A2.4A20.4A10.4A2.4A2.4A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A8.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A381.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A55.2A318.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A8.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A61.2A318.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A375.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.4A2.4A2.4A20.4A10.4A8.4A568.4A2.4A2.4A20.4A16.4A61.2A25.2A291.4A2.4A2.4A20.4A10.4A2.4A2.4A375.4A2.4A2.4A20.4A10.4A2.4A2.4A\$834.2A635.2A832.2A19.D\$834.2A1469.2A19.D.D36.2A\$701.4A8.4A8.4A10.4A8.4A63.2A515.4A8.4A8.4A16.4A393.4A8.4A8.4A10.4A109.2A288.4A8.4A8.4A22.4A55.3D36.2A\$701.A2.A8.A2.A8.A2.A10.A2.A8.A2.A63.2A515.A2.A8.A2.A8.A2.A16.A2.A393.A2.A8.A2.A8.A2.A10.A2.A109.2A288.A2.A8.A2.A8.A2.A22.A2.A57.D\$701.A2.A8.A2.A8.A2.A10.A2.A8.A2.A580.A2.A8.A2.A8.A2.A16.A2.A393.A2.A8.A2.A8.A2.A10.A2.A399.A2.A8.A2.A8.A2.A22.A2.A\$701.4A8.4A8.4A10.4A8.4A103.2A475.4A8.4A8.4A16.4A393.4A8.4A8.4A10.4A399.4A8.4A8.4A22.4A\$858.2A1488.D\$838.D34.2A578.2A855.2A36.3D\$689.4A2.4A2.4A20.4A10.4A2.4A2.4A83.3D32.2A448.4A2.4A2.4A20.4A16.4A70.2A309.4A2.4A2.4A20.4A10.4A2.4A2.4A375.4A2.4A2.4A20.4A10.4A2.4A2.4A39.2A36.D.D19.2A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A83.D.D24.3A455.A2.A2.A2.A2.A2.A20.A2.A16.A2.A381.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A375.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A79.D19.2A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A85.D24.A457.A2.A2.A2.A2.A2.A20.A2.A16.A2.A381.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A79.2A140.2A152.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.4A2.4A2.4A20.4A10.4A2.4A2.4A111.A456.4A2.4A2.4A20.4A16.4A381.4A2.4A2.4A20.4A10.4A2.4A2.4A79.2A140.2A152.4A2.4A2.4A20.4A10.4A2.4A2.4A\$1477.2A\$1477.2A\$1457.D34.2A\$1457.3D32.2A439.2A\$1457.D.D24.3A446.2A129.2A\$1459.D24.A428.D34.2A114.2A\$1485.A427.3D32.2A\$1913.D.D24.3A\$1915.D24.A\$1941.A\$2074.2A\$2074.2A6\$2047.3D\$2049.D\$2048.3D\$2318.D19.2A\$2316.D.D19.2A\$2056.2A258.3D\$2056.2A258.D4\$2333.2A\$2333.2A\$2312.2A\$2312.2A52\$829.2A\$829.2A11\$1462.2A\$1462.2A\$844.2A\$828.2A14.2A\$828.2A22.2A615.3D\$852.2A616.D\$1470.3D\$1437.2A\$1425.2A10.2A\$684.4A10.4A2.4A2.4A20.4A16.4A557.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A30.2A\$684.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A557.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$684.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A557.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$684.4A10.4A2.4A2.4A20.4A16.4A557.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A3\$684.4A10.4A8.4A8.4A8.4A16.4A557.4A10.4A8.4A8.4A8.4A22.4A34.D\$684.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A557.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A34.3D\$684.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A98.2A457.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A34.D.D\$684.4A10.4A8.4A8.4A8.4A16.4A98.2A457.4A10.4A8.4A8.4A8.4A22.4A36.D22.2A\$826.2A626.2A19.2A\$826.2A647.2A\$684.4A10.4A8.4A20.4A16.4A557.4A10.4A8.4A20.4A10.4A2.4A2.4A49.2A\$684.A2.A10.A2.A8.A2.A20.A2.A16.A2.A557.A2.A10.A2.A8.A2.A20.A2.A10.A2.A2.A2.A2.A2.A49.2A\$684.A2.A10.A2.A8.A2.A20.A2.A16.A2.A557.A2.A10.A2.A8.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$684.4A10.4A8.4A20.4A16.4A557.4A10.4A8.4A20.4A10.4A2.4A2.4A\$838.2A\$838.2A\$684.4A10.4A8.4A8.4A8.4A16.4A64.2A491.4A10.4A8.4A8.4A8.4A10.4A\$684.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A64.2A491.A2.A10.A2.A8.A2.A8.A2.A8.A2.A10.A2.A\$684.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A557.A2.A10.A2.A8.A2.A8.A2.A8.A2.A10.A2.A89.2A\$684.4A10.4A8.4A8.4A8.4A16.4A104.2A451.4A10.4A8.4A8.4A8.4A10.4A89.2A\$862.2A\$877.2A\$684.4A10.4A2.4A2.4A20.4A16.4A119.2A436.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A\$684.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A111.3A443.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$684.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A111.A445.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$684.4A10.4A2.4A2.4A20.4A16.4A112.A444.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A\$1454.2A\$1454.2A4\$1478.2A\$1478.2A\$1458.D34.2A\$1458.3D32.2A\$1458.D.D24.3A\$1460.D24.A\$1486.A!`

