One of the old c/2 period 14 spaceships found by Paul Tooke has a duoplet spark which is not reachable by a glider. I found another spaceship which makes that spark accessible, and so the new spaceship is able to to turn a forwards glider into a backwards glider. (The other expected reaction using the duoplet spark to turn a forwards glider into another forwards glider doesn't work.)
Here is the new spaceship along with an old spaceship showing ways to turn gliders in various directions using c/2 period 14 spaceships.
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#C Three glider turning reactions using c/2 period 14 spaceships.
#C The spaceship in the first two reactions was found by Paul Tooke.
#C The spaceship in the last reaction is a modification by David Bell
#C of a spaceship found by Paul Tooke.
x = 218, y = 67, rule = B3/S23
198bo$194boob3o$192boobo3boo$192bo4bobboo$191boobo5bo$189boobo7boo$
190bo7boboboo$187booboboo3boobobo$97bo3bo85boobo5bo3boboboo$21bo3bo70b
3ob3o84bobbobo7bo3boo$20b3ob3o68booboboboo64bo17boobo6boo3bob3o$19boob
oboboo66boo7boo62b3oboo15boobo13boo$18boo7boo66bo7bo62boo3boboo11boo4b
o$19bo7bo66boo7boo60boobbo4bo12boobbo$18boo7boo63boobobo3boboboo59bo5b
oboo12bo$16boobobo3boboboo60bobobobooboobobo59boo7boboo9bo3boo$15bobob
obooboobobo60boobobbobobobobboboo54boobobo7bo13bobbo$14boobobbobobobo
bboboo41bo14boboboboobobobooboboo55boboboo3booboboo7b4o$13boboboboobob
obooboboo42bo12boobobobobbobobbobobbo52boobobo3bo5boboo6bo3boboo$12boo
bobobobbobobbobobbo40b3o11bo3bobo11bobboo51boo3bo7bobobbo$11bo3bobo11b
obboo63booboo59b3obo3boo6boboo5booboobo$21booboo61boobooboo9boo54boo
13boboo14bo14b3o$11boobooboo9boo56bo87bo4boo6bo3bo12b5obbo$10bo78bo3bo
81bobboo8bobo12boobobo3bo$13bo3bo68boo19b3o68bo8booboo13bo6bo$10boo19b
3o56b3o13bo3bo63boo3bo8bobo10bobo6bo$14b3o13bo3bo70bo4boo61bobbo8boobo
boboo6booboo6bobo$29bo4boo62b3o3booboobobo63b4o5booboboboo5boboboo3boo
boboo$22b3o3booboobobo52bobbob3ob3oboobo4boboo59boobo3bo4bobo3bobo4boo
bo6boobobobo$13bobbob3ob3oboobo4boboo49boobooboo3bobo4bo3bo4bo69booboo
booboobbo3boboo3bobbo3boo$11boobooboo3bobo4bo3bo4bo48bobbobo3bo5bo71bo
booboo20boo4boobbobo3bo$11bobbobo3bo5bo62bobobbo9boo7boo58bo10b3ob3ob
3obboobobo11bo$13bobobbo9boo7boo47boobooboboo79bo3bo20boo14boo$10boob
ooboboo72boboo80bobo18bobb4o$16boboo67bobbobo82booboo13boobbobo$11bobb
obo73boboboo80bobo14boo4bobboo$14boboboo66boo3bobo13b3o63booboboboo11b
oo8bo$10boo3bobo13b3o52b4ob3o12bo3bo62booboboboo12boobbo3bobo$10b4ob3o
12bo3bo50booboo15bo4boo61bobo3bobo13boboo$9booboo15bo4boo55boobo3b3o3b
ooboobobo59booboobooboo9boobobobo$15boobo3b3o3booboobobo48boobobb3oboo
b3oboobo4boboo78b3obobo$9boobobb3oboob3oboobo4boboo49boo9bobo4bo3bo4bo
57b3ob3ob3o12booboo$11boo9bobo4bo3bo4bo48bobobobobbo5bo89boo$11bobobob
