A process whose communities can only be seen with memory. Four groups of
four actions sit on a ring and neighbouring groups share one action
(s1, ..., s4); the other two actions of group \(k\) (p<k>_1,
p<k>_2) are its own. A walk starts in a random group at a random action
of it and each step moves to another action of the current group, chosen
at random; on reaching a shared action the walk switches to the
neighbouring group with probability 0.05. At a shared action a
first-order network sees both groups equally, while a second-order state
such as "p1_1 -> s2" knows it came from group 1. The planted group of
every state is in ring_communities.
Format
A list of 200 character vectors, one walk each, 40 actions long,
over the 12 actions s1-s4 and p1_1-p4_2.
See also
hg_communities(), which recovers the four groups from these
sequences.
Examples
length(ring_sequences)
#> [1] 200
ring_hon <- hon(ring_sequences, max_order = 2L)
ring_hon
#> Higher-order network: 12 states, 36 nodes, 189 rules (highest order 2, min_freq 1, 200 sequences)
#> path from to count probability from_order to_order
#> p1_1 -> s1 p1_1 s1 166 0.317399618 1 2
#> p1_1 -> s2 p1_1 s2 176 0.336520076 1 2
#> p1_1 -> p1_2 p1_1 p1_2 181 0.346080306 1 1
#> p1_1 -> s1 -> p1_1 p1_1 -> s1 p1_1 51 0.310975610 2 1
#> p1_1 -> s1 -> p1_2 p1_1 -> s1 p1_2 56 0.341463415 2 1
#> p1_1 -> s1 -> p4_1 p1_1 -> s1 p4_1 2 0.012195122 2 1
#> p1_1 -> s1 -> p4_2 p1_1 -> s1 p4_2 1 0.006097561 2 1
#> p1_1 -> s1 -> s2 p1_1 -> s1 s2 49 0.298780488 2 2
#> p1_1 -> s1 -> s4 p1_1 -> s1 s4 5 0.030487805 2 2
#> p1_1 -> s2 -> p1_1 p1_1 -> s2 p1_1 59 0.341040462 2 1
#> ... 179 more rows