Traffic jam redux

[dvgrn]

Some improvements that hotdogPi made recently to the LifeWiki traffic jam article got us into some trouble in follow-up discussion on Discord, because more and more explanation seemed to be needed to explain exactly how the three infinite families of traffic jam oscillators from 1994 can be extended. The three families were 100+4n, 102+6n, and 100+10n; other families showed up later, like I think p112+14n in 1999.

There are two different kinds of corners, a "fast corner" (25 ticks) and a "slow corner" (75 ticks). Sometimes to get the next oscillator in a family, it seems to me you have to switch to a different kind of corner. So is it really the same family? Or maybe are there four families, like 102+12n and 108+12n?

(I'm just temporarily confused, and would like to try to get everything sorted out here before attempting to make any further adjustments to the LifeWiki article.)

[dvgrn]

Another side issue is the somewhat awkward size of the long thin example oscillators in the current article, with 25 signals in each one.

It occurs to me that those patterns don't really have to be long and thin. A first rebuild of a p2700 loop suitable for making a p108 oscillator looks like this:

Code: Select all

x = 385, y = 363, rule = B3/S23
36bo2bo$36bo$18b4o13bo4bo$17bo4bo11bobo2b2o$17bo3bobo8b2obo$18bo3bobo
348b2o$24bo347b4o$24bo7bo2bo321bo13bo2bobo$21bo2bo4bo4b2o317b4obo11bob
o2b2o$6b2o14b2o5bo323b3obobo9bobo$6b2o21bo328bobo7b2o$359bo8b3o$25b3o
3b3o324b2o9bobo$5b3o350b2o10b2o$5b2obo2b2o16bo328b2o4b3o$7b2o2b2o16bo$
7b2o20bo332bo5bo$15b3o344bo5bo$362bo5bo12b2o$13bo5bo361b2o$13bo5bo344b
3o$13bo5bo7b3o21b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo
10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo29bo$
36b3o25bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo28bobo$15b3o
7bo5bo17bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo
8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo23b2o2bo2bo$10b
2o13bo5bo2bo5bo8bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo
17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo32b2obo$9b4o12bo5bo2bo5bo8bo5bo4b3o
3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o
3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o
3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o23b2o$8bo2bobo20bo5bo319b3o10bo$7bobo
2b2o13b3o21b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o
10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo20bo$6bobo
27b3o25bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo5bo5bo8bo$5b
2o17bo39bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo5bo5bo$5b3o
16bo333bo5bo4b3o3b3o$6bobo15bo$7b2o351b3o10bo$20b3o3b3o344bo$373bo4b4o
$24bo352bo4bo$24bo352bo3bobo$24bo335bo17bo3bobo$360bo23bo$360bo23bo$
381bo2bo$356b3o3b3o17b2o$22b3o$360bo$20bo5bo333bo$20bo5bo333bo$20bo5bo
2$22b3o2$360b3o2$358bo5bo$24bo333bo5bo$24bo333bo5bo$24bo$360b3o$20b3o
3b3o2$24bo$24bo$24bo335bo$360bo$360bo2$356b3o3b3o$22b3o$360bo$20bo5bo
333bo$20bo5bo333bo$20bo5bo2$22b3o2$360b3o2$358bo5bo$24bo333bo5bo$24bo
333bo5bo$24bo$360b3o$20b3o3b3o2$24bo$24bo$24bo335bo$360bo$360bo2$356b
3o3b3o$22b3o$360bo$20bo5bo333bo$20bo5bo333bo$20bo5bo2$22b3o2$360b3o2$
358bo5bo$24bo333bo5bo$24bo333bo5bo$24bo$360b3o$20b3o3b3o2$24bo$24bo$
24bo335bo$360bo$360bo2$356b3o3b3o$22b3o$360bo$20bo5bo333bo$20bo5bo333b
o$20bo5bo2$22b3o2$360b3o2$358bo5bo$24bo333bo5bo$24bo333bo5bo$24bo$360b
3o$20b3o3b3o2$24bo$24bo$24bo335bo$360bo$360bo2$356b3o3b3o$22b3o$360bo$
20bo5bo333bo$20bo5bo333bo$20bo5bo2$22b3o2$360b3o2$358bo5bo$24bo333bo5b
o$24bo333bo5bo$24bo$360b3o$20b3o3b3o2$24bo$24bo$24bo335bo$360bo$360bo
2$356b3o3b3o$22b3o$360bo$20bo5bo333bo$20bo5bo333bo$20bo5bo2$22b3o2$
360b3o2$358bo5bo$24bo333bo5bo$24bo333bo5bo$24bo$360b3o$20b3o3b3o2$24bo
$24bo$24bo335bo$360bo$360bo2$356b3o3b3o$22b3o$360bo$20bo5bo333bo$20bo
5bo333bo$20bo5bo2$22b3o2$360b3o2$358bo5bo$24bo333bo5bo$24bo333bo5bo$
24bo$360b3o$20b3o3b3o2$24bo$24bo$24bo335bo$360bo$360bo2$356b3o3b3o$22b
3o$360bo$20bo5bo333bo$20bo5bo333bo$20bo5bo2$22b3o2$360b3o2$358bo5bo$
24bo333bo5bo$24bo333bo5bo$24bo$360b3o$20b3o3b3o2$24bo$24bo$24bo335bo$
360bo$360bo2$356b3o3b3o$22b3o$360bo$20bo5bo333bo$20bo5bo333bo$20bo5bo
2$22b3o2$360b3o2$358bo5bo$24bo333bo5bo$24bo333bo5bo$24bo$360b3o$20b3o
3b3o2$24bo$24bo$24bo335bo$360bo$360bo2$356b3o3b3o$22b3o$360bo$20bo5bo
333bo$20bo5bo333bo$20bo5bo2$22b3o2$360b3o2$358bo5bo$24bo333bo5bo$24bo
333bo5bo$24bo$360b3o$20b3o3b3o2$24bo$24bo$24bo335bo$360bo$360bo2$356b
3o3b3o$22b3o$360bo$20bo5bo333bo$20bo5bo333bo$20bo5bo2$22b3o2$360b3o2$
358bo5bo$24bo333bo5bo$24bo333bo5bo$24bo$360b3o$20b3o3b3o2$24bo$24bo$
24bo335bo$360bo$360bo2$356b3o3b3o$22b3o$360bo$20bo5bo333bo$20bo5bo333b
o$20bo5bo2$22b3o2$360b3o2$358bo5bo$24bo333bo5bo$24bo333bo5bo$24bo$360b
3o$b2o17b3o3b3o$o2bo$o23bo$o23bo$obo3bo17bo335bo$bobo3bo352bo$2bo4bo
352bo$3b4o4bo$11bo344b3o3b3o$11bo10b3o351b2o$360bo15bobo$7b3o3b3o4bo5b
o333bo16b3o$20bo5bo5bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo
23bo15bo17b2o$11bo8bo5bo5bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23b
o23bo23bo31bobo$11bo20bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo
10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o
10bo10b3o13b2o2bobo$11bo10b3o346bobo2bo$3b2o23b3o3b3o4bo5bo4b3o3b3o4bo
5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo
5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo
5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo12b4o$5bob2o32bo5bo17bo5bo17bo5bo17bo5b
o17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5b
o13b2o$bo2bo2b2o23bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5b
o8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo
5bo7b3o$bobo28bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo$
2bo29bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo
10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o7bo5bo$18b
3o344bo5bo$2b2o361bo5bo$2b2o12bo5bo$16bo5bo344b3o$16bo5bo332bo20b2o$
355bo16b2o2b2o$18b3o4b2o328bo16b2o2bob2o$13b2o10b2o350b3o$13bobo9b2o
324b3o3b3o$14b3o8bo$15b2o7bobo328bo21b2o$13bobo9bobob3o323bo5b2o14b2o$
8b2o2bobo11bob4o317b2o4bo4bo2bo$8bobo2bo13bo321bo2bo7bo$9b4o347bo$10b
2o348bobo3bo$349bob2o8bobo3bo$344b2o2bobo11bo4bo$344bo4bo13b4o$348bo$
345bo2bo!