obbo5bo62bobobo10boo7boo46b3o29b3ob3o$13bobobo10boo7boo50bobbobooboo
64bo10bo17bo$13bobbobooboo65boo3b3o3boo61bo11boo16boo$12boo3b3o3boo63b
obobobobbo3bo74bo4bo9bobo$12bobobobobbo3bo64bobo9bo7bo69b3oboo4b3o$14b
obo9bo7bo54bobbo6booboob3ob3o63boobboo3boboo3bo18bo$14bobo6booboob3ob
3o56bo8boobb3o3boo65boobbo4bobbo18b3o$16boo7boobb3o3boo54b3o7boo3bo5b
oo62bobbo5bobb3obbo14b3oboo$15bo9boo3bo5boo53b3o13boo3bo64bo8boboboboo
7bo4boobobbo$31boo3bo52b3o20boo74bo3bob4obooboobobo4boboo$13boo21boo
51b3o18boboboo72boobboboboo7bobobboboboo$3o10boobbo16boboboo48bo3bo16b
oobobo71bobo8boobobob3o8bo$bbo10b3obo15boobobo51bobbo14bo3boboboo67bo
11bo8boo7boo$bo30bo3boboboo51bo18bo3boo68bobbo7bo$15bo20bo3boo66boo3bo
b3o69b3o$15boo15boo3bob3o75boo68b3o$15bobo23boo47boo$15bobo75bo$17boo
73bo97boo$15bobo74bobo95boo$16bo76bo$$188bo$189bo!
Using the new glider turning spaceship, I made another series of puffers which has a smaller increment in the periods.
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#C A c/2 period 1022 (2 * 7 * 73) dirty puffer.
#C This begins a series of puffers with periods of the form 1022 + 224N.
#C This uses a period 14 puffer by Jason Summers, and period 14 spaceships
#C by Paul Tooke and David Bell that can reflect forward or backward gliders.
#C A glider hits the puffer's wick and ignites it, which burns forwards
#C through the wick until a forward glider is released and converted to a
#C backward glider and then to a forward glider to complete the cycle.
#C To create the next puffer in the series, shift the lower period 14
#C spaceship at the right edge to the right by 11 cells, downwards by 39
#C cells, and advance it by 12 generations. That will increase the period
#C by 224 generations.
#C David I. Bell, 31 January 2026
x = 136, y = 134, rule = B3/S23
7b3o67b3o$6bobb5o59b5obbo$5bo3bobobooboo13bo11bo11bo13booboobobo3bo$5b
o6bo3boboo10b3o9b3o9b3o10boobo3bo6bo$7bo6bo4b4o5booboboo5booboboo5boob
oboo5b4o4bo6bo$4bobo6bo3bobo3bo3bobbobobbo3bobbobobbo3bobbobobbo3bo3bo
bo3bo6bobo$3boobob3o8bo4bobo3bobo3bobo3bobo3bobo3bobo3bobo4bo8b3oboboo
$bbobobo3bo5boboo4bobo3bobo3bobo3bobo3bobo3bobo3bobo4boobo5bo3bobobo$b
oobo10b4obobbooboobooboobooboobooboobooboobooboobooboobbob4o10boboo$o
3bo5boobboo7booboobooboobooboobooboobooboobooboobooboo7boobboo5bo3bo$
13boo3boo47boo3boo$ooboo6bobbo3bo49bo3bobbo6booboo$12bo5b51o5bo$17boo
bb3obob5obob5obob5obob5obobooboboobboo$25bo7bo7bo7bo7bo5bo$37bo7bo$29b
o5booboo3booboo5bo$29bo5bo3bo3bo3bo5bo$29bo5bo3bo3bo3bo5bo$36bobo5bobo
$37bo7bo54bo$96boob3o$94boobo3boo$26boo27boo37bo4bobboo$26bobo25bobo
36boobo5bo$27boo7booboobooboo7boo35boobo7boo$36booboobooboo45bo7bobob
oo$37booboboboo43booboboo3boobobo$40bobo46boobo5bo3boboboo$35bobo7bobo
