Series E · Nine At A Time · Three Phases · Period 3
The Turn Comes Home
a clocked 27-cell ternary lattice · 3 × 9 = 27
27 cells, but never all at once. The clock lights 9 at a time — one 3×3 plane per phase — and sweeps three phases to cover all 27, then returns home. The high trit picks the phase; the low two address the nine. Watch the turn come home every third tick.
PHASE 0 · trit −1
PHASE 1 · trit 0
PHASE 2 · trit +1
3tick (phase)
9width (per phase)
27cycle (full lattice)
3period (home)
how to read it: the cube is 3 planes of 9. each phase lights one plane (9 cells) — the cells whose high trit equals the phase. three phases sweep all 27 and the clock returns to phase 0 — the turn comes home. it's time-division over the ternary lattice: a 9-wide window, a 3-phase clock, 27 addressed without 27 simultaneous lines. balanced ternary: high trit = phase, low two trits = the nine.
27 CELLS · 9 LIVE PER PHASE · 3 PHASES · PERIOD 3 · THE TURN COMES HOME
HIGH TRIT = PHASE · LOW TWO TRITS = THE NINE · 3 (TICK) × 9 (WIDTH) = 27 (CYCLE)
TIME-DIVISION OVER A TERNARY LATTICE · THE DUTY-CYCLE CLOCK OVER THE 27-CELL REGISTER
THE TURN COMES HOME · A PURPLE PAPER · SERIES E · JUNE 2026