From here it should be easy to fold the loop up into a much much smaller shape, just by adding more corners. I'm just not clear yet whether that will actually make them easier to look at in the context of a LifeWiki article, or if a simple square like the above might be better.

EDIT: I'm thinking that a loop like this would make a better illustration. This is the same p2700 loop folded up in a reasonably clean way:

Code: Select all

x = 326, y = 196, rule = B3/S23
36bo2bo$36bo$18b4o13bo4bo$17bo4bo11bobo2b2o$17bo3bobo8b2obo$18bo3bobo$
24bo287bo2bo$24bo7bo2bo276bo$21bo2bo4bo4b2o258b4o13bo4bo$6b2o14b2o5bo
263bo4bo11bobo2b2o$6b2o21bo263bo3bobo8b2obo$294bo3bobo$25b3o3b3o266bo$
5b3o292bo7bo2bo$5b2obo2b2o16bo267bo2bo4bo4b2o$7b2o2b2o16bo268b2o5bo$7b
2o20bo275bo$15b3o$301b3o3b3o$13bo5bo301b2o$13bo5bo285bo15b2o$13bo5bo7b
3o21b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o
10bo10b3o10bo10b3o10bo24bo15b2o$36b3o25bo23bo23bo23bo23bo23bo23bo23bo
23bo23bo24bo16bo$15b3o7bo5bo17bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5b
o8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo10b3o27bobo$10b2o13bo
5bo2bo5bo8bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5b
o17bo5bo44b3obobo$9b4o12bo5bo2bo5bo8bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo
4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo
4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo20b4obo$8bo2bobo20bo5bo248bo
5bo5bo18bo$7bobo2b2o13b3o21b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo
10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo8bo5bo5bo$6bobo27b3o25bo
23bo23bo23bo23bo23bo23bo23bo23bo23bo20bo10b3o$5b2o17bo39bo23bo23bo23bo
23bo23bo23bo23bo23bo23bo10b3o$5b3o16bo272b3o3b3o4bo5bo$6bobo15bo285bo
5bo$7b2o292bo8bo5bo$20b3o3b3o272bo$301bo10b3o4b2o$24bo293b4o$24bo292bo
bo2bo$24bo292b2o2bobo$322bobo$299b3o22b2o$323b3o$297bo5bo18bobo$22b3o
272bo5bo18b2o$297bo5bo$20bo5bo$20bo5bo272b3o$20bo5bo2$22b3o2$240b2o14b
2o43bo$236b2o2b2o13b4o42bo$236b2o2bob2o10bo2bobo41bo$24bo216b3o9bobo2b
2o$24bo227bobo42b3o3b3o$24bo226b2o$241b2o8b3o47bo$b2o17b3o3b3o212b2o9b
obo46bo$b2o243b3o4b2o14b2o30bo$24bo244b2o$bo22bo219bo5bo$obo21bo219bo
5bo19bo$o2bo2b2o236bo5bo18bobo$4bob2o256b2o2bo2bo27b3o$2b2o7bo234b3o
15b2obo$11bo248bo7b2o27bo5bo$11bo10b3o235bo36bo5bo$260bo36bo5bo$7b3o3b
3o4bo5bo$20bo5bo5bo23bo23bo23bo23bo23bo23bo23bo23bo23bo7b3o3b3o34b3o$
11bo8bo5bo5bo23bo23bo23bo23bo23bo23bo23bo23bo23bo$11bo20bo10b3o10bo10b
3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo
11bo$4bo2bo3bo10b3o235bo$4bo23b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5b
o4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5b
o4b3o3b3o4bo5bo4b3o3b3o7bo3bo2bo$3bo4bo32bo5bo17bo5bo17bo5bo17bo5bo17b
o5bo17bo5bo17bo5bo17bo5bo17bo5bo27bo33bo$2bobo2b2o23bo8bo5bo8bo8bo5bo
8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo14bo
4bo32bo$2obo28bo23bo23bo23bo23bo23bo23bo23bo23bo23bo14b2o2bobo31bo$32b
o10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o
10bo10b3o10bo19bob2o$18b3o276b3o3b3o$o2bo247b3o$2b2o12bo5bo245bo2bo29b
