Network Automata are usually processed synchronously. That is, each node's state is based strictly on the activity of its neighbourhood in the previous timestep. For this reason, it doesn't matter in what order the nodes are updated. However, it is sometimes beneficial to update the states of the nodes asynchronously. There are various ways to implement such behaviour, but normally one specifies an update order for the nodes, or one allows the nodes to be updated in a random order, such that a nodes's state is based on the activity of its neighbourhood immediately. In practice, this means that, in each "timestep", only a single node is updated. The "true" timestep is complete once all nodes have been updated in an update cycle.
There are other ways to implement asynchronous dynamics in discrete
systems, but Netomaton supports the sequential kind of asynchronous updates,
described above, in the AsynchronousRule class.
The following example implements the elementary rule 60 sequential automaton from Wolfram's NKS Notes on Chapter 9, section 10: "Sequential cellular automata" (http://www.wolframscience.com/nks/notes-9-10--sequential-cellular-automata/):
import netomaton as ntm
network = ntm.topology.cellular_automaton(n=21)
initial_conditions =[0]*10 + [1] + [0]*10
r = ntm.AsynchronousRule(activity_rule=ntm.rules.nks_ca_rule(60),
update_order=range(1, 20))
trajectory = ntm.evolve(initial_conditions=initial_conditions, network=network,
timesteps=19*20, activity_rule=r)
# plot every 19th row, including the first, as a cycle is completed every 19 rows
activities = ntm.get_activities_over_time_as_list(trajectory)
ntm.plot_grid(activities[::19])
The full source code for this example can be found here.