Introduction to the Modeling and Analysis of Complex Systems

12.2. PHASE SPACE VISUALIZATION 213def config(x):return [1 if x & 2**i > 0 else 0 for i in range(L - 1, -1, -1)]def cf_number(cf):return sum(cf[L - 1 - i] * 2**i for i in range(L))def update(cf):nextcf = [0] * Lfor x in range(L):count = 0for dx in range(-r, r + 1):count += cf[(x + dx) % L]nextcf[x] = 1 if count > (2 * r + 1) * 0.5 else 0return nextcffor x in xrange(2**L):g.add_edge(x, cf_number(update(config(x))))ccs = [cc for cc in nx.connected_components(g.to_undirected())]n = len(ccs)w = ceil(sqrt(n))h = ceil(n / w)for i in xrange(n):subplot(h, w, i + 1)nx.draw(nx.subgraph(g, ccs[i]), with_labels = True)show()The result is shown in Fig. 12.1. From this visualization, we learn that there are twomajor basins of attraction with 36 other minor ones. The inside of those two major basinsof attraction is packed and quite hard to see, but if you zoom into their central parts usingpylab’s interactive zoom-in feature (available from the magnifying glass button on the plotwindow), you will find that their attractors are “0” (= [0, 0, 0, 0, 0, 0, 0, 0, 0], all zero) and“511” (= [1, 1, 1, 1, 1, 1, 1, 1, 1], all one). This means that this system has a tendency toconverge to a consensus state, either 0 or 1, sensitively depending on the initial condition.Also, you can see that there are a number of states that don’t have any predecessors.Those states that can’t be reached from any other states are called “Garden of Eden”