02. Particles

At the beginning of a Particle World simulation, the spatial environment is established and the agents are placed upon it. Recall that agents have only two uniquely held properties—location and heading—and so each agent will keep track of its own values for these variables (NetLogo does this automatically for turtles). How should they be initially assigned? There are lots of possibilities. For example, all the agents might start in the same location, or be evenly spaced in a grid pattern, or be arranged in a circle, or in the shape of a T-rex, or be placed on the grid in locations representing actual places in the real world. Similar concerns apply to their directional headings. If we don’t have good reasons to choose one of these, or if we have a good reason to think it doesn’t matter, we might as well draw both locations and headings at random from a uniform distribution of choices, and this is what we have done.

In the Particle World model, we are concerned with the number of collisions that occur over the course of the simulation, as a function of both whimsy and num-particles.

In order to make sense of how the model details map onto the real-world system, it helps to explain the model system verbally. The subsequently presented formal details can then be used to clarify how the model works without requiring the reader to simultaneously figure out the underlying analogy to the real world.

Particle World Description

This model features a population of spatially embodied agents moving through continuous space, each using a correlated walk. When agents collide, they become confused, and each sets off in a new direction. We run each model simulation for 10,000 time steps and compare the number of collisions during that time.

Initialization

A population of 𝑁 agents is initialized with each agent placed at a random real-valued locations on an 𝐿 × 𝐿 grid with periodic boundaries. Each agent 𝑖 has a direction heading θ_𝑖, which is initially chosen at random from a uniform distribution of integers [0, 359]. Each agent is fully defined by its location and directional heading. Other model parameters are the whimsy, 𝑤, which determines the turning angle agents use on each time step, and the speed, 𝑠, which determines the size of the step they take when moving. Finally, we keep track of the cumulative number of collisions over time, 𝐶(𝑡).

Dynamics

At each time step, each agent, in a random order, turns, moves, and collides.

1. An agent first turns by adding to its direction heading an integer value that is randomly drawn from a uniform distribution in [0, 𝑤]. The agent then subtracts a newly drawn value from the same distribution from its directional heading. In other words, its new directional heading is θ_𝑖 +ɛ, where ɛ is randomly drawn from a binomial distribution bounded in [−𝑤, 𝑤].
2. The agent then moves 𝑠 units forward.
3. If there are any other agents with a position within one unit of the focal agent’s new location (defined by the Euclidean distance between the centers of each agent), a collision occurs between the focal agent and all of these other nearby agents. In this case, all of the agents involved in the collision update their heading to a new value randomly selected from the uniform distribution [0, 359]. Each of the involved agents then moves forward 0.1 spatial units in order to move away from the site of the collision and avoid cycles of perpetual collision. If a collision occurs, the cumulative collision counter 𝐶(𝑡) is incremented by one.

(explanation on correlated random walk, reread again!)

We can learn so much when we give ourselves license to simply try things for the sake of trying them. Play is important even when coding artificial worlds, partly because play helps you to develop stronger competence in turning your ideas into reality.