gh-eq-f8a9f5a625f3208fdocumented-equation
Read the equation
This is a rotation of the unit circle by 1/φ per update. In exact real arithmetic the irrational increment prevents an exact return after a positive integer number of steps. An implementation stores finite-precision values, so mathematical irrationality alone does not guarantee a nonrepeating computer state.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| phase_Fib | Wrapped phase |
| φ | Golden ratio |
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 is a golden-ratio rotation, not a recurrence that computes successive Fibonacci integers.
Original context
Read the surrounding source passage
## 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 ``` **Explanation**: Averaging the two phases creates a combined modulation signal for the gates. ## 7.4 Gate Transition Rule ``` flip_i = 1 if (i mod 1000) < (bias · 1000), else 0 gate_i(t+1) = (gate_i(t) XOR input_i) XOR flip_i ``` **Explanation**: Each of the 5000 gates performs XOR with its input, then conditionally flips based on the phase bias. Gates in the lower portion of each 1000-gate block are more likely to flip, creating structured diffusion patterns.
Exact original notation
phase_Fib(t+1) = (phase_Fib(t) + 1/φ) mod 1
Related builds
Sources & provenance
01
That AI Guy Core — Mathematical Reference v1.0.0
Lines 445–445
02
That AI Guy Core — Mathematical Reference v1.0.0
Lines 445–445