o$16bo5bo226bo5bo12b2o31bo$16bo5bo226bo5bo45bo$249bo5bo$18b3o4b2o$13b
2o10b2o224b3o$13b2o$13b2o284b3o$14bo9b3o$13bobo8b2obo2b2o265bo5bo$8b3o
bobo11b2o2b2o221bo43bo5bo$8b4obo12b2o225bo43bo5bo$12bo240bo$299b3o$
249b3o3b3o2$253bo$253bo$253bo47bo$18bo2bo13b2o264bo$21bo15bob2o260bo$
17bo4bo10bo2bo2b2o$17b2o2bobo9bobo261b3o3b3o$22bob2o8bo216b3o$301bo$
34b2o213bo5bo45bo$22bo2bo3bo4b2o213bo5bo18b2o25bo$6b2o14b2o5bo219bo5bo
18b2o$6b2o21bo244b2o$6b2o243b3o21bo$6bo18b3o3b3o240bobo$5bobo261b3obob
o23b3o$6bobob3o16bo239b4obo$7bob4o16bo243bo23bo5bo$8bo20bo223bo10b3o
30bo5bo$15b3o235bo43bo5bo$253bo8bo5bo$13bo5bo242bo5bo30b3o$13bo5bo229b
3o3b3o4bo5bo$13bo5bo7b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o
10bo10b3o10bo10b3o10bo10b3o10bo10b3o$40bo23bo23bo23bo23bo23bo23bo23bo
23bo20bo10b3o$15b3o7bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo
8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo5bo$25bo5bo17bo5bo17bo5bo17bo5bo
17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo5bo18b2o27bo$8b2o15bo5bo4b3o
3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o
3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo20b2o2b2o27bo$8b2o
2b2o254b2o2bob2o25bo$6b2obo2b2o13b3o10bo10b3o10bo10b3o10bo10b3o10bo10b
3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o27b3o$6b3o31bo23bo23bo
23bo23bo23bo23bo23bo23bo24bo39b3o3b3o$24bo15bo23bo23bo23bo23bo23bo23bo
23bo23bo24bo$24bo232bo15b2o26bo$7b2o15bo248b2o26bo$7b2o244b3o3b3o39bo$
20b3o3b3o$257bo$24bo225b2o5bo$24bo225b2o5bo4b2o$24bo236bo2bo34b3o$251b
o9bo$250bobo8bo35bo5bo$245b2o2bo2bo8bobo3bo29bo5bo$245b2obo13bobo3bo
28bo5bo$22b3o224b2o12bo4bo$264b4o31b3o$20bo5bo$20bo5bo$20bo5bo2$22b3o
276bo$301bo$301bo2$297b3o3b3o$24bo$24bo276bo$24bo276bo$301bo$b2o17b3o
3b3o$o2bo$o23bo$o23bo$obo3bo17bo274b3o$bobo3bo$2bo4bo289bo5bo$3b4o4bo
285bo5bo$11bo285bo5bo12b2o$11bo10b3o290bo2bo$299b3o16bo$7b3o3b3o4bo5bo
291bo$20bo5bo5bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo15bo3bobo$
11bo8bo5bo5bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo14bo3bobo$11b
o20bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo
10b3o10bo10b3o10bo10b3o10bo10b3o10bo14bo4bo$11bo10b3o287b4o$3b2o23b3o
3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o
3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o
3b3o4bo5bo4b3o3b3o7bo$5bob2o32bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo
17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo20bo$bo2bo2b2o23bo8bo5bo8bo8bo5bo8b
o8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo
8bo8bo5bo8bo11bo$bobo28bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo23bo$
2bo29bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo
10b3o10bo10b3o10bo10b3o10bo10b3o10bo7b3o3b3o$18b3o$2b2o304bo$2b2o12bo
5bo285bo4bo2bo$16bo5bo285bo7bo$16bo5bo271b3o15bo4bo$312b2o2bobo$18b3o
4b2o265bo5bo18bob2o$13b2o10b2o265bo5bo$13bobo9b2o265bo5bo$14b3o8bo291b
o2bo$15b2o7bobo267b3o4b2o14b2o$13bobo9bobob3o257b2o10b2o$8b2o2bobo11bo
b4o257bobo9b2o$8bobo2bo13bo262b3o8bo$9b4o278b2o7bobo$10b2o277bobo9bobo
b3o$284b2o2bobo11bob4o$284bobo2bo13bo$285b4o$286b2o!