41bobbobo7bo3boo$26boo8boo7boo8boo13bo17boobo6boo3bob3o$26bobo7boo7boo
7bobo12b3oboo15boobo13boo$27boo25boo12boo3boboo11boo4bo$67boobbo4bo12b
oobbo$68bo5boboo12bo$38bo5bo22boo7boboo9bo3boo$37bobo3bobo19boobobo7bo
13bobbo$26boo8bobbo3bobbo8boo9boboboo3booboboo7b4o$26bobo8boo5boo8bobo
6boobobo3bo5boboo6bo3boboo$27boo25boo7boo3bo7bobobbo$63b3obo3boo6boboo
5booboobo$62boo13boboo14bo14b3o$38bo5bo31bo4boo6bo3bo12b5obbo$37bobo3b
obo31bobboo8bobo12boobobo3bo$26boo8bobbo3bobbo8boo23bo8booboo13bo6bo$
26bobo8boo5boo8bobo19boo3bo8bobo10bobo6bo$27boo25boo19bobbo8booboboboo
6booboo6bobo$78b4o5booboboboo5boboboo3booboboo$75boobo3bo4bobo3bobo4b
oobo6boobobobo$38bo5bo41booboobooboobbo3boboo3bobbo3boo$37bobo3bobo30b
obooboo20boo4boobbobo3bo$26boo8bobbo3bobbo8boo18bo10b3ob3ob3obboobobo
11bo$26bobo8boo5boo8bobo20bo3bo20boo14boo$27boo25boo22bobo18bobb4o$77b
ooboo13boobbobo$78bobo14boo4bobboo$38bo5bo30booboboboo11boo8bo$37bobo
3bobo29booboboboo12boobbo3bobo$26boo8bobbo3bobbo8boo18bobo3bobo13boboo
$26bobo8boo5boo8bobo17booboobooboo9boobobobo$27boo25boo38b3obobo$74b3o
b3ob3o12booboo$94boo$38bo5bo50b3ob3o$37bobo3bobo30bo17bo$26boo8bobbo3b
obbo8boo19boo16boo$26bobo8boo5boo8bobo21bo4bo9bobo$27boo25boo26b3oboo
4b3o$77boobboo3boboo3bo18bo$80boobbo4bobbo18b3o$38bo5bo33bobbo5bobb3o
bbo14b3oboo$37bobo3bobo33bo8boboboboo7bo4boobobbo$26boo8bobbo3bobbo8b
oo33bo3bob4obooboobobo4boboo$26bobo8boo5boo8bobo33boobboboboo7bobobbob
oboo$27boo25boo32bobo8boobobob3o8bo$87bo11bo8boo7boo$88bobbo7bo$38bo5b
o44b3o$37bobo3bobo43b3o$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27b
oo25boo36boo$92boo20bo3bo$113b3ob3o$38bo5bo67booboboboo$37bobo3bobo44b
o20boo7boo$26boo8bobbo3bobbo8boo34bo20bo7bo$26bobo8boo5boo8bobo31boo
21boo7boo$27boo25boo31bobo19boobobo3boboboo$89bo18bobobobooboobobo$
107boobobbobobobobboboo$38bo5bo61boboboboobobobooboboo$37bobo3bobo59b
oobobobobbobobbobobbo$26boo8bobbo3bobbo8boo47bo3bobo11bobboo$26bobo8b
oo5boo8bobo57booboo$27boo25boo48boobooboo9boo$103bo$106bo3bo$38bo5bo
58boo19b3o$37bobo3bobo61b3o13bo3bo$26boo8bobbo3bobbo8boo65bo4boo$26bob
o8boo5boo8bobo58b3o3booboobobo$27boo25boo50bobbob3ob3oboobo4boboo$104b
oobooboo3bobo4bo3bo4bo$104bobbobo3bo5bo$38bo5bo61bobobbo9boo7boo$37bob
o3bobo57boobooboboo$26boo8bobbo3bobbo8boo52boboo$26bobo8boo5boo8bobo
47bobbobo$27boo25boo51boboboo$103boo3bobo13b3o$103b4ob3o12bo3bo$102boo
boo15bo4boo$108boobo3b3o3booboobobo$26boo27boo45boobobb3oboob3oboobo4b
oboo$26bobo25bobo47boo9bobo4bo3bo4bo$27boo25boo48bobobobobbo5bo$106bob
obo10boo7boo$106bobbobooboo$105boo3b3o3boo$105bobobobobbo3bo$107bobo9b
o7bo$107bobobo4booboob3ob3o$106boobobo6boobb3o3boo$107bobobo6boo3bo5b
oo$107b3obo12boo3bo$108b3o18boo$109bo17boboboo$126boobobo$125bo3bobob
oo$109bo19bo3boo$108bobo14boo3bob3o$108bobo23boo$109bo!
