Lab 9: Brownian Resonance

Mythic Preface#

"Chaos dances. Harmony listens. Resonance emerges."
Brownian motion is the whisper of entropy. Overlay it with rhythm, and you hear the cosmos breathe.

Objective#

Simulate Brownian motion and overlay harmonic resonance.

Core Equations#

Brownian path:

[ x(t) = x_0 + \sum_{i=1}^{n} \Delta x_i ]

Resonance overlay:

[ R(t) = x(t) \cdot \sin(2\pi f t) ]

Tasks#

• Generate Brownian path
• Apply sinusoidal overlay
• Visualize resonance emergence

Engineer’s Notes#

Use np.cumsum(np.random.normal(...)) for Brownian path. Choose f = 0.1 for slow resonance. Normalize for clarity.