Lab 6: Dimensional Nested Loops — Reproducibility
Objective#
To ensure reproducibility of nested loop simulations and resonance emergence across systems.
Required Tools#
- Python 3.10+
- NumPy
- Matplotlib or Plotly
- Optional: Jupyter Notebook for visualization
Protocol#
1. Initialize Triadic Dimensions#
python#
dimensions = [1, 3, 5, 7, 9]
2. Define Resonance Operator#
python#
def resonance_operator(Di, Dj, Dk): return (Di * Dj + Dj * Dk + Dk * Di) / (Di + Dj + Dk)
3. Simulate Nested Loops#
python#
for i in range(len(dimensions) - 2): Ri = resonance_operator(dimensions[i], dimensions[i+1], dimensions[i+2]) print(f"R_{i}{i+1}{i+2} =", Ri)
4. Visualize Echo Function#
python#
import numpy as np import matplotlib.pyplot as plt t = np.linspace(0, 10, 1000) omega = 2 * np.pi echo = np.sin(omega * t) * resonance_operator(3, 5, 7) plt.plot(t, echo) plt.title("Dimensional Echo Function") plt.xlabel("Time") plt.ylabel("Echo Amplitude") plt.show()