A bit more math, singing that Sycl song.

VEXEL: One point-unit in the geometry, containing the mathematical state and data fields for that coordinate.

NGine: The active transformation associated with each VEXEL. It reads the VEXEL, consults neighboring state, rules, and lookup tables, and produces the next state.

VEXAFRACTA: The complete N × N × N volume formed from stacked VEXEL planes.

Conceptual relationship:

NGine(Vi, Ni, R, L) → Vi

Where:

  • Vi is the current VEXEL.
  • Ni is its neighborhood.
  • R is the rule set.
  • L is the collection of lookup tables.
  • Vi′ is the resulting next state.

Conceptually, every VEXEL has an NGine.

Physically, the GPU does not store millions of separate copies of the code. One compiled NGine kernel is executed across many VEXELs, with each invocation operating on a different coordinate and state record.

The VEXEL holds.
The NGine acts.
The VEXAFRACTA emerges.