This series uses the first placement of the upper period 14 spaceship at the right edge that I tried, and only adjusts the bottom spaceship.
By adjusting the top spaceship too, I hope that it might provide more periods.
EDIT:
Yes, performing a shift of both period 14 spaceships will give more periods.
In fact, if my calculations are correct, combining both types of shifts will give c/2 puffers for all odd multiples of 14 starting with 8470.
This is calculated using the period increments of 1092 and 224 for the two types of shifts. Divided by 28 this gives the values 39 and 8. These are relatively prime, so all integers starting with 39 * 8 - 39 - 8 + 1 = 266 can be represented by adding multiples of 39 and 8. Multiplying 266 by 28 and adding the base period 1022 gives 8470.
Here is the first puffer which begins the infinite set of all odd multiples of 14 puffers starting with 8470.
Code: Select all
#C A c/2 period 8470 (2 * 7 * 5 * 11 * 11) dirty puffer.
#C This is the first puffer in an infinite set of c/2 puffers having
#C periods for all odd multiples of 14 which are 8470 and over.
#C This was constructed from a base period 1022 puffer whose period 14
#C spaceships were shifted by two different methods. The first method
#C was to shift the bottom right spaceship to the right by 11 cells,
#C down by 39 cells, and advanced by 12 generations, repeated 4 times.
#C The second method was to shift the two period 14 spaceships on the
#C right along with the glider diagonally to the bottom right by 77
#C cells, repeated 6 times.
#C David I. Bell, 31 January 2026
x = 642, y = 747, rule = B3/S23
7b3o67b3o$6bobb5o59b5obbo$5bo3bobobooboo13bo11bo11bo13booboobobo3bo$5b
o6bo3boboo10b3o9b3o9b3o10boobo3bo6bo$7bo6bo4b4o5booboboo5booboboo5boob
oboo5b4o4bo6bo$4bobo6bo3bobo3bo3bobbobobbo3bobbobobbo3bobbobobbo3bo3bo
bo3bo6bobo$3boobob3o8bo4bobo3bobo3bobo3bobo3bobo3bobo3bobo4bo8b3oboboo
$bbobobo3bo5boboo4bobo3bobo3bobo3bobo3bobo3bobo3bobo4boobo5bo3bobobo$b
oobo10b4obobbooboobooboobooboobooboobooboobooboobooboobbob4o10boboo$o
3bo5boobboo7booboobooboobooboobooboobooboobooboobooboo7boobboo5bo3bo$
13boo3boo47boo3boo$ooboo6bobbo3bo49bo3bobbo6booboo$12bo5b51o5bo$17boo
bb3obob5obob5obob5obob5obobooboboobboo$25bo7bo7bo7bo7bo5bo$37bo7bo$29b
o5booboo3booboo5bo$29bo5bo3bo3bo3bo5bo$29bo5bo3bo3bo3bo5bo$36bobo5bobo
$37bo7bo3$26boo27boo$26bobo25bobo$27boo7booboobooboo7boo$36boobooboob
oo$37booboboboo$40bobo$35bobo7bobo$26boo8boo7boo8boo$26bobo7boo7boo7bo
bo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5b
oo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8b
oo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bo
bo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$
26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo
8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3b
obbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bo
bbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26b
oo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo
$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo
3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$
37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo
5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$
38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25b
oo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27b
oo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo
$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo
8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo
5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo
8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$
26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo
8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3b
obbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bo
bbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26b
oo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo
$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo
3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$
37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo
5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$
38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25b
oo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27b
oo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo
$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo
8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo
5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo
8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$
26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo
8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3b
obbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bo
bbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26b
oo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo
$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo
3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$
37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo
5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$
38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25b
oo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27b
oo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo
$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo
8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo
5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo
8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$
26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo
8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3b
obbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bo
bbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26b
oo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo
$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo
3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$
37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo
5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$
38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25b
oo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27b
oo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo
$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo
8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo
5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo
8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$
26bobo8boo5boo8bobo$27boo25boo$$562bo$38bo5bo513boob3o$37bobo3bobo510b
oobo3boo$26boo8bobbo3bobbo8boo499bo4bobboo$26bobo8boo5boo8bobo498boobo
5bo$27boo25boo497boobo7boo$554bo7boboboo$551booboboo3boobobo$38bo5bo
506boobo5bo3boboboo$37bobo3bobo505bobbobo7bo3boo$26boo8bobbo3bobbo8boo
475bo17boobo6boo3bob3o$26bobo8boo5boo8bobo474b3oboo15boobo13boo$27boo
25boo474boo3boboo11boo4bo$529boobbo4bo12boobbo$530bo5boboo12bo$38bo5bo
484boo7boboo9bo3boo$37bobo3bobo481boobobo7bo13bobbo$26boo8bobbo3bobbo
8boo471boboboo3booboboo7b4o$26bobo8boo5boo8bobo468boobobo3bo5boboo6bo
3boboo$27boo25boo469boo3bo7bobobbo$525b3obo3boo6boboo5booboobo$524boo
13boboo14bo14b3o$38bo5bo493bo4boo6bo3bo12b5obbo$37bobo3bobo493bobboo8b
obo12boobobo3bo$26boo8bobbo3bobbo8boo485bo8booboo13bo6bo$26bobo8boo5b
oo8bobo481boo3bo8bobo10bobo6bo$27boo25boo481bobbo8booboboboo6booboo6bo
bo$540b4o5booboboboo5boboboo3booboboo$537boobo3bo4bobo3bobo4boobo6boob
obobo$38bo5bo503booboobooboobbo3boboo3bobbo3boo$37bobo3bobo492bobooboo
20boo4boobbobo3bo$26boo8bobbo3bobbo8boo480bo10b3ob3ob3obboobobo11bo$
26bobo8boo5boo8bobo482bo3bo20boo14boo$27boo25boo484bobo18bobb4o$539boo
boo13boobbobo$540bobo14boo4bobboo$38bo5bo492booboboboo11boo8bo$37bobo
