This project was inspired by the at-risk globally Loggerhead Turtles that migrate across the Atlantic using a stochastic movement model integrating random walks, cognitive modeling, and diffusion-limited aggregation(DLA).
The simulation is a random walk with noise: each “paddle” or step updates the turtle’s position, and converts its orientation into Delta x, Delta y movements using trigonometry. Over thousands of paddles, these minute deviations generate realistic path trajectories rather than a perfectly straight line.
Instead of treating the turtle as a random particle, the simulation adds a direction bias towards a target destination to imitate magnetoreception. The turtle avoiding land is motivated by the same constraint dynamics of DLA. In DLA, particles diffuse randomly, although they don't pass through occupied regions, so the environment shapes the final path. Coastlines act as a geometry rejected area when a subsequent step updates on land, the code rejects the step and retries until a limit. This creates a boundary limited diffusion process that the turtle’s migration path emerges from the interaction between randomness, navigation bias, and environmental constraints. Overall, the result is an interpretable agent-based simulation: random walk dynamics generate exploration, cognitive bias provides long-range directionality, and DLA-style boundary constraints shape the trajectory around continents—producing a plausible ocean-only route from the Canary Islands toward South America.