DNA phase increment: the declared decimal constant

Read the equation

This version advances its DNA phase by 0.013618 of a turn per update. The document’s nearby approximation δ≈1/φ³ is numerically incorrect: 1/φ³≈0.2360679775. The written decimal is exactly 6809/500000, so its ideal rational rotation repeats after 500000 updates; floating-point arithmetic can produce a different numerical orbit.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

• Preserve the declared value and the incorrect approximation as separate source statements.

Original context

## 1.2 DNA Phase Increment (δ)

```
δ = 0.013618
```

**Explanation**: This value (approximately 1/φ³) determines the rate at which the DNA helix phase advances. It creates quasi-periodic oscillations that prevent the system from falling into repetitive loops while maintaining coherent behavior.

## 1.3 Tau (τ)

```
τ = 1/(2π) = 0.159154943...
```

**Explanation**: Used in frequency calculations to convert between angular and linear frequency domains.

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# 2. Golden Ratio Mathematics

## 2.1 Golden Basis Function

```
ψ_k(x) = sin(2π · φ^k · x) + cos(2π · φ^k · x)

δ = 0.013618

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