[dvgrn]

This is the same p2700 loop folded up in a reasonably clean way...

Oh, good. I must have just done something wrong in my earlier attempts at adjusting the p102+6n family.

Once I have the p2700 loop, I can adjust it to make a p2550 loop (which is what's needed to make the smallest +/-6n family member, p102):

Code: Select all

x = 313, y = 196, rule = B3/S23
36bo2bo$36bo$18b4o13bo4bo$17bo4bo11bobo2b2o$17bo3bobo8b2obo$18bo3bobo$
24bo$24bo7bo2bo265b2o$21bo2bo4bo4b2o264b4o$6b2o14b2o5bo255bo13bo2bobo$
6b2o21bo251b4obo11bobo2b2o$281b3obobo9bobo$25b3o3b3o252bobo7b2o$5b3o
279bo8b3o$5b2obo2b2o16bo256b2o9bobo$7b2o2b2o16bo256b2o10b2o$7b2o20bo
256b2o4b3o$15b3o$290bo5bo$13bo5bo270bo5bo$13bo5bo270bo5bo12b2o$13bo5bo
7b3o21b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b
3o10bo10b3o10bo52b2o$36b3o25bo23bo23bo23bo23bo23bo23bo23bo23bo35b3o$
15b3o7bo5bo17bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo
5bo8bo8bo5bo8bo8bo5bo8bo10b3o10bo29bo$10b2o13bo5bo2bo5bo8bo5bo17bo5bo
17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo32bo28bobo$9b4o12bo5b
o2bo5bo8bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo
4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo
8bo23b2o2bo2bo$8bo2bobo20bo5bo224bo5bo32b2obo$7bobo2b2o13b3o21b3o10bo
10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o
10bo8bo5bo4b3o3b3o23b2o$6bobo27b3o25bo23bo23bo23bo23bo23bo23bo23bo23bo
31b3o10bo$5b2o17bo39bo23bo23bo23bo23bo23bo23bo23bo23bo10b3o10bo20bo$5b
3o16bo255bo5bo5bo8bo$6bobo15bo255bo5bo5bo$7b2o277bo5bo4b3o3b3o$20b3o3b
3o$288b3o10bo$24bo276bo$24bo276bo4b4o$24bo280bo4bo$305bo3bobo$288bo17b
o3bobo$288bo23bo$288bo23bo$22b3o284bo2bo$284b3o3b3o17b2o$20bo5bo$20bo
5bo261bo$20bo5bo261bo$288bo$22b3o2$216bo$212b4obo12b2o$212b3obobo11b2o
2b2o52b3o$24bo192bobo8b2obo2b2o$24bo193bo9b3o55bo5bo$24bo192b2o67bo5bo
$217b2o67bo5bo$b2o17b3o3b3o188b2o10b2o$b2o219b3o4b2o14b2o41b3o$24bo
219bo2bo$bo22bo195bo5bo20bo$obo21bo195bo5bo20bo$o2bo2b2o212bo5bo14bo3b
obo$4bob2o232bo3bobo41bo$2b2o7bo210b3o15bo4bo42bo$11bo224bo4b4o43bo$
11bo10b3o211bo$236bo47b3o3b3o$7b3o3b3o4bo5bo$20bo5bo5bo23bo23bo23bo23b
o23bo23bo23bo23bo7b3o3b3o47bo$11bo8bo5bo5bo23bo23bo23bo23bo23bo23bo23b
o23bo63bo$11bo20bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o
10bo10b3o10bo10b3o10bo11bo51bo$4bo2bo3bo10b3o211bo$4bo23b3o3b3o4bo5bo
4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo
4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o7bo$3bo4bo32bo5bo17bo5bo17bo5bo17b
o5bo17bo5bo17bo5bo17bo5bo17bo5bo27b2o$2bobo2b2o23bo8bo5bo8bo8bo5bo8bo
8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo14b2obo$2obo28bo
23bo23bo23bo23bo23bo23bo23bo23bo14b2o2bo2bo41b3o$32bo10b3o10bo10b3o10b
o10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo19bobo$18b3o
224bo40bo5bo$o2bo223b3o56bo5bo$2b2o12bo5bo221b2o40bo5bo$16bo5bo202bo5b
o12b2o$16bo5bo202bo5bo56b3o$225bo5bo$18b3o4b2o$13b2o10b2o200b3o$13b2o$
