This does not apply to every 1D replicator.
The replicator itself is A.
The replicator shifted left one cell is A<.
The replicator shifted right one cell is A>.
The replicator shifted up one cell is A^.
The replicator shifted down one cell is Av.
An empty space is 0.
Reactions are described as follows:
A(transformations) or 0+A(transformations) or 0=A(transformations) or 0
If one transforms the inputs in the same way, the output will have the identical transformation applied to it, too.
For example:
A+A+A^
(A)^+(A)^=(A^)^
A^+A^=A^^
Example with a simple Rule 90 replicator
0+0=0
0+A=A
A+0=0
A+A=0
x=31, y = 47, rule = B2a/S
15bo$15bo2$14bobo$14bobo2$13bo3bo$13bo3bo2$12bobobobo$12bobobobo2$11bo
7bo$11bo7bo2$10bobo5bobo$10bobo5bobo2$9bo3bo3bo3bo$9bo3bo3bo3bo2$8bobo
bobobobobobo$8bobobobobobobobo2$7bo15bo$7bo15bo2$6bobo13bobo$6bobo13bo
bo2$5bo3bo11bo3bo$5bo3bo11bo3bo2$4bobobobo9bobobobo$4bobobobo9bobobobo
2$3bo7bo7bo7bo$3bo7bo7bo7bo2$2bobo5bobo5bobo5bobo$2bobo5bobo5bobo5bobo
2$bo3bo3bo3bo3bo3bo3bo3bo$bo3bo3bo3bo3bo3bo3bo3bo2$obobobobobobobobobo
bobobobobobo$obobobobobobobobobobobobobobobo!
Example with a more complicated replicator
0+0=0
0+A=A
A+0=0
A+A=Av
A+Av=0
Av+A=0
x=132, y = 131, rule = B2e35y7e/S1c2ace3an
65b2o$64bo2bo$65b2o14$57b2o14b2o$56bo2bo12bo2bo$57b2o14b2o14$49b2o13bo
2bo13b2o$48bo2bo12b4o12bo2bo$49b2o13bo2bo13b2o14$41b2o46b2o$40bo2bo44b
o2bo$41b2o46b2o14$33b2o14b2o30b2o14b2o$32bo2bo12bo2bo28bo2bo12bo2bo$
33b2o14b2o30b2o14b2o14$25b2o13bo2bo13b2o14b2o13bo2bo13b2o$24bo2bo12b4o
12bo2bo12bo2bo12b4o12bo2bo$25b2o13bo2bo13b2o14b2o13bo2bo13b2o14$17b2o
45bo2bo45b2o$16bo2bo44b4o44bo2bo$17b2o45bo2bo45b2o14$9b2o14b2o29bo2bo
12bo2bo29b2o14b2o$8bo2bo12bo2bo28b4o12b4o28bo2bo12bo2bo$9b2o14b2o29bo
2bo12bo2bo29b2o14b2o14$b2o13bo2bo13b2o13bo2bo12bo2bo12bo2bo13b2o13bo2b
o13b2o$o2bo12b4o12bo2bo12b4o11bo4bo11b4o12bo2bo12b4o12bo2bo$b2o13bo2bo
13b2o13bo2bo12bo2bo12bo2bo13b2o13bo2bo13b2o!
Unknown classification
AKA the WHAT HAVE I DONE replicator.
x=4, y = 3, rule = B2e3eijkq5aey6a8/S1c2aci3a4c5kq6n
b2o$o2bo$b2o!