3bobo491booboboboo12boobbo3bobo$26boo8bobbo3bobbo8boo480bobo3bobo13bob
oo$26bobo8boo5boo8bobo479booboobooboo9boobobobo$27boo25boo500b3obobo$
536b3ob3ob3o12booboo$556boo$38bo5bo512b3ob3o$37bobo3bobo492bo17bo$26b
oo8bobbo3bobbo8boo481boo16boo$26bobo8boo5boo8bobo483bo4bo9bobo$27boo
25boo488b3oboo4b3o$539boobboo3boboo3bo18bo$542boobbo4bobbo18b3o$38bo5b
o495bobbo5bobb3obbo14b3oboo$37bobo3bobo495bo8boboboboo7bo4boobobbo$26b
oo8bobbo3bobbo8boo495bo3bob4obooboobobo4boboo$26bobo8boo5boo8bobo495b
oobboboboo7bobobboboboo$27boo25boo494bobo8boobobob3o8bo$549bo11bo8boo
7boo$550bobbo7bo$38bo5bo506b3o$37bobo3bobo505b3o$26boo8bobbo3bobbo8boo
$26bobo8boo5boo8bobo$27boo25boo498boo$554boo$$38bo5bo$37bobo3bobo506bo
$26boo8bobbo3bobbo8boo496bo$26bobo8boo5boo8bobo493boo$27boo25boo493bob
o$551bo$$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo
$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo
8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo
5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo
8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$
26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo
8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3b
obbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bo
bbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26b
oo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo
$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo
3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$
37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo
5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$
38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25b
oo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo$27b
oo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo8bobo
$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo5boo
8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo8boo$26bobo8boo
5boo8bobo$27boo25boo564bo3bo$619b3ob3o$618booboboboo$38bo5bo572boo7boo
$37bobo3bobo572bo7bo$26boo8bobbo3bobbo8boo560boo7boo$26bobo8boo5boo8bo
bo558boobobo3boboboo$27boo25boo558bobobobooboobobo$613boobobbobobobobb
oboo$612boboboboobobobooboboo$38bo5bo566boobobobobbobobbobobbo$37bobo
3bobo564bo3bobo11bobboo$26boo8bobbo3bobbo8boo563booboo$26bobo8boo5boo
8bobo553boobooboo9boo$27boo25boo553bo$612bo3bo$609boo19b3o$38bo5bo568b
3o13bo3bo$37bobo3bobo582bo4boo$26boo8bobbo3bobbo8boo564b3o3booboobobo$
26bobo8boo5boo8bobo555bobbob3ob3oboobo4boboo$27boo25boo554boobooboo3bo
bo4bo3bo4bo$610bobbobo3bo5bo$612bobobbo9boo7boo$38bo5bo564boobooboboo$
37bobo3bobo569boboo$26boo8bobbo3bobbo8boo553bobbobo$26bobo8boo5boo8bob
o556boboboo$27boo25boo553boo3bobo13b3o$609b4ob3o12bo3bo$608booboo15bo
4boo$38bo5bo569boobo3b3o3booboobobo$37bobo3bobo562boobobb3oboob3oboobo
4boboo$26boo8bobbo3bobbo8boo553boo9bobo4bo3bo4bo$26bobo8boo5boo8bobo
553bobobobobbo5bo$27boo25boo556bobobo10boo7boo$612bobbobooboo$611boo3b
3o3boo$38bo5bo566bobobobobbo3bo$37bobo3bobo567bobo9bo7bo$26boo8bobbo3b
obbo8boo556bobo6booboob3ob3o$26bobo8boo5boo8bobo558boo7boobb3o3boo$27b
oo25boo558bo9boo3bo5boo$630boo3bo$612boo21boo$38bo5bo567boobbo16bobob
oo$37bobo3bobo566b3obo15boobobo$26boo8bobbo3bobbo8boo574bo3boboboo$26b
obo8boo5boo8bobo557bo20bo3boo$27boo25boo558boo15boo3bob3o$614bobo23boo
$614bobo$38bo5bo571boo$37bobo3bobo568bobo$26boo8bobbo3bobbo8boo558bo$
26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3bobbo
8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo3b
obbo8boo$26bobo8boo5boo8bobo$27boo25boo!
There is a different glider impact on the period 14 puffer which produces much less debris (including no gliders) than the one I have been using in my recent posts. This can be used as a basis of puffer series similar to the ones using the previous impact.
Code: Select all
#C A c/2 period 1554 (2 * 7 * 3 * 37) dirty rake.