13b2o273bo$14bo9b3o261bo$13bobo8b2obo2b2o256bo$8b3obobo11b2o2b2o197bo$
8b4obo12b2o201bo54b3o3b3o$12bo216bo$288bo$225b3o3b3o54bo$288bo$229bo$
229bo$36bo2bo189bo$36bo$18b4o13bo4bo247b3o$17bo4bo11bobo2b2o$17bo3bobo
8b2obo250bo5bo$18bo3bobo202b3o56bo5bo$24bo261bo5bo$24bo7bo2bo189bo5bo$
21bo2bo4bo4b2o189bo5bo18b2o36b3o$6b2o14b2o5bo195bo5bo18bobo$6b2o21bo
221b3o$227b3o22b2o$25b3o3b3o216bobo$5b3o237b2o2bobo36bo$5b2obo2b2o16bo
215bobo2bo37bo$7b2o2b2o16bo216b4o38bo$7b2o20bo199bo10b3o4b2o$15b3o211b
o54b3o3b3o$229bo8bo5bo$13bo5bo218bo5bo43bo$13bo5bo205b3o3b3o4bo5bo43bo
$13bo5bo7b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo
10b3o10bo10b3o66bo$40bo23bo23bo23bo23bo23bo23bo23bo20bo10b3o$15b3o7bo
5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo
8bo5bo5bo$10b2o13bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5b
o17bo5bo5bo18bo$9b4o12bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo
4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo
20b4obo$8bo2bobo230b3obobo37b3o$7bobo2b2o13b3o10bo10b3o10bo10b3o10bo
10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o27bobo$6bobo31bo23bo
23bo23bo23bo23bo23bo23bo24bo16bo35bo5bo$5b2o17bo15bo23bo23bo23bo23bo
23bo23bo23bo24bo15b2o35bo5bo$5b3o16bo208bo15b2o35bo5bo$6bobo15bo224b2o
$7b2o220b3o3b3o50b3o$20b3o3b3o$233bo$24bo201b2o5bo$24bo200bo2bo4bo4b2o
$24bo203bo7bo2bo48bo$228bo59bo$222bo3bobo59bo$221bo3bobo8b2obo$221bo4b
o11bobo2b2o39b3o3b3o$22b3o197b4o13bo4bo$240bo47bo$20bo5bo213bo2bo44bo$
20bo5bo261bo$20bo5bo2$22b3o2$288b3o2$286bo5bo$24bo261bo5bo$24bo261bo5b
o$24bo$288b3o$b2o17b3o3b3o$b2o$24bo$bo22bo$obo21bo263bo$o2bo2b2o280bo$
4bob2o280bo$2b2o7bo$11bo272b3o3b3o$11bo10b3o279b2o$288bo15b2o$7b3o3b3o
4bo5bo261bo15b2o$20bo5bo5bo23bo23bo23bo23bo23bo23bo23bo23bo23bo39bo16b
o$11bo8bo5bo5bo23bo23bo23bo23bo23bo23bo23bo23bo23bo55bobo$11bo20bo10b
3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo
10b3o10bo10b3o10bo10b3o13b3obobo$4bo2bo3bo10b3o247bo26b4obo$4bo23b3o3b
3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b
3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo4b3o3b3o4bo5bo8bo8bo
5bo15bo$3bo4bo32bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo17bo5bo
17bo5bo17bo5bo17bo5bo$2bobo2b2o23bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8b
o8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo8bo8bo5bo4b3o3b3o4bo5bo7b3o
$2obo28bo23bo23bo23bo23bo23bo23bo23bo23bo23bo$32bo10b3o10bo10b3o10bo
10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o10bo10b3o
10bo10b3o7bo5bo$18b3o251bo20bo5bo$o2bo268bo20bo5bo$2b2o12bo5bo$16bo5bo
272b3o4b2o$16bo5bo260bo17b4o$283bo16bobo2bo$18b3o4b2o256bo16b2o2bobo$
13b2o10b2o278bobo$13b2o264b3o3b3o19b2o$13b2o291b3o$14bo9b3o256bo21bobo
$13bobo8b2obo2b2o251bo5b2o14b2o$8b3obobo11b2o2b2o245b2o4bo5b2o$8b4obo
12b2o248bo2bo$12bo266bo9bo$279bo8bobo$273bo3bobo8bo2bo2b2o$272bo3bobo
13bob2o$272bo4bo12b2o$273b4o!

