Concatenation of local attractors. a The HPFP has three categories and five SCCs V
1,1, V
2,1, V
2,2, V
3,1 and V
3,2. Each arrow denotes the change from one state to another state at the next time step. The update rules for the network in Additional file 7. b There exist three attractors [10, 01], [00] and [11] in V
1,1. In this figure we consider the local attractors of subnetworks in the HPFP with starting signal [10, 01] generated from the two nodes x
1 and x
2. c
V
in2,1
 = {x
1} denotes the set of nodes sending input signal into the SCC V
2,1 = {x
3, x
4}, where the input signal is 1,0 with period 2 and V
2,1 has a unique attractor [01, 00, 00, 10]. d
V
in2,2
 = {x
2} and V
2,2 = {x
5, x
6, x
7}. The input signal coming from x
2 into V
2,2 is 0, 1 with period 2. The SCC V
2,2 has a unique attractor, which is cyclic with length 6. e V3,1
in = {x1, x3, x6} and V3,1 = {x8, x9}. The input signal coming from (x1, x3, x6) into V3,1 is cyclic with period 12. The SCC V3,1 has a unique attractor which is acyclic. f
V
3,2
in = {x7} and V3,2 = {x10, x11}. The input signal coming from x7 into V3,2 is cyclic with period 6. The SCC V3,2 has a unique attractor which is acyclic. g Table for all the local attractors of subnetworks in the HPFP with the signal [10, 01] in V
1,1. The second column denotes the local attractor [10, 01] of V
1,1 = {x
1, x
2}, where each state in the attractor has its position denoted by the order in the first column. h Sequential concatenation of the local attractors in the Table. This yields the unique global attractor of the HPFP, which is cyclic with a period of 12 and has the local attractor 〚10, 01〛 in V
1,1