Graph Diffusion: Modeling a Bug's Random Walk
In this multi-lesson mathematical modeling unit, students explore how a "very dumb bug" moves through a maze by making random choices. They represent mazes as graphs, build probability tables, construct probability trees, and track how the bug's location evolves over time. The unit introduces diffusion on graphs through an intuitive, playful lens grounded in randomness and student-designed mazes.
What Students Do
- Convert mazes into graphs with nodes and edges.
- Build probability tables describing the bug's movement rules.
- Construct and analyze probability trees for multi-step paths.
- Model diffusion on a graph using probability distributions.
- Run physical random-walk experiments and compare them to theory.
- Reflect on randomness, intelligence, and how local rules create global behavior.
Why This Unit Matters
Random walks are a foundational idea across mathematics, computer science, biology, and physics. By grounding the concept in a simple "bug in a maze" narrative, students build intuition for diffusion processes and probabilistic modeling - all without formal prerequisites. The unit blends hands-on experimentation with accessible mathematical structure.