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Monte Carlo Analysis of Boid Simulations with Obstacles: A Physics-Based Perspective

Quoc Chuong Nguyen

TL;DR

This work extends the classic Boids flocking model by adding Obstacle Avoidance and Wander rules and analyzes the resulting dynamics through Monte Carlo simulations in obstacle-rich environments. The authors formulate a weighted Newtonian framework that combines separation, alignment, cohesion with the new rules, and they introduce physics-inspired metrics (Average Speed, Flocking Radius, Turn Rate, Dispersion) to quantify emergent flocking behavior. Key findings show that the separation and cohesion balance largely controls flock size and clustering, while alignment has a limited effect, with boids attaining stable speeds and directions after moderate iterations, illustrating an energy-efficient, collective motion akin to natural flocking. The study provides a computational framework for understanding obstacle-influenced flocking and offers data and code resources for replication and further exploration.

Abstract

Boids, developed by Craig W. Reynolds in 1986, is one of the earliest emergent models where the global pattern emerges from the interaction between many individuals within the local scale. In the original model, Boids follow three rules: separation, alignment, and cohesion; which allow them to move around and create a flock without intention in the empty environment. In the real world, however, the Boids' movement also faces obstacles preventing the flock's direction. In this project, I propose two new simple rules of the Boids model to represent the more realistic movement in nature and analyze the model from the physics perspective using the Monte Carlo method. From those results, the physics metrics related to the forming of the flocking phenomenon show that it is reasonable to explain why birds or fishes prefer to move in a flock, rather than sole movement.

Monte Carlo Analysis of Boid Simulations with Obstacles: A Physics-Based Perspective

TL;DR

This work extends the classic Boids flocking model by adding Obstacle Avoidance and Wander rules and analyzes the resulting dynamics through Monte Carlo simulations in obstacle-rich environments. The authors formulate a weighted Newtonian framework that combines separation, alignment, cohesion with the new rules, and they introduce physics-inspired metrics (Average Speed, Flocking Radius, Turn Rate, Dispersion) to quantify emergent flocking behavior. Key findings show that the separation and cohesion balance largely controls flock size and clustering, while alignment has a limited effect, with boids attaining stable speeds and directions after moderate iterations, illustrating an energy-efficient, collective motion akin to natural flocking. The study provides a computational framework for understanding obstacle-influenced flocking and offers data and code resources for replication and further exploration.

Abstract

Boids, developed by Craig W. Reynolds in 1986, is one of the earliest emergent models where the global pattern emerges from the interaction between many individuals within the local scale. In the original model, Boids follow three rules: separation, alignment, and cohesion; which allow them to move around and create a flock without intention in the empty environment. In the real world, however, the Boids' movement also faces obstacles preventing the flock's direction. In this project, I propose two new simple rules of the Boids model to represent the more realistic movement in nature and analyze the model from the physics perspective using the Monte Carlo method. From those results, the physics metrics related to the forming of the flocking phenomenon show that it is reasonable to explain why birds or fishes prefer to move in a flock, rather than sole movement.

Paper Structure

This paper contains 11 sections, 3 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Model
  3. Description
  4. Mathematical formulations
  5. Metrics
  6. Experiments
  7. Experiemental setup
  8. Experimental Results
  9. Discussion and Future Works
  10. Contact me
  11. Data availability

Figures (2)

  • Figure 1: the visualization of the Boid simulation using the code in \ref{['sec:data-availability']}. The black triangle represents the Boid, and the red circles are obstacles
  • Figure 2: The results of the experiment with the setting in \ref{['sub:exp-setup']}. The variation in $w_{a}$ has minimal impact on the behavior of Boids, as demonstrated in Fig. \ref{['fig:alignment']}. However, changes in separation ($w_{s}$) and cohesion ($w_{c}$) significantly influence the size and formation of the flock. Figures \ref{['fig:separation']} and \ref{['fig:cohesion']} show that flocks remain small and tightly clustered when $w_{c}$ exceeds $w_{s}$, whereas the opposite causes the flock to spread out. Over time, the results further reveal that the velocity of each Boid remains stable, both in magnitude (evidenced by the average speed) and direction (indicated by the turn rate).