1/4×4=1 State Machine

### 1/4x4=1 State Machine ## Overview The 1/4×4=1 state machine models a fundamental unit of state using electron colonies. The core principle: 1 carrier electron cycles through 4 colonies to represent 1 bit of state information. ## Core Logic: 1/4×4=1 ``` 1 carrier ÷ 4 colonies × 4 colonies = 1 complete state cycle ``` Breaking it down: - **1/4**: One carrier electron distributed across 4 colonies - **×4**: Carrier visits all 4 colonies sequentially - **=1**: After 4 ticks, one complete state cycle (D increments) Each colony contains 9 total electrons: - 4 up-spin electrons (static) - 4 down-spin electrons (static) - 1 carrier electron (dynamic - hops between colonies) ## Physics Mapping | Component | Physical Meaning | |-----------|------------------| | Colony | Localized electron group, 9 electrons total | | Up/Down Electrons | Spin-aligned particles, fixed position | | Carrier | Mobile electron that defines active state | | D Counter | Counts complete cycles = stable bit states | | OUT Pulse | Emitted when D increments = observable state change | ## Operation at 10kHz 1. **Clock Tick**: Every 100μs (10kHz), carrier hops to next colony 2. **Colony Sequence**: 0 → 1 → 2 → 3 → 0 → 1 → 2 → 3 → ... 3. **D Increment**: D++ each time carrier returns to Colony 0 4. **OUT Pulse**: OUT=1 for one tick when D increments ## Mathematical Properties ``` Ticks per D increment = 4 Frequency of D = Clock / 4 = 10kHz / 4 = 2.5kHz Bit rate = 2.5kbps per carrier ``` The 1/4 factor accounts for the carrier spending 1/4 of time in each colony. Multiplying by 4 colonies recovers unity: each full rotation = 1 bit. ## C Implementation Details ### Colony Struct ```c typedef struct { uint8_t up_electrons; // Always 4 uint8_t down_electrons; // Always 4 uint8_t has_carrier; // 0 or 1 uint8_t colony_id; // 0-3 } Colony; ``` ### Tick Function ```c void tick() { colonies[current].has_carrier = 0; current = (current + 1) % 4; colonies[current].has_carrier = 1; tick_count++; if (current == 0) { d_counter++; out_pulse = 1; } } ``` ### Main Loop ```c while (1) { usleep(100); // 100us = 10kHz tick(); } ``` ## Compilation & Execution ```bash gcc -o 1over4x4 1over4x4.c -Wall -O2 ./1over4x4 ``` Expected output shows carrier cycling through colonies with D incrementing every 4 ticks. ## Applications This architecture models: - Quantum dot cellular automata (QCA) - Single-electron transistor logic - Charge-coupled state machines - Fundamental clocked logic gates The 1/4×4=1 principle ensures conservation: 1 carrier is never created/destroyed, only relocated. After 4 relocations, system returns to ground state with D incremented. ## Timing Diagram ``` Clock: ____|ˉ|____|ˉ|____|ˉ|____|ˉ|____|ˉ|____ Col 0: [C] . . . [C] . . Col 1: . [C] . . . [C] . Col 2: . . [C] . . . [C] Col 3: . . . [C] . . . D: 0_______________1_______________2____ OUT: ________________|ˉ|_______________|ˉ|__ ``` ## License Public domain. Use for education, research, hardware design.