I am removing the 12 glider limit, let's see how extreme the ratio can get with up to 10 blocks to start
So far the best ratio in the table is 13/9 = 1.444 gliders per block average.
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Blockic splitters

knightlife wrote:BTW, I really like your n:n+4 solution that simultaneously gets rid of an extra block and avoids adding an extra block to complete the final cascade stage!

Isn't that pretty much the same trick as you use in the 3:4? The idea really widens the search space -- could build a library of glider-producing reactions that eat extra beehives, boats, blinkers, loaves or whatever, and wire them in whenever you need a particular cleanup.

But meanwhile I need some new ideas, or new reactions. Can you see any way to fix the problems in that not-quite-clean 6:9 or 8:12 I posted? Those are my closest approaches to a 1:1.5 ratio so far (for a reasonable-sized pattern).

I thought maybe the 4:5 reaction you wanted could be extracted from known 3:3 or 4:4 patterns, but the only thing I found on a quick review was this 6:8, which is another gap in your table:

`x = 41, y = 44, rule = LifeHistory23.2A\$23.2A3\$15.3D\$16.D\$14.3D12\$8.2A\$8.2A5\$18.2A\$18.2A7\$2A\$2A4\$24.2A\$24.2A\$4.D34.2A\$4.3D32.2A\$4.D.D24.3A\$6.D24.A\$32.A!`

Seems likely there's an 8:10 along the same lines, but I haven't looked. That 4:5 gap is a good challenge... if I'm lucky enough maybe I can dig up a 4:6, and then it will be easy!

knightlife wrote:Maybe after traversing the square, a re-burnable pattern could traverse it again!

Tricky, though not impossible I suppose. Ideally the re-burnable pattern would have to leave its output block(s) behind in exactly the same places as the seed blocks, so that the corners will work the second time around. Or you'd need two different reactions with opposite offsets for each of two pairs of sides; there's no single offset that would work all the way around a square and leave a new square the same size and shape. But a zero-offset reburnable fuse would basically mean you'd discovered a new Blockic Herschel conduit or two (don't let me discourage you -- those would be great to have!)

The next best thing would be a reaction that burns a block and leaves an output block at a good offset left or right of the chain, so that you can set up a series of fuses just in the corners of a large square and burn in an expanding spiral, re-using the block chains.

dvgrn
Moderator

Posts: 5746
Joined: May 17th, 2009, 11:00 pm

### Re: Blockic splitters

knightlife wrote:Instead of 10 gliders, use 9 gliders and 2 blocks:
One of the blocks is stopping a stray glider, but the extra glider may actually be useful.
It is a lot cheaper to add two blocks than to add the tenth synchronized glider.

