Read the equation
A gate flips when its index modulo 1000 falls below the threshold 1000×bias. The next bit is the XOR of its old value, its input bit, and that deterministic mask bit. With five groups of 1000 gates, the threshold mask repeats across the five groups; differences can still come from their old states and input bits.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| gate_i | Bit stored at gate i |
| input_i | Input bit |
| flip_i | Deterministic threshold mask |
| bias | Threshold fraction |
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
The threshold rule is deterministic, not a probability of flipping. For fixed input and mask, applying the same XOR twice restores the initial bit.
Original context
Read the surrounding source passage
## 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. --- # 8. Neural Brain Dynamics (dna_v9) The 88-agent neural brain uses the following exact equations: ## 8.1 Input Processing ``` F_in = input + N(0, 0.1) ``` **Where**: - `N(0, 0.1)` = Gaussian noise with mean 0 and std 0.1 **Explanation**: Each agent receives the input signal plus random noise, ensuring diverse responses across the population.
Exact original notation
flip_i = 1 if (i mod 1000) < (bias · 1000), else 0 gate_i(t+1) = (gate_i(t) XOR input_i) XOR flip_i