#C David I. Bell, 31 January 2026
x = 162, y = 169, rule = B3/S23
7b3o67b3o$6bobb5o59b5obbo$5bo3bobobooboo13bo11bo11bo13booboobobo3bo$5b
o6bo3boboo10b3o9b3o9b3o10boobo3bo6bo$7bo6bo4b4o5booboboo5booboboo5boob
oboo5b4o4bo6bo$4bobo6bo3bobo3bo3bobbobobbo3bobbobobbo3bobbobobbo3bo3bo
bo3bo6bobo$3boobob3o8bo4bobo3bobo3bobo3bobo3bobo3bobo3bobo4bo8b3oboboo
$bbobobo3bo5boboo4bobo3bobo3bobo3bobo3bobo3bobo3bobo4boobo5bo3bobobo$b
oobo10b4obobbooboobooboobooboobooboobooboobooboobooboobbob4o10boboo$o
3bo5boobboo7booboobooboobooboobooboobooboobooboobooboo7boobboo5bo3bo$
13boo3boo47boo3boo$ooboo6bobbo3bo49bo3bobbo6booboo$12bo5b51o5bo$17boo
bb3obob5obob5obob5obob5obobooboboobboo$25bo7bo3bo3bo3bo3bo7bo5bo$29bo
7bo7bo7bo$37bo7bo$26bo5bo17bo5bo$26bo6bo15bo6bo$26bo29bo$27bo6bo13bo6b
o$28b3ob3o13b3ob3o$34b4obbobobb4o$35bo3bo3bo3bo$35bo3bo3bo3bo$36b3o5b
3o$26boo27boo$26bobo25bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8bobbo
3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo$26boo8b
obbo3bobbo8boo$26bobo8boo5boo8bobo$27boo25boo3$38bo5bo$37bobo3bobo80bo
$26boo8bobbo3bobbo8boo65boob3o$26bobo8boo5boo8bobo63boobo3boo$27boo25b
oo64bo4bobboo$119boobo5bo$117boobo7boo$38bo5bo73bo7boboboo$37bobo3bobo
69booboboo3boobobo$26boo8bobbo3bobbo8boo58boobo5bo3boboboo$26bobo8boo
5boo8bobo58bobbobo7bo3boo$27boo25boo40bo17boobo6boo3bob3o$95b3oboo15b
oobo13boo$94boo3boboo11boo4bo$38bo5bo48boobbo4bo12boobbo$37bobo3bobo
48bo5boboo12bo$26boo8bobbo3bobbo8boo36boo7boboo9bo3boo$26bobo8boo5boo
8bobo34boobobo7bo13bobbo$27boo25boo36boboboo3booboboo7b4o$89boobobo3bo
5boboo6bo3boboo$89boo3bo7bobobbo$38bo5bo44b3obo3boo6boboo5booboobo$37b
obo3bobo42boo13boboo14bo14b3o$26boo8bobbo3bobbo8boo45bo4boo6bo3bo12b5o
bbo$26bobo8boo5boo8bobo46bobboo8bobo12boobobo3bo$27boo25boo50bo8booboo
13bo6bo$102boo3bo8bobo10bobo6bo$101bobbo8booboboboo6booboo6bobo$38bo5b
o59b4o5booboboboo5boboboo3booboboo$37bobo3bobo55boobo3bo4bobo3bobo4boo
bo6boobobobo$26boo8bobbo3bobbo8boo55booboobooboobbo3boboo3bobbo3boo$
26bobo8boo5boo8bobo45bobooboo20boo4boobbobo3bo$27boo25boo45bo10b3ob3ob
3obboobobo11bo$103bo3bo20boo14boo$104bobo18bobb4o$38bo5bo58booboo13boo
bbobo$37bobo3bobo58bobo14boo4bobboo$26boo8bobbo3bobbo8boo44booboboboo
11boo8bo$26bobo8boo5boo8bobo44booboboboo12boobbo3bobo$27boo25boo45bobo
3bobo13boboo$100booboobooboo9boobobobo$120b3obobo$38bo5bo55b3ob3ob3o
12booboo$37bobo3bobo74boo$26boo8bobbo3bobbo8boo64b3ob3o$26bobo8boo5boo
8bobo45bo17bo$27boo25boo46boo16boo$104bo4bo9bobo$108b3oboo4b3o$38bo5bo
