Week 23 — Coding Projects

Core

Simulate Markov chains and random walks.

• NumPy: Build transition matrices. Simulate chains. Estimate empirical stationary distribution. Implement 1D or 2D random walk.
• Metal: Many random walks in parallel with state update kernels. · Reading: MBT — buffer-based simulation loops, state update kernels.
• Vulkan: Random-walk state update compute pipeline with iterative state updates. · Reading: Vulkan Book — compute simulation framework, iterative state updates.
• CUDA: Massive random-walk simulation with random-state management. · Reading: CUDA Book — simulation kernels, random-state management.
• Stretch: Add absorbing states and hitting-time experiments. Compare empirical and matrix-power distributions.
• Verify: Row-stochastic transitions sum to 1 · Long-run empirical distribution matches theory in easy cases · Random-walk intuition is visible.