Here it is with the other 24 signals loaded back into it:

Code: Select all

x = 313, y = 196, rule = B3/S23
36bo2bo$36bo$18b4o13bo4bo$17bo4bo11bobo2b2o$17bo3bobo8b2obo$18bo3bobo$
24bo$24bo7bo2bo265b2o$21bo2bo9b2o264b4o$6b2o14b2o261bo13bo2bobo$6b2o
273b4obo11bobo2b2o$29bo251b3obobo9bobo$28b3o255bobo7b2o$5b3o279bo8b3o$
5b2obo2b2o273b2o9bobo$7b2o2b2o273b2o10b2o$7b2o277b2o4b3o$15b3o$290bo5b
o$13bo5bo270bo5bo$13bo5bo270bo5bo12b2o$13bo5bo7b3o21b3o10bo10b3o34bo
10b3o34bo10b3o34bo10b3o34bo52b2o$36b3o25bo34b3o10bo35bo11bo47bo47bo35b
3o$15b3o7bo5bo17bo5bo8bo8bo5bo4b3o11bo3bo9bo8bo5bo5bo13bobo10bo8bo5bo
20bo11bo8bo5bo11bo7b2o11bo10b3o40bo$10b2o13bo5bo2bo5bo8bo5bo17bo5bo3bo
3bo10bo3bo18bo5bo4bobo11bo3bo18bo5bo5bo12b2ob2o18bo5bo4bobo4bo7b3o63bo
bo$9b4o12bo5bo2bo5bo8bo5bo4b3o3b3o4bo5bo3bo3bo10bo3bo5b3o3b3o4bo5bo3bo
3bo11bobo6b3o3b3o4bo5bo3b2ob2o12bo7b3o3b3o4bo5bo4b3o7bo4bobo6b3o3b3o4b
o5bo6b3o2bobo18b2o2bo2bo$8bo2bobo20bo5bo42bo3bo11b3o30bobo13bo32bo47b
2o7bo26bo5bo6b7o7bo11b2obo$7bobo2b2o13b3o21b3o10bo10b3o6b3o25bo10b3o7b
o26bo10b3o34bo10b3o34bo8bo5bo4b2obob4o8bo14b2o$6bobo27b3o25bo47bo47bo
47bo47bo19bo8b4obob2o7bo$5b2o17bo39bo47bo47bo47bo47bo10b3o7bo7b7o9bo$
5b3o16bo259bobo2b3o9bo$6bobo15bo$7b2o288b3o3b3o$20b3o3b3o$301bo$24bo
276bo$24bo276bo4b4o$24bo280bo4bo$305bo3bobo$288bo17bo3bobo$288bo23bo$
288bo23bo$22b3o284bo2bo$284b3o3b3o17b2o$20bo5bo$20bo5bo261bo$20bo5bo
261bo$288bo$22b3o2$216bo$212b4obo12b2o$212b3obobo11b2o2b2o52b3o$217bob
o8b2obo2b2o$218bo9b3o55bo5bo$217b2o67bo5bo$217b2o67bo5bo$b2o20b3o191b
2o10b2o$b2o219b2o5b2o14b2o41b3o$21bo5bo194bob3o17bo2bo$bo19bo5bo192b2o
25bo$obo18bo5bo192b2o2b2obo19bo$o2bo2b2o211b3obo3bo13bo3bobo$4bob2o15b
3o193b3obo3bo12bo3bobo$2b2o19b2o194b2ob2o2bo13bo4bo41b4o$23b2o195b2o3b
obo8bo4b4o42bob2o$22b3o195bobo3b2o8bo48bob2o$10bobo208bo2b2ob2o7bo52bo
bo$9bo2bo7bo5bo193bo3bob3o59bo3b2o$10bobo7bo5bo5bo47bo47bo47bo43bo3bob
3o3b3o3b3o42bo4b2ob2o$20bo5bo5bo25b3o19bo25b3o19bo25b2obo5b2o11bo28b2o
4b2o7bob2o2b2o60b2ob2o$32bo10b3o21b3o10bo10b3o21b3o10bo10b3o13b4o4b2o
11bo10b3o12b3ob2o2bo2bo12b2o8bo51bobobo$4bo2bo14b3o31bo47bo4b3o3bo36bo
2bo2bo3bobo35bob4o3b2ob2o7b3obo10bo48bobobo$4bo23b3o3b3o4bo5bo8bo4b3ob
o5bo4b3o3b3o4bo5bo8bo9b2o3bo4b3o3b3o4bo5bo8bo3bo5b2o3bo4b3o3b3o4bo5bo
8bo2bobo4bobo2bo8b2o10bo48b2ob2o$3bo4bo32bo5bo8bo5bob3o4bo17bo5bo8bo3b
2o9bo17bo5bo8bo3b2o5bo3bo17bo5bo8bo2bobo4bobo2bo27b2o40b2ob2o4bo$2bobo
2b2o23bo8bo5bo23bo8bo8bo5bo12bo3b3o4bo8bo8bo5bo11bobo3bo2bo2bo8bo8bo5b
o10b2ob2o3b4obo23b2obo41b2o3bo$2obo28bo25b3o19bo25b3o19bo26b2o4b4o11bo
25bo2bo2b2ob3o25b2o2bo2bo39bobo$32bo10b3o21b3o10bo10b3o21b3o10bo10b3o
13b2o5bob2o10bo10b3o13b2o4b2o33bobo42b2obo$18b3o224bo41b2obo$o2bo223b
3o57b4o$2b2o12bo5bo221b2o$16bo5bo202bo5bo12b2o$16bo5bo202bo5bo$225bo5b
o$18b3o4b2o$13b2o10b2o200b3o$13b2o$13b2o273bo$14bo9b3o261bo$13bobo8b2o
bo2b2o256bo$8b3obobo11b2o2b2o$8b4obo12b2o256b3o3b3o$12bo$288bo$229b2o
57bo$226b3obo57bo$231b2o$225bob2o2b2o$36bo2bo185bo3bob3o$36bo188bo3bob
