a + bi: The Orientation of Reality

A complex number has two irreducible components. One is matter. One is space. The operator between them is the question that keeps them permanently distinct. When this system applies itself to itself and adds back its own nature — z² + c — it generates gravity, mass, spacetime geometry, and the Higgs field as necessary consequences. Not as analogy. Not as metaphor. As derivation.This paper derives the structure of physical reality from a single mathematical primitive: the complex number a + bi. We show that the iterative equation z² + c is the mathematical form of the axiom “orientation capacity actualizes” — and that Einstein’s field equations, the Higgs mechanism, and the mass-energy equivalence E=mc² emerge from this iteration as special cases observable from inside the attractor the iteration generates.We derive a falsifiable prediction: gravitational wave chirps from binary black hole mergers should showdiscrete frequency jumps at period-doubling bifurcation ratios converging on the Feigenbaum constant δ ≈4.669, detectable in existing public LIGO/Virgo/KAGRA data. We construct the detection algorithm,generate prototype waveforms, and demonