Single-Channel Quadratic Growth Challenge
Posted: October 11th, 2017, 7:54 pm
Here’s a challenge for anyone who wants to work their way into building self-constructing circuitry, in small easy steps. This came up recently over in the ConwayLife Lounge. (invite link)
Imagine a pattern along the lines of the most recent spiral-growth pattern -- except that instead of building a simple Snark at each corner, it builds a glider splitter. One branch turns 90 degrees as before, but the other branch just continues straight, with a small lateral offset. An elbow is placed on both output lanes so that the construction can be repeated on both branches.*
This is all pretty darn easy nowadays, with slmake and a Snarkmaker recipe available.
… I post things like this every now and then, and usually nobody takes me up on the challenge, so then I have to do it myself.
Someone should please explain why this is. I’m intending this challenge in particular to be what Bill Gosper calls an “insurmountable opportunity”, seeing as it’s a good first step on the way to a completed honest-to-Golly quadratic-growth replicator.
* The elbow on the straight-ahead branch could possibly be set up to do a mirror-image construction. If both branches have the same chirality, you end up with a branching pattern that looks kind of like Langton's Loops replication. I haven't looked much at what would happen with other branching options, like two different chiralities, a T-shaped glider splitter, etc.
Imagine a pattern along the lines of the most recent spiral-growth pattern -- except that instead of building a simple Snark at each corner, it builds a glider splitter. One branch turns 90 degrees as before, but the other branch just continues straight, with a small lateral offset. An elbow is placed on both output lanes so that the construction can be repeated on both branches.*
This is all pretty darn easy nowadays, with slmake and a Snarkmaker recipe available.
- First use slmake to compile Scorbie’s G-to-2G without the Snark, but with the two extra elbow blocks.
- Then use the current Snarkmaker recipe to make a Snark out of the elbow that you just used to build the G-to-2G.
Code: Select all
Snarkmaker: 93,91,118,91,151,90,159,91,92,90,136,90,90,154,90,101,104,165,129,91,109,91,93,91,97,90,91,111,91,116,91,94,330,91,90,95,91,90,90,91,123,90,91,152,90,90,93,91,116,91,131,91,95,188,113,91,91,147,122,91,173,91,91,133,247,92,90,109,91,93,91,129,148,91,93,154,90,134,91,91,90,91,91,111,91,91,91,91,91,109,90,93,91,91,158,94,113,91,90,91,96,90,142,91,109,91,94,91,91,179,91,90,94,91,114,90,166,90,90,90,91,117,90,96,90,90,95,91,91,109,91,93,90,156,91,91,94,91,90,147,117,91,144,90,91,128,100,91,90,105,91,91,109,91,94,91,91,124,91,105,90,169,91,90,116,91,142,90,90,91,109,91,93,91,92,91,90,90,95,102,91,91,91,130,91,90,136,91,91,119,113,90,91,114,90,109,91,94,91,91,179,91,90,94,91,102,91,151,90,90,101,90,91,125,184,90,90,90,109,91,94,91,91,179,91,90,94,91,102,91,151,90,90,101,90,91,125,184,90,90,90,109,91,93,90,140,150,132,212,103,90,98,90,148,90,90,91,91,91,119,101,108,90,91,91,119,90,109,91,94,91,90,99,90,112,90,91,105,90,121,118,103,90,144,117,95,91,109,91,93,91,92,91,90,90,95,102,91,91,91,130,91,90,136,91,91,119,113,90,91,114,91,109,90,93,91,91,181,90,95,110,114,100,160,90,143,91,119,90,106,129,109,91,93,91,92,91,90,90,162,91,91,90,129,91,113,90,90,90,90,109,91,93,90,140,150,142,91,90,111,91,91,193,97,91,91,155,90,98,90,91,93,91,151,90,139,180,103,115,167,91,120,139,135,91,91,170,109,91,93,90,155,106,91,121,90,90,91,137,90,232,90,91,91,94,90,171,90,91,103,102,109,91,93,91,137,90,166,91,102,90,104,91,96,96,91,90,90,90,166,90,90,93,90,91,109,91,94,91,91,124,91,105,91,119,91,132,99,90,90,90,150,160,116,91,91,91,90,96,90,90,109,91,93,90,171,90,90,91,90,91,90,91,129,144,90,90,120,90,91,91,169,90,91,109,91,93,91,118,90,91,91,91,104,219,91,135,105,154,90,91,164,91,132,90,90,140,94,93,90,96,90,90,91,149,90,90,161,100,109,91,93,91,92,91,90,90,124,91,142,90,90,91,91,112,90,102,102,103,90,90,90,117,112,90,189,90,90,109,91,93,91,92,91,90,90,162,91,91,90,129,91,113,90,90,90,90,109,91,93,91,92,90,97,91,116,91,145,90,91,98,90,90,188,91,91,91,90,115,91,109,91,93,91,97,91,90,91,120,91,117,91,123,90,118,91,146,110,160,90,109,91,93,90,129,148,90,93,90,143,96,92,90,165,90,118,90,90,91,91,109,91,94,91,91,93,90,158,90,91,90,90,116,104,109,91,94,91,91,167,90,90,91,95,90,90,148,90,151,90,90,136,134,155,115,103,91,109,91,93,90,155,106,91,121,90,90,91,137,90,232,90,91,91,94,90,171,90,91,103,101,109,91,94,91,91,136,91,91,90,168,90,90,110,90,90,93,91,111,91,91,90,132,91,91,93,91,118,90,137,91,173,93,158,90,90,90,118,90,91,90,151,154,167,91,133,90,119,178,155,90,90,90,109,91,94,91,91,95,91,90,93,218,142,90,91,161,90,138,90,162,91,90,140,95,109,109,91,93,91,92,91,98,201,91,129,90,90,90,90,90,103,90,108,90,104,90,109,91,93,90,129,148,90,93,90,143,96,92,90,165,90,118,90,90,91,91,109,91,94,91,91,179,91,90,94,91,111,90,90,90,171,91,110,91,154,90,132,91,109,91,94,91,91,124,90,144,90,90,90,165,119,90,104,90,100,90,90,91,109,91,93,91,92,91,90,90,162,91,91,90,129,91,113,90,90,90,91,109,91,94,91,91,95,91,90,93,218,172,90,90,90,116,112,341,107,106,90,163,91,90,109,91,93,90,169,90,91,103,91,133,90,90,91,91,90,110,91,93,90,112,171,90,109,91,94,91,91,171,91,90,113,90,97,114,90,105,90,139,90,113,90,106,98,121,90,109,91,94,91,91,124,90,142,90,90,146,91,153,90,102,91,152,108,97,91,109,91,94,91,91,124,90,170,90,90,91,90,99,91,90,91,110,121,161,117,115,137,90,91,90,109,90,93,91,91,128,90,139,91,90,97,91,124,157,91,90,90,129,144,91,91,147,130,91,90,90,91,90,140,90,92,90,90,109,91,93,90,156,91,91,102,91,91,90,90,106,91,166,90,125,91,90,126,91,109,91,94,91,91,179,91,90,94,91,102,91,151,90,90,101,90,91,125,184,90,90,90,93,91,151,90,139,180,103,115,167,91,120,139,135,91,91,170,109,90,93,91,91,128,90,139,91,90,97,91,124,157,91,90,90,129,144,91,91,147,130,91,90,90,91,90,140,90,92,90,90,109,91,93,91,145,215,114,91,121,91,150,91,91,153,91,141,90,91,91,90,123,91,109,90,101,169,213,133,195,90,132,143,91,139,138,158,151,99,91,108,99,91,90,91,91,90,91,131,91,109,91,93,90,156,91,91,96,132,91,91,106,91,90,119,185,91,96,90,132,90,91,90,142,109,91,94,91,91,124,90,170,90,90,91,90,99,91,90,91,110,121,161,117,115,137,90,91,90,109,91,93,90,155,106,91,121,90,90,91,137,90,232,90,91,91,94,90,171,90,91,103,102,109,91,93,90,129,148,91,102,91,91,145,178,91,115,90,90,91,104,90,90,92,249,90,90,91,109,91,94,91,90,152,91,90,91,117,90,91,111,91,91,118,90,145,90,100,116,90,90,99,90,109,91,94,91,91,128,126,90,161,151,90,109,91,90,90,94,144,106,90,94,90,90,90,109,91,94,91,91,124,91,105,90,169,91,90,116,91,142,90,90,91,109,91,93,90,140,150,108,91,90,111,91,91,194,98,90,169,90,109,91,94,91,91,141,90,171,90,155,90,111,91,90,130,90,91,90,97,90,90,109,91,94,91,91,121,90,90,90,90,90,90,99,90,165,119,90,106,90,90,91,109,91,94,91,91,93,90,95,90,113,90,99,90,156,90,90,90,138,170,109,91,94,91,91,92,90,169,90,90,90,107,90,90,91,90,95,91,91,109,91,93,90,171,90,90,91,90,91,90,91,129,144,90,90,120,90,91,91,169,90,91,109,90,95,245,90,131,135,90,90,154,90,91,91,91,111,90,90,91,91,128,91,96,91,109,91,94,91,91,124,91,105,91,119,91,132,99,90,90,90,150,160,116,91,91,91,90,96,90,91,93,91,116,91,151,90,109,111,127,91,1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- Then… you’re done already. (!)
- -- Well, you might want to decide how far to push the elbow blocks before you start building.
- And you have to design something to store the completed recipe in, but that’s easy.
- A simple loop with a couple of Snarks and two of the same G-to-2Gs would work fine.
- Or you can borrow or improve on the existing storage unit from the triple wickstretcher
- You’ll eventually want to scatter some eaters and things all around the Recipe Storage Unit, EDIT: and add some to the splitter recipe too -- see below.
- That way the quadratically-growing streams of gliders won’t bend around and blow everything up.
- Though that would be kind of cool too, of course.
- It’s easy enough to cross (or burn) that bridge when you come to it.
Code: Select all
x = 123, y = 108, rule = B3/S23
41b2o$41b2o8$121b2o$121b2o20$44b2o11bo$44b2o10bobo$56bobo31b2o$55b2ob
3o2b2o25bo$61bo2bo23bobo$55b2ob3o3bobo21b2o$55b2obo6b2o7$52b2o13b2o$
52b2o13b2o$37b2o$36bo2bo$35bob2o$35bo$34b2o$49b2o$49bo$50b3o23b2o$52bo
24bo$74b3o$74bo7b2o$83bo$80b3o$80bo18$3b2o$4bo$2bo$2b5o14b2o$7bo13bo$
4b3o12bobo$3bo15b2o$3b4o$b2o3bo3b2o$o2b3o4b2o$2obo$3bo$3b2o3$11b2o$12b
o$9b3o$9bo11$36b2o$36bobo$36bo!
Someone should please explain why this is. I’m intending this challenge in particular to be what Bill Gosper calls an “insurmountable opportunity”, seeing as it’s a good first step on the way to a completed honest-to-Golly quadratic-growth replicator.
* The elbow on the straight-ahead branch could possibly be set up to do a mirror-image construction. If both branches have the same chirality, you end up with a branching pattern that looks kind of like Langton's Loops replication. I haven't looked much at what would happen with other branching options, like two different chiralities, a T-shaped glider splitter, etc.