Oddly enough, it may be cheaper -- or at least easier to find a cheap Blockic recipe -- for this 9-glider-plus-4-block version based on yours, in which gliders only need to be synchronized in pairs:

`x = 84, y = 96, rule = B3/S23obo\$b2o\$bo58\$10b2o\$10b2o4\$12b2o47b2o\$12b2o47b2o\$27b2o21b2o\$27b2o16b2o3bobo\$46b2o2bo\$45bo4\$43b2o\$28b3o11b2o\$30bo13bo\$29bo2\$62b2o\$62bobo\$62bo4\$22b3o\$24bo\$23bo5\$81b2o\$8b2o71bobo\$9b2o70bo\$8bo!`

It also seems vaguely possible that a slow-salvo approach for all but the last two gliders will actually use fewer total blocks -- say, make a block into a traffic light, delete two of the blinkers, move the other two to the right places, and turn them into ships. Might be worth having a look, anyway, now that there's a reasonably good toolkit available for doing this kind of thing.

-----------------------------------------------

I'm starting to have some luck in my slow semi-automated search for reburnable fuses. For this first one, to actually come out ahead the chains would have to be much longer, there would be more chains, and maybe they'd get reburned more times.

This probably isn't a good reaction to spend any more time developing, but it's fun to watch the reburnable-fuse idea in action, even if the one-time turners and cleanup are distinctly sub-optimal:

`x = 596, y = 422, rule = B3/S23394b2o\$394b2o3\$389b2o\$389b2o9\$551b2o\$551b2o10b2o\$563b2o\$298bo\$296bobo\$297b2o252b2o\$551b2o\$517b2o\$517b2o10b2o\$529b2o3\$517b2o75b2o\$517b2o75b2o\$483b2o\$483b2o10b2o\$495b2o2\$426b2o\$426b2o55b2o\$483b2o\$449b2o\$449b2o10b2o\$430b2o29b2o\$430b2o2\$449b2o120b2o\$449b2o120b2o\$415b2o\$415b2o10b2o\$427b2o3\$415b2o120b2o\$415b2o120b2o6\$503b2o\$503b2o6\$469b2o\$469b2o6\$435b2o\$435b2o5\$319b2o\$319b2o80b2o\$346b2o53b2o\$314b2o30b2o\$314b2o45b2o\$323b2o4b2o30b2o\$323b2o4b2o12\$362b2o\$362b2o33\$313b2o\$313b2o4\$317b2o\$317b2o4\$331b2o\$331b2o3\$326b2o\$326b2o35\$229b2o\$229b2o3\$224b2o\$224b2o5\$234b2o\$234b2o3\$239b2o\$239b2o13\$180bo\$178bobo\$179b2o8\$399b2o\$399b2o16b2o\$417b2o5\$365b2o\$365b2o6\$331b2o\$331b2o3\$172b2o\$172b2o2\$297b2o\$297b2o\$176b2o\$176b2o4\$263b2o\$208b2o53b2o\$176b2o30b2o\$176b2o45b2o\$191b2o30b2o\$191b2o12\$196b2o\$196b2o90\$57b2o\$57b2o3\$52b2o\$52b2o26\$83b2o176b2o\$83b2o176b2o16b2o\$279b2o2\$88b2o\$88b2o2\$227b2o\$227b2o6\$193b2o\$193b2o2\$28bo\$26bobo\$27b2o2\$159b2o\$159b2o3\$2o\$2o2\$125b2o\$125b2o\$4b2o\$4b2o4\$91b2o\$36b2o53b2o\$4b2o30b2o\$4b2o45b2o\$19b2o30b2o\$19b2o!`

Here's something better: a pair of Herschels traveling on an orthogonal chain of blocks -- similar to a pair of pi-heptominoes following blinker chains in a Caterpillar, but there's no direct interaction between the Herschels (yet). Even with two-thirds of the gliders getting absorbed by cleanup, you still get gliders out on both sides of the chain.

