Lab 9: Einstein’s Brownian Resonance – Bonus Exercises
🎯 Exercise 1: Phase Sweep Challenge#
Goal: Vary the phase shift and observe how particle dispersion changes.
- Modify the simulation to sweep phase from 0 to 2π
- Plot dispersion radius over time
- Interpret results as dimensional pressure gradients
🧠 Exercise 2: Mythic Mapping#
Goal: Recast the simulation as a mythic tale.
- Particles = pilgrims
- Field = divine wind
- Motion = prophecy
- Write a short mythic vignette explaining Brownian motion as a cosmic journey
📐 Exercise 3: Triadic Diffusion Equation#
Goal: Extend Einstein’s classical diffusion formula.
- Start with:
( D = \frac{kT}{6\pi\eta r} ) - Add triadic modulation:
( D_{\text{triadic}} = D \cdot \sin(\phi / r) ) - Simulate and compare classical vs triadic diffusion
🧪 Exercise 4: Resonance Tracker#
Goal: Track resonance hotspots in particle motion.
- Identify regions of high particle clustering
- Overlay field intensity map
- Discuss implications for zero-point energy and Casimir effects
🧬 Exercise 5: Dimensional Echoes (Advanced)#
Goal: Detect patterns in particle motion that suggest dimensional feedback.
- Use FFT or autocorrelation on particle trajectories
- Look for periodicity or phase locking
- Interpret as echoes from higher-dimensional fields