Wandering Position Simulator

A minimal, reproducible simulator for insect-like trajectories that create dense, meditative line drawings.

Overview

This project simulates the path of a small insect moving on a flat surface. The model is a correlated random walk with reflective boundaries. The output is a continuous 2D trajectory that you can render as an artwork. It is simple, fast, and reproducible, and it provides parameters that control straightness, step size, and domain size.

Example output of the simulator with 1,000,000 steps, step length 0.3, kappa 50, in a 1600x900 domain.

Inspiration

The idea is inspired by works where an artist follows the path of an insect and records its motion as a drawing. In particular, Yukinori Yanagi’s Wandering Position traces the movement of a single ant within a bounded field, producing a dense web of lines that makes invisible constraints visible. This simulator recreates the aesthetic of such paths algorithmically while keeping the dynamics interpretable and minimal.

Mathematics (short)

We model heading and position in discrete time:

• Heading update (directional persistence)

$$ \theta_{t+1} = \theta_t + \Delta_t,\qquad \Delta_t \sim \mathrm{vonMises}(\mu=0,\kappa) $$

where $\kappa \ge 0$ is the concentration parameter. Larger $\kappa$ means smaller random turns and straighter motion.

• Position update (constant step length $s$)

$$ \mathbf{x}_{t+1} = \mathbf{x}_{t} + s \begin{bmatrix} \cos\theta_{t+1} \\ \sin\theta_{t+1} \end{bmatrix} $$

where $s > 0$ is the fixed step length.

• Boundary handling (rectangular domain)

  If the next point exits the rectangle, we reflect it elastically and flip the heading across the corresponding axis. This preserves step length and creates realistic “bounces” along the edges.

This simple CRW captures short-term directional memory observed in many biological foragers while staying easy to tune and reason about.

Features

• Correlated random walk with von Mises turning noise
• Reflective rectangular boundaries
• Reproducible randomness with a seed
• High-resolution rendering suitable for prints
• Minimal, dependency-light code

Installation

pip install -r requirements.txt
# requirements: numpy, matplotlib

Quick start (Python API)

from simulator import simulate_correlated_walk
pos = simulate_correlated_walk(
    n_steps=1_000_000,
    step_length=0.3,
    kappa=50.0,
    bounds=(1600, 900),
    seed=42
)
# pos is an (N, 2) array of x,y points. Plot as you like.

Parameters

• n_steps Number of steps to simulate. Larger values create denser drawings.
• step_length Size of each step in pixels or arbitrary units.
• kappa von Mises concentration. Higher → straighter motion; lower → more wandering.
• bounds (width, height) of the rectangular domain.
• seed Random seed for exact reproducibility.

Tips

• Start with kappa around 20–50.
• Increase n_steps for denser textures; increase bounds to reduce density.
• For dramatic strokes, occasionally sample a larger step_length.
• Map speed to linewidth to emulate pen pressure (optional extension).

How it works (implementation notes)

1. Initialize position at the center and a random heading.
2. At each step, sample a small turning angle from a von Mises distribution centered at 0.
3. Advance by a constant step.
4. If the point exits the domain, reflect the point and heading across the wall.
5. Store the path; render as connected segments with a gentle color gradient.

Acknowledgements

Conceptually inspired by artistic practices that trace insect motion, notably Yukinori Yanagi’s Wandering Position series. This repository aims to provide a transparent, educational model that others can study, extend, and adapt for creative use.

License

MIT (see LICENSE).