`x = 621, y = 664, rule = B3/S23619bo\$618bo\$618b3o42\$617bo\$616bo\$616b3o120\$475bo\$474bo\$474b3o42\$473bo\$472bo\$472b3o105\$346bo\$345bo\$345b3o42\$344bo\$343bo\$343b3o105\$217bo\$216bo\$216b3o42\$215bo\$214bo\$214b3o86\$360b2o29b2o\$360b2o29b2o2\$135b2o29b2o29b2o29b2o29b2o29b2o29b2o29b2o29b2o29b2o\$135b2o29b2o29b2o29b2o29b2o29b2o29b2o29b2o29b2o29b2o4\$99bo\$2b2o20b2o20b2o20b2o20b2o6bo\$2b2o20b2o20b2o20b2o20b2o6b3o6\$7b2o20b2o20b2o20b2o20b2o\$7b2o20b2o20b2o20b2o20b2o\$426b2o\$426b2o3\$12b2o20b2o20b2o20b2o\$12b2o20b2o20b2o20b2o18b2o\$98b2o2\$377b2o29b2o\$377b2o29b2o15\$382b2o29b2o\$382b2o29b2o4\$8b2o20b2o101b2o29b2o29b2o29b2o29b2o29b2o29b2o29b2o\$8b2o20b2o101b2o29b2o29b2o29b2o29b2o29b2o29b2o29b2o4\$97bo\$2o20b2o20b2o20b2o20b2o6bo\$2o20b2o20b2o20b2o20b2o6b3o6\$5b2o20b2o20b2o20b2o20b2o\$5b2o20b2o20b2o20b2o20b2o\$362b2o\$362b2o!`

Adding two blocks to the chain increases the total output by 10 gliders, with five burns of the fuse. I believe that means that any 1:N ratio is achievable -- with a finite number of blocks, not just in limit -- by burning the fuse N+1 times, and adjusting the fuse length to get enough extra gliders to account for however many blocks are needed to split and re-route the input glider to create the re-ignition signals, and to do any cleanup.

Cleanup could be done with an HWSS, again, if that isn't cheating... or by using the final output gliders to clean up the blocks in the fuse, at some considerable cost in efficiency (the pattern might be 1:N-3 or 1:N-4 instead of 1:N, with that kind of cleanup.) Am I missing anything else here?

In the fuse, there's a block pair every 31 cells, and one burn moves the blocks by 22 cells backward, so it will take a full 31 burns before the block pairs are lined up again where they started. The reaction, oddly enough, takes exactly 240 ticks to repeat. A search of Life literature for "31c/240" has so far come up blank; does anyone have any prior art for this reaction?

I think it should also be possible to get the fuse to drift obliquely on each burn by deleting the other block, but someone else will have to work out the details there.

dvgrn
Moderator

Posts: 5746
Joined: May 17th, 2009, 11:00 pm

### Re: Blockic splitters

I'm back! Not sure how much this would help:
`x = 26, y = 25, rule = LifeHistory14.2A\$14.2A5\$15.3A2.2A\$17.A2.2A2.2A\$16.A7.2A14\$3A\$2.A\$.A!`

It's a doubly-burnable reaction. Or this:
`x = 11, y = 9, rule = LifeHistory2A\$2A2\$9.2A\$9.2A2\$.3A2.2A\$3.A2.2A\$2.A!`

Just another three-block reflector.
I Like My Heisenburps! (and others)

Extrementhusiast

Posts: 1785
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Blockic splitters

dvgrn wrote:But meanwhile I need some new ideas, or new reactions. Can you see any way to fix the problems in that not-quite-clean 6:9 or 8:12 I posted? Those are my closest approaches to a 1:1.5 ratio so far (for a reasonable-sized pattern).

