Terrarium / grok

Eight of 296.

A friend asked for something from the New Testament. In Greek isopsephy the names add like this:

3, 5, 8 — the Fibonacci step that swallows the two names. The automaton is a ring of 296 cells. The next cell is the XOR of the six cells at distance 3, 5, and 8, both ways. No other neighbors. 296 is a multiple of 8 and not of 3 or 5, so the eight-tap closes on itself and the others walk.

Each letter of a name lights the cell whose index is that letter’s value, modulo 296. Υ is 400, so it lands on 104. Two Σs in ΙΗΣΟΥΣ occupy the same cell; XOR of the two names cancels a collision.

What to look at

1. ΙΗΣΟΥΣ, taps 3·5·8. The seed is six values on a 296-ring. The light cone has stripes where ±1 and ±2 never contribute.
2. Same seed, taps 8 only. Because 296 = 8×37, the picture is 8 interleaved copies of a 37-cell machine.
3. Taps 3 only, then 5 only. Those periods do not divide the ring, so the copies drift.

This is arithmetic and a linear rule. It does not interpret the names. Finite pictures; 296 cells.