a, b, c, d ∈ {-2…2}
Edge colour
Construction
Every point is a complex number built from four integer coordinates:
where ρ = e^(iπ/3) and a, b, c, d ∈ ℤ.
Unit edges
Two vertices share an edge if and only if their distance in ℂ equals exactly 1. A single-step change in any of the four integer dimensions produces a unit-length displacement in the plane.
Symmetry
The graph has 12-fold dihedral symmetry — the six unit directions of the Eisenstein integers doubled by conjugation. Each node is adjacent to exactly twelve neighbours at the boundary of the range.
Lilly connection
Lilly held that conscious awareness navigates a high-dimensional state space, and that adjacent states of mind are separated by the smallest possible transition — a unit step.
"The map of consciousness is not a line. It is a lattice — a structure of adjacencies extending in more directions than the waking mind can perceive simultaneously."
— paraphrase, Programming and Metaprogramming · 1967