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The angle at index k is a full turn divided by φᵏ. Successive angles shrink by the factor 1/φ. This sequence differs from the angle θₖ=2πk/φ used in this document’s kernel section, so the two formulas are versioned local definitions rather than interchangeable rotations.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| θ_k | Angle for index k in radians |
| k | Index |
| φ | Golden ratio |
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Original context
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## 2.3 Golden Spiral Rotation ``` θ_k = 2π / φ^k ``` **Explanation**: Used in the Lattice Engine to rotate transformation kernels. Each strand operates at a different angular frequency, creating rich interference patterns that enable emergent computation. --- # 3. G^16 Family Functions The 16 cognitive families, each implementing a specific mathematical dynamic: ## 3.1 Family 0: Continuous Dynamics ``` f₀(x) = x + 0.1 · (dx_norm - x) ``` **Equation Type**: First-order ODE approximation: x' = F(x,t) **Explanation**: Models smooth, continuous change toward the input signal. The 0.1 coefficient creates a gradual approach, preventing sudden jumps. This family handles flowing, analog-like processes.
Exact original notation
θ_k = 2π / φ^k