Fractal Eisenstein

fractaleisenstein integershexagonal latticecomplex multiplicationantenna arraysmathematicsvisualizationcetz

A fractal defined on the Eisenstein integer lattice built by translating scaled copies of a four-point seed at the vertices {0, 1, ω, ω²} with ω = exp(2πi/3). At each stage p, every current site is replicated at offsets Δ_p r_p v for seed vertices v, where Δ_p = 2^(p-1) and r_p = exp((p-1)πi/3). A final rotation centers the pattern. This is a complex integer lattice structure that can be labeled as a space-filling fractal rather than a curve.