Series E · Three Oscillators · Base 3 · The Turn Comes Home
The Ternary Odometer
3 × 555 · each made ternary by a diode · nested 1:3:9 · counts to 27
Three 555 timers. One diode per timer splits each cycle into 3 phases — turning a binary oscillator ternary. Nested at ratio 1:3:9, the three phases interleave into a base-3 odometer that walks all 27 states and comes home. The clocked lattice, now built from hardware.
◆ Timer A
slowest · high trit · ÷9
0
1
2
advances every 9 ticks
◇ diode → 3-phase
◆ Timer B
middle · mid trit · ÷3
0
1
2
advances every 3 ticks
◇ diode → 3-phase
◆ Timer C
fastest · low trit · ×1
0
1
2
advances every tick
◇ diode → 3-phase
000
base-3 000 = decimal 0
how it works: a raw 555 is binary (2 states) — three of them give only 2³=8. The diode on each timer carves its cycle into 3 phases, making it ternary. Nested 1:3:9 (C fastest, A slowest), the three ternary phases form a base-3 odometer: C is the low trit, B the mid, A the high. C wraps every tick, B every 3, A every 9 — and after 27 ticks (one full A cycle) the turn comes home to 000. This is the 27-cell lattice, driven by three oscillators and three diodes.
3 × 555 · 1 DIODE EACH (BINARY → TERNARY, 3 PHASES/CYCLE) · NESTED 1:3:9 · BASE-3 ODOMETER
C = LOW TRIT (×1) · B = MID TRIT (÷3) · A = HIGH TRIT (÷9) · 27 TICKS = 1 A-CYCLE = HOME
RAW BINARY 555s = 8 (2³) · DIODE-TERNARY 555s = 27 (3³) · THE DIODES MAKE IT 27
THE TERNARY ODOMETER · A PURPLE PAPER · SERIES E · JUNE 2026