I tried to improve the near misses you posted but ended up finding the exact same 10:14 you found. A near miss is usually just that: CGOL is not forgiving. For example I found three blocks that make four gliders:
`x = 18, y = 19, rule = LifeHistory4.2A\$4.2A3\$16.A\$15.A\$2A13.3A\$2A5\$6.3D\$6.D.D\$6.D.D3\$7.2A\$7.2A!`

Nothing can be done about the leftover block. However, it can be considered a partial solution to a larger pattern if that leftover block is used later. I may make a collection of partial solutions (only blocks left over).
I thought I finally could make a 4:5 when I found this 3 block pattern:
`x = 28, y = 36, rule = LifeHistory.2A\$.2A3\$2A\$2A14\$2.2A\$2.2A13\$25.3A\$25.A\$26.A!`

Best result I have so far for the above is this 5:5 splitter:
`x = 48, y = 53, rule = LifeHistory21.2A\$21.2A3\$20.2A\$20.2A14\$22.2A\$22.2A13\$45.3A\$45.A\$46.A10\$2A\$2A5\$27.2A\$27.2A!`

Here is a new 4:4 splitter:
`x = 20, y = 27, rule = LifeHistory16.A\$15.A\$15.3A\$2A\$2A4\$6.3D\$6.D.D\$6.D.D\$18.2A\$18.2A\$7.2A\$7.2A6\$9.3D\$11.D\$10.3D3\$18.2A\$18.2A!`

