Surface dynamics /Border dynamics/Edge dynamics refers to things spatially constrained to a continuous border between two well-defined stable tilings.
Due to the spatial constraint, a surface/borderline is neighbored by 2 tilings. It cannot neighbor 3 tiling which will define a point. However transient bubbles can be seen as the third neighboring tilting to some extent, but such argument needs careful generalisation.
The 'rich' dynamics should better be interpreted as 'trapped and rich', i.e. the border is not expanding nor contracting (if you use a torus this can be better visualised, cuz bubbles would inevitably contract due to topological constraint). Thus, any dynamics at border should not rely too much on the macrodynamics of the border, but it should be restricted to the border.
On a related case, such surface dynamics can also create soliton that escape the surface. Many rules in this other post should serve as good examples.
It also seems Wolfram's classification could be adapted here. However its interpretation is largely context-dependent anyway. So we might be better off referring to particular exemplar rules to establish any comparison.
Attached are some characteristic dynamics.
surface replicator
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x = 20, y = 27, rule = B468/S01245678:T20,0
12ob7o$20o$20o$20o$20o$20o$20o$20o$3o2b11ob3o$16ob3o$20o$10ob9o$9ob10o
$20o$13o2b5o$20o$20o$20o$20o$4ob15o$5ob14o$12ob7o$12ob7o$20o$20o$11ob
8o$6bobo!
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x = 30, y = 39, rule = B012678/S0134:T30,0
7$24b4o$b3o18b8o$7o14bob7o$6obo13b9o$6o13b11o$8obo9b11o$10o9b11o$11o7b
12o$12o6b12o$14ob15o$30o$30o$30o$30o$30o$30o$30o$30o$30o$30o$30o$30o$
14ob15o$14bob11o!
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x = 30, y = 25, rule = B0124/S02:T30,0
14b6ob4o$14b14o$b3ob3obo2b17o$30o$30o$30o$30o$30o$30o$30o$30o$30o$30o$
30o$30o$30o$30o$30o$30o$30o$9ob20o$8o3b2ob2ob2ob10o$8o14b8o$5o18b7o$3o
21b6o!
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x = 30, y = 42, rule = B0168/S024:T30,0
3$2bo2bo$3bo3bo$bob4o$o2b4o$2b7o$4b6o$o2b16o$3b16o$3b16o$4b16o$3bob15o
$5b15o5bo$5b15o5bo$3bob18o$5b20o$2bob21obo$bo5b19o$2b2o3b19o2bo$o6bob
18o$b3ob3o3b18o$o4bo5b18o$bo3bo3b19o$bo3bo3b19obo$bobo3bob18o$9b18obo$
2bob2o2b19o2bo$9b16o$10bobob4o2b5o$12bo3bo2bob3o4bo$18bobobo$13bo5b3o$
25bo$18bobo2bo$19b3o2$13bo!
Code: Select all
x = 30, y = 69, rule = B012567/S0123:T30,0
2$9bo$5bo2b3o7b3o$6b7o2bo2bob4obo$3bo3b9o2b3o3bo$4bo2b11obob4obo$8b12o
2b5o$7b19o$8b19o$8b20o$7b22o$7bob19o$8b21o$9b7obob7obo$bo8bo2b2o3b2ob
8o$11bo6bob10o$o10b2o7b10o$4o7b3o7b9o$3obo7bo4bobob9o$4obo5bobo2bobob
10o$6o5b5o3b11o$5o8b3o4b10o$7o6b2o2bob11o$7o5b6o2b10o$6o4b2obo3b13o$6o
2bo2b19o$10obobo2b10ob3o$b5ob3o7b11obo$bob5o10b7o4bo$ob4o4bo5bobob5o2b
3o$o3b6o7bob6o3b2o$bob11o8b2o4b2o$6b8o3b2o4bo2b4o$8b6o5bob3ob3o$7b7o8b
o2bo$8b5o10b2o2bo$5b9obo7bo2bo$3b14obo5bo$3b15o6bobo$3b15o$2b13o7b4o$
15o7b5o$15o7b8o$15o8b7o$17o4b2ob6o$22ob7o$22obob5o$20o4b6o$20o6b4o$20o
6b4o$4o4b12o5b5o$2o7b11o5bob3o$2o7b13o5b3o$b2o5b14o5bo$6b2ob15o3bo$3bo
2b19o$3bo2b20o$4bob20o$4bob18obo$6b2o2b14o$11b10obo$11b8o$12b7o$10b9o$
12b7o$14b6o!