Advance the DNA phase modulo one

Read the equation

Adding δ advances phase by a fixed fraction of a turn and reduction modulo one wraps it into [0,1). For the exact decimal δ=0.013618, the phase returns after 500000 increments because the fraction is rational in lowest terms. A finite-precision implementation needs its own numerical orbit analysis.

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

• This declared decimal does not generate an aperiodic exact rotation.

Original context

## 7.1 DNA Phase Update

```
phase_DNA(t+1) = (phase_DNA(t) + δ) mod 1
```

**Where**:
- `δ = 0.013618` (DNA delta constant)

**Explanation**: The DNA phase advances by a small golden-ratio-related increment each step, creating quasi-periodic patterns.

## 7.2 Fibonacci Phase Update

```
phase_Fib(t+1) = (phase_Fib(t) + 1/φ) mod 1
```

**Explanation**: The Fibonacci phase advances by the golden ratio inverse, creating a different quasi-periodic pattern that never exactly repeats the DNA phase.

## 7.3 Combined Phase Bias

```
bias = (phase_DNA + phase_Fib) / 2
```

phase_DNA(t+1) = (phase_DNA(t) + δ) mod 1

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