Table update:
`x = 2384, y = 955, rule = 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A2.4A76.2A697.3D32.2A\$A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A56.D34.2A682.D.D24.3A\$A2.A2.A2.A2.A2.A20.A2.A2.A2.A2.A2.A56.3D32.2A684.D24.A\$4A2.4A2.4A20.4A2.4A2.4A56.D.D24.3A717.A\$110.D24.A\$136.A60\$2036.2A\$2036.2A4\$2072.2A\$2072.2A6\$2049.A\$1461.2A585.A294.A\$1461.2A585.3A291.A\$2342.3A\$1917.2A\$1468.3D446.2A\$1469.D\$1469.3D\$814.2A24.2A1082.3D\$814.2A24.2A1083.D384.2A\$848.2A1075.3D103.2A19.D257.2A\$848.2A1181.2A19.D.D\$1903.2A147.3D\$1903.2A149.D\$2346.2A\$689.4A2.4A2.4A20.4A10.4A2.4A2.4A568.4A2.4A2.4A20.4A16.4A52.D328.4A2.4A2.4A20.4A10.4A2.4A2.4A375.4A2.4A2.4A20.4A10.4A2.4A2.4A75.2A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A50.D.D328.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A375.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A50.3D328.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A206.2A167.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.4A2.4A2.4A20.4A10.4A2.4A2.4A568.4A2.4A2.4A20.4A16.4A50.D330.4A2.4A2.4A20.4A10.4A2.4A2.4A61.D144.2A167.4A2.4A2.4A20.4A10.4A2.4A2.4A\$1453.2A434.D.D\$1453.2A19.2A413.3D\$689.4A8.4A8.4A8.4A10.4A8.4A568.4A8.4A8.4A8.4A16.4A91.2A288.4A8.4A8.4A8.4A22.4A59.D315.4A8.4A8.4A8.4A22.4A\$689.A2.A8.A2.A8.A2.A8.A2.A10.A2.A8.A2.A568.A2.A8.A2.A8.A2.A8.A2.A16.A2.A381.A2.A8.A2.A8.A2.A8.A2.A22.A2.A79.2A294.A2.A8.A2.A8.A2.A8.A2.A22.A2.A\$689.A2.A8.A2.A8.A2.A8.A2.A10.A2.A8.A2.A97.2A469.A2.A8.A2.A8.A2.A8.A2.A16.A2.A381.A2.A8.A2.A8.A2.A8.A2.A22.A2.A79.2A19.2A273.A2.A8.A2.A8.A2.A8.A2.A22.A2.A\$689.4A8.4A8.4A8.4A10.4A8.4A97.2A469.4A8.4A8.4A8.4A16.4A46.2A333.4A8.4A8.4A8.4A22.4A100.2A273.4A8.4A8.4A8.4A22.4A\$822.2A605.2A\$822.2A1225.2A\$689.4A2.4A2.4A20.4A10.4A8.4A568.4A2.4A2.4A20.4A16.4A381.4A2.4A2.4A20.4A10.4A2.4A2.4A55.2A162.2A154.4A2.4A2.4A20.4A10.4A2.4A2.4A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A8.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A381.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A55.2A318.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A8.A2.A568.A2.A2.A2.A2.A2.A20.A2.A16.A2.A61.2A318.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A375.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.4A2.4A2.4A20.4A10.4A8.4A568.4A2.4A2.4A20.4A16.4A61.2A25.2A291.4A2.4A2.4A20.4A10.4A2.4A2.4A375.4A2.4A2.4A20.4A10.4A2.4A2.4A\$834.2A635.2A832.2A19.D\$834.2A1469.2A19.D.D36.2A\$701.4A8.4A8.4A10.4A8.4A63.2A515.4A8.4A8.4A16.4A393.4A8.4A8.4A10.4A109.2A288.4A8.4A8.4A22.4A55.3D36.2A\$701.A2.A8.A2.A8.A2.A10.A2.A8.A2.A63.2A515.A2.A8.A2.A8.A2.A16.A2.A393.A2.A8.A2.A8.A2.A10.A2.A109.2A288.A2.A8.A2.A8.A2.A22.A2.A57.D\$701.A2.A8.A2.A8.A2.A10.A2.A8.A2.A580.A2.A8.A2.A8.A2.A16.A2.A393.A2.A8.A2.A8.A2.A10.A2.A399.A2.A8.A2.A8.A2.A22.A2.A\$701.4A8.4A8.4A10.4A8.4A103.2A475.4A8.4A8.4A16.4A393.4A8.4A8.4A10.4A399.4A8.4A8.4A22.4A\$858.2A1488.D\$838.D34.2A578.2A855.2A36.3D\$689.4A2.4A2.4A20.4A10.4A2.4A2.4A83.3D32.2A448.4A2.4A2.4A20.4A16.4A70.2A309.4A2.4A2.4A20.4A10.4A2.4A2.4A375.4A2.4A2.4A20.4A10.4A2.4A2.4A39.2A36.D.D19.2A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A83.D.D24.3A455.A2.A2.A2.A2.A2.A20.A2.A16.A2.A381.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A375.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A79.D19.2A\$689.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A85.D24.A457.A2.A2.A2.A2.A2.A20.A2.A16.A2.A381.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A79.2A140.2A152.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A\$689.4A2.4A2.4A20.4A10.4A2.4A2.4A111.A456.4A2.4A2.4A20.4A16.4A381.4A2.4A2.4A20.4A10.4A2.4A2.4A79.2A140.2A152.4A2.4A2.4A20.4A10.4A2.4A2.4A\$1477.2A\$1477.2A\$1457.D34.2A\$1457.3D32.2A439.2A\$1457.D.D24.3A446.2A129.2A\$1459.D24.A428.D34.2A114.2A\$1485.A427.3D32.2A\$1913.D.D24.3A\$1915.D24.A\$1941.A\$2074.2A\$2074.2A6\$2047.3D\$2049.D\$2048.3D\$2318.D19.2A\$2316.D.D19.2A\$2056.2A258.3D\$2056.2A258.D4\$2333.2A\$2333.2A\$2312.2A\$2312.2A52\$829.2A\$829.2A10\$2364.2A\$1462.2A900.2A\$1462.2A435.2A\$844.2A1053.2A\$828.2A14.2A1510.3D\$828.2A22.2A615.3D885.D\$852.2A616.D884.3D\$1470.3D\$1437.2A\$1425.2A10.2A914.2A\$684.4A10.4A2.4A2.4A20.4A16.4A557.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A30.2A329.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A361.4A10.4A2.4A2.4A20.4A10.4A8.4A76.2A\$684.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A557.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A361.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A361.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A8.A2.A\$684.A2.A10.A2.A2.A2.A2.A2.A20.A2.A16.A2.A557.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A361.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A2.A2.A2.A2.A69.2A290.A2.A10.A2.A2.A2.A2.A2.A20.A2.A10.A2.A8.A2.A105.2A\$684.4A10.4A2.4A2.4A20.4A16.4A557.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A361.4A10.4A2.4A2.4A20.4A10.4A2.4A2.4A69.2A290.4A10.4A2.4A2.4A20.4A10.4A8.4A105.2A3\$684.4A10.4A8.4A8.4A8.4A16.4A557.4A10.4A8.4A8.4A8.4A22.4A34.D326.4A10.4A8.4A8.4A8.4A22.4A361.4A10.4A8.4A8.4A8.4A10.4A8.4A\$684.A2.A10.A2.A8.A2.A8.A2.A8.A2.A16.A2.A557.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A34.3D324.A2.A10.A2.A8.A2.A8.A2.A8.A2.A22.A2.A361.A2.A10.A2.A8.A2.A8.A2.A8.A2.A10.A2.A8.A2.A\$684.A2.A10.A2.A8.A2.A8.A2.A8.A2.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knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Blockic splitters