3o$18b4o13bo4bo185bo2b2ob2o54b3o$17bo4bo11bobo2b2o184bobo3b2o$17bo3bob
o8b2obo189b2o3bobo53bo5bo$18bo3bobo199b2ob2o2bo54bo5bo$24bo199b3obo3bo
53bo5bo$24bo7bo2bo188b3obo3bo$21bo2bo4bo4b2o189b2o2b2obo17b2o36b3o$6b
2o14b2o5bo195b2o23bobo$6b2o21bo197bob3o19b3o$227b2o23b2o$25b3o3b3o216b
obo$5b3o237b2o2bobo36bo$5b2obo2b2o16bo215bobo2bo37bo$7b2o2b2o16bo203bo
bo10b4o36bo2b2o$7b2o20bo202bo3bo10b2o37bo3b2o$242bo42bo3b2obo$12b2o
215b2o5b4ob2obo40bo6bo$12b3o13bo199bo3bo7bo4bo39bo2b4o$11b2ob2o11b3o
172bobo23bo4bo7bo3bo39bo2bob2o$12b3o11b2ob2o9bo34b3o10bo34b3o10bo10bo
23b3o10bo16bo3bo13b3o7bob2ob4o5b2o40b2o$13bo13b3o10bo47bo47bo9bo4bo32b
o10bo35bo59b2o$28bo11bo7b3o22bo5bo8bo7bobo22bo5bo8bo16bo15bo5bo8bo8bob
2ob4o5b2o8bo5bo13bo3bo44b2obo2bo$10b2o36bobo12b3o7bo5bo16bo2bo11bobo7b
o5bo16b2obo6b2o3bobo7bo5bo16bo4bo7bo3bo7bo5bo14bobo7bo37b4o2bo$9b4o23b
3o3b3o3b3o12bobo7bo5bo4b3o3b3o3bobo11bo2bo7bo5bo4b3o3b3o3bobo3b2o6bob
2o7bo5bo4b3o3b3o3bo3bo7bo4bo7bo5bo20b4obo35bo6bo$8bo2bobo49b3o45bobo
38bo40b2o5b4ob2obo35b3obobo34bob2o3bo$7bobo2b2o26bo34b3o10bo34b3o10bo
17bo4bo11b3o10bo21bo12b3o27bobo34b2o3bo$6bobo31bo47bo47bo21bo25bo11bo
3bo32bo16bo36b2o2bo$5b2o33bo47bo47bo47bo12bobo33bo15b2o38bo$5b3o225bo
15b2o38bo$6bobo15bo224b2o$7b2o14b3o203b3o3b3o$22b2ob2o$23b3o207bo$24bo
201b2o5bo$225bo2bo4bo4b2o$228bo7bo2bo48bo$228bo59bo$222bo3bobo59bo$
221bo3bobo8b2obo$221bo4bo11bobo2b2o39b3o3b3o$222b4o13bo4bo$240bo47bo$
240bo2bo44bo$288bo$23bo$22b3o$21b2ob2o$22b3o$23bo264b3o2$286bo5bo$24bo
261bo5bo$24bo261bo5bo$24bo$288b3o$b2o17b3o3b3o$b2o$24bo$bo22bo$obo21bo
263bo$o2bo2b2o280bo$4bob2o280bo$2b2o7bo273bo5bo$11bo272bob4obo$11bo8bo
263bo3bo15b2o$19b3o263b3o3bo12b2o$7b3o3b3o2bobobo266b3o12b2o$17b3ob3o
32bo23bo23bo23bo23bo23bo23bo23bo23bo56bo$11bo6bobobo9bo23bo23bo14bo8bo
23bo14bo8bo23bo14bo8bo23bo14bo8bo55bobo$11bo7b3o9b3o13bo8bo10b3o10bo
14bo8bo10b3o10bo14bo8bo10b3o10bo14bo8bo10b3o10bo14b2o4b4o10b3o10bo11b
3o12b3obobo$4bo2bo3bo8bo9bobobo11b3o46bo47bo3bobo41bo5bo47bo26bo11bo3b
3o8b4obo$4bo24b3ob3o9bobobo2b3o3b3o4bo5bo4b3o3b3o15b3o3b3o4bo5bo4b3o3b
3o13bo3bo3b3o4bo5bo4b3o3b3o12b2ob3o3b3o4bo5bo4b3o3b3o11b2o5bo2b3o4bo5b
o8bo14bo3bo11bo$3bo4bo21bobobo9b3ob3o14bo5bo19b3o3b3o13bo5bo19b3o3bo3b
o11bo5bo19b3o3b3ob2o10bo5bo19b3o2bo5b2o9bo5bo20bob4obo$2bobo2b2o22b3o
11bobobo6bo8bo5bo8bo23bo8bo5bo8bo17bobo3bo8bo5bo8bo17bo5bo8bo5bo8bo17b
o14bo5bo4b3o3b3o7bo5bo4b3o$2obo28bo13b3o7bo23bo14bo8bo23bo14bo8bo23bo
14bo8bo23bo14b4o4b2o38bo$47bo8bo10b3o10bo14bo8bo10b3o10bo14bo8bo10b3o
10bo14bo8bo10b3o10bo14bo8bo10b3o10bo14bo5bo5bo$95bo47bo47bo47bo32bo14b
o5bo5bo$o2bo268bo20bo5bo$2b2o$19bo275b3o4b2o$18b3o262bo17b4o$18b2obo
261bo16bobo2bo$20b2o3b2o256bo16b2o2bobo$13b2o6b2o2b2o278bobo$13b2o5bo
258b3o3b3o19b2o$13b2o291b3o$14bo9b3o256bo21bobo$13bobo8b2obo2b2o251bo
5b2o14b2o$8b3obobo11b2o2b2o245b2o4bo5b2o$8b4obo12b2o248bo2bo$12bo266bo
9bo$279bo8bobo$273bo3bobo8bo2bo2b2o$272bo3bobo13bob2o$272bo4bo12b2o$
273b4o!