58boobboo3boboo3bo18bo$37bobo3bobo60boobbo4bobbo18b3o$26boo8bobbo3bobb
o8boo47bobbo5bobb3obbo14b3oboo$26bobo8boo5boo8bobo48bo8boboboboo7bo4b
oobobbo$27boo25boo60bo3bob4obooboobobo4boboo$116boobboboboo7bobobbobob
oo$114bobo8boobobob3o8bo$38bo5bo68bo11bo8boo7boo$37bobo3bobo68bobbo7bo
$26boo8bobbo3bobbo8boo58b3o$26bobo8boo5boo8bobo58b3o$27boo25boo$$118b
oo$38bo5bo73boo20bo3bo$37bobo3bobo93b3ob3o$26boo8bobbo3bobbo8boo81boob
oboboo$26bobo8boo5boo8bobo59bo20boo7boo$27boo25boo61bo20bo7bo$114boo
21boo7boo$113bobo19boobobo3boboboo$38bo5bo70bo18bobobobooboobobo$37bob
o3bobo87boobobbobobobobboboo$26boo8bobbo3bobbo8boo75bobobobooboboboobo
boo$26bobo8boo5boo8bobo74boobobobobbobobbobobbo$27boo25boo74bo3bobo11b
obboo$140booboo$130boobooboo9boo$38bo5bo84bo$37bobo3bobo86bo3bo$26boo
8bobbo3bobbo8boo72boo19b3o$26bobo8boo5boo8bobo76b3o13bo3bo$27boo25boo
92bo4boo$141b3o3booboobobo$132bobbob3ob3oboobo4boboo$38bo5bo85booboob
oo3bobo4bo3bo4bo$37bobo3bobo84bobbobo3bo5bo$26boo8bobbo3bobbo8boo75bob
obbo9boo7boo$26bobo8boo5boo8bobo72boobooboboo$27boo25boo79boboo$130bo
bbobo$133boboboo$38bo5bo84boo3bobo13b3o$37bobo3bobo83b4ob3o12bo3bo$26b
oo8bobbo3bobbo8boo71booboo15bo4boo$26bobo8boo5boo8bobo77boobo3b3o3boob
oobobo$27boo25boo72boobobb3oboob3oboobo4boboo$130boo9bobo4bo3bo4bo$
130bobobobobbo5bo$38bo5bo87bobobo10boo7boo$37bobo3bobo86bobbobooboo$
26boo8bobbo3bobbo8boo74boo3b3o3boo$26bobo8boo5boo8bobo74bobobobobbo3bo
$27boo25boo77bobo9bo7bo$133bobobo4booboob3ob3o$132boobobo6boobb3o3boo$
38bo5bo88bobobo6boo3bo5boo$37bobo3bobo87b3obo12boo3bo$26boo8bobbo3bobb
o8boo77b3o18boo$26bobo8boo5boo8bobo78bo17boboboo$27boo25boo96boobobo$
151bo3boboboo$135bo19bo3boo$38bo5bo89bobo14boo3bob3o$37bobo3bobo88bobo
23boo$26boo8bobbo3bobbo8boo78bo$26bobo8boo5boo8bobo$27boo25boo5$26boo
27boo$26bobo25bobo$27boo25boo!
To create a c/2 puffer whose period p is 8470 or larger and is an odd multiple of 14, calculate d = (p - 1022) / 28.
Then find nonnegative integers m and n such that d = 39 * m + 8 * n.
Then m is the number of shifts using both period 14 ships, and n is the number of shifts using just the lower period 14 ship.
For example, for period 8470, d is 266, m is 6, and n is 4.
For another example, for period 9002, d is 285, m is 3 and n is 21.
The m and n values can be found for reasonable d values by simply iterating over all the m and n values from 0 to d / 39 and 0 to d / 8. I don't know if there is a direct way to find them.
BCNU,
-dbell
