# Density classification with a small-world network

This demo is inspired by "Collective dynamics of ‘small-world’ networks",
by Duncan J. Watts and Steven H. Strogatz (Nature 393, no. 6684
(1998): 440). Towards the end of the paper, they state:

> For cellular automata charged with the computational task of density classification, we find that a simple ‘majority-rule’ running on a small-world graph can outperform all known human and genetic algorithm-generated rules running on a ring lattice.


The code below attempts to reproduce the experiment they are referring to:

```python
import netomaton as ntm
import numpy as np

network = ntm.topology.watts_strogatz_graph(n=149, k=8, p=0.5)

initial_conditions = np.random.randint(0, 2, 149)

print("density of 1s: %s" % (np.count_nonzero(initial_conditions) / 149))

trajectory = ntm.evolve(initial_conditions=initial_conditions, network=network,
                        activity_rule=ntm.rules.majority_rule, timesteps=149)

ntm.plot_activities(trajectory)
```

<img src="../../resources/small_world.png" width="50%"/>

The full source code for this example can be found [here](small_world_density_classification_demo.py).