How about we just put two of these folded-up templates in the article, one for each of the tricky 25-signal loops, with a "Details" section explaining how to extend each? The third family is already represented nicely by the p110 traffic jam pattern, with much smaller loops with only five signals.

[hotdogPi]

Since not everyone has Discord:

While "102+6n" and "102+18n" both appear in the Oscillator page, neither actually exists. What actually matters is mod 4.

On the traffic jam page, there are examples for 102 (2 mod 4) and 104 (0 mod 4). These can be extended, so 154 would have the 102 design since 154 is 2 mod 4. Then you just have to find the appropriate sparkers, which for 154 would be the p7 pipsquirter. Not all periods have working sparkers, especially ones that are twice a prime.

If the period is a multiple of 10, only five signals are needed rather than 25, so the loop can be made much smaller. This is further true for multiples of 50, which only require one signal (see the p200 for an example).

[dvgrn]

On the traffic jam page, there are examples for 102 (2 mod 4) and 104 (0 mod 4). These can be extended, so 154 would have the 102 design since 154 is 2 mod 4.

Yup. I was able to confirm by experiment that the p2700 loop can perfectly well be extended by just two traffic lights at a time, not four (as long as appropriate sparkers are found for the new +50 period).

So with an extensible traffic-jam oscillator family that uses p5 sparkers, the details should be able to specify "two traffic lights at a time" -- right?

Stable version?
-- Hang on, I'm drawing a blank here: in these decadent modern days, do we have a stable or p2 version of that traffic-light push that's used at those corners? If we do, then it ought to get mentioned in the article. If we don't, then somebody ought to invent one...! It would allow for really easy loop adjustability with none of these worries about supported periods.