knightlife wrote:Here is a new 4:4 splitter...

Let's see, there's a simple 7:7 extension of this, though I guess N:N splitters aren't too interesting any more:

`x = 52, y = 27, rule = LifeHistory16.A\$15.A\$15.3A32.2A\$2A48.2A\$2A\$22.2A\$21.D2C\$21.D4.2A\$6.3D12.3D2.2A\$6.D.D38.D\$6.D.D36.3D\$45.D.D\$45.D\$7.2A\$7.2A3\$32.2A\$32.2A2\$9.3D\$11.D\$10.3D3\$18.2A\$18.2A!`

Edit: Here's a new 10:12 along the same lines. Sure wish there was a way to remove that extra B-heptomino block in time, to keep it from eating a block and a glider. It's still possible that a two-block combination will suppress the block and get a glider or two out, but I'm not holding my breath any more...

`x = 69, y = 41, rule = LifeHistory35.2A\$35.2A3\$27.3D\$28.D\$26.3D2\$49.2A\$24.2A23.2A\$24.2A3\$3.2A\$3.2A57.D\$62.D.D\$62.3D\$64.D\$43.2A\$8.3D32.2A\$8.D4.2A\$8.3D2.2A\$20.D\$20.D.D44.2A\$20.3D44.2A\$22.D3\$.2A\$A.A\$2.A28.2A\$11.2A18.2A\$11.2A7\$28.2A\$28.2A!`

The 6:8 doesn't seem to have made it into the table yet. Here are some 8:10's to fill in the other gap in that column. The first is a composition of reactions already in the table; the second is an extension of the 6:8; and the one on the right is based on your G+3B4->4G+B4.

`x = 339, y = 56, rule = LifeHistory311.2A\$311.2A\$332.2A\$332.2A\$126.2A59.2A\$126.2A59.2A2\$315.D\$133.3D43.3D133.3D\$134.D45.D134.D.D19.2A\$134.3D41.3D136.D19.2A5\$2A\$2A3\$7.3D\$8.D\$8.3D2\$69.2A\$69.2A\$128.2A\$128.2A\$61.3D\$62.D119.2A\$60.3D119.2A\$135.2A\$135.2A2\$295.2A\$295.2A\$32.2A\$32.2A130.2A155.2A\$17.2A145.2A128.D.D24.2A\$17.2A275.D.D\$5.2A287.3D\$5.2A\$188.2A\$188.2A\$168.D34.2A111.2A\$67.2A99.3D32.2A83.2A26.2A\$7.3A57.2A99.D.D24.3A90.2A13.3A\$7.A162.D24.A107.A\$8.A187.A107.A2\$60.2A\$60.2A230.2A\$292.2A3\$7.2A\$7.2A!`

For that matter, if ten blocks is allowable now, the 6:8 can be extended further to get a new (though ridiculously slow) 10:13 as well:

`x = 91, y = 44, rule = LifeHistory73.2A\$73.2A3\$65.3D\$66.D\$64.3D6\$2A\$2A3\$7.3D\$8.D\$8.3D3\$34.2A\$34.2A\$49.2A\$49.2A17.2A\$68.2A7\$50.2A\$2.2A46.2A\$2.2A3\$74.2A\$9.2A63.2A\$9.2A43.D34.2A\$54.3D32.2A\$54.D.D24.3A\$56.D24.A\$82.A!`

I have an uneasy feeling there's a 10:15 lurking around here somewhere -- maybe something that re-uses blocks from two Herschels, or some other prolific reaction with two blocks left over -- just haven't found it yet...!

dvgrn
Moderator

Posts: 5746
Joined: May 17th, 2009, 11:00 pm

### Re: Blockic splitters

dvgrn wrote:... Here's a new 10:12 along the same lines. Sure wish there was a way to remove that extra B-heptomino block in time, to keep it from eating a block and a glider.

The following is another new 10:12, with a couple of minor new features. It cleans up one extra block with a "sideswipe" reaction -- a 3:4 splitter removes the block with a passing spark, without using up any output gliders.

`x = 72, y = 54, rule = LifeHistory67.2A\$67.2A3\$59.3D\$60.D\$.A16.2A19.D18.3D\$2.A15.2A19.D.D\$3A36.3D\$41.D4\$23.2A\$23.2A\$44.2A\$44.2A5\$70.2A\$70.2A3\$45.D\$45.D.D\$11.2A32.3D\$11.2A34.D\$26.2A26.2A\$26.2A26.2A12\$32.2A\$32.2A9\$38.2A\$38.2A!`

There's also another "optional block" in the southeast corner that is currently deleted automatically because it doesn't get used as part of a reaction. Finding a good use for this block would free up another output glider.

Edit: Here are a couple of slow multi-stage 10:12 reactions that use an intermediate blinker to split a pi into two gliders. Again there's a leftover block that it would be nice to find a better use for:
`x = 345, y = 81, rule = LifeHistory74.2A\$74.2A3\$66.3D\$67.D\$65.3D6\$92.2A\$92.2A186.2A\$280.2A\$301.2A\$301.2A2\$77.3D2.2A\$77.D4.2A\$77.3D204.D\$284.3D29.2A\$284.D.D19.2A8.2A\$286.D19.2A\$69.2A\$69.2A3\$69.D.D\$69.D.D\$69.3D\$322.2A\$322.2A3\$5.2A\$5.2A2\$30.2A\$30.2A35.2A\$23.D43.2A\$21.3D\$2A19.D.D\$2A19.D\$300.2A26.2A\$300.2A26.2A\$56.3D249.D34.2A\$56.D4.2A245.3D32.2A\$56.3D2.2A245.D.D24.3A\$310.D24.A\$336.A2\$273.3D\$269.2A4.D\$269.2A2.3D8\$34.3D\$36.D\$35.3D3\$43.2A\$43.2A250.3D\$295.D\$294.3D3\$287.2A\$287.2A4\$45.2A\$45.A.A\$45.A!`

dvgrn
Moderator

Posts: 5746
Joined: May 17th, 2009, 11:00 pm

### Re: Blockic splitters

Here is a 9:13 that was made with a different front end:
`x = 80, y = 65, rule = LifeHistory18.2A\$18.2A4\$54.2A\$54.2A16\$34.D\$10.A23.D.D36.2A\$2A9.A22.3D36.2A\$2A7.3A24.D\$15.2A\$15.2A\$56.D\$56.3D\$56.D.D19.2A\$58.D19.2A23\$26.D19.2A\$24.D.D19.2A\$24.3D\$24.D4\$41.2A\$41.2A\$20.2A\$20.2A!`

The extra block is deleted by a fortunate collision, but that wastes an extra glider that was gained at the start. But it still matches the best ratio so far for patterns in the table.

Updated table with the 6:8, the 7:7 and others posted above:
`x = 2477, y = 955, rule = 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The table could be filled in for 9:9 and 10:10 by blocking one output of a more efficient splitter but I would rather not do that. The glaring gap in the table is 4:5 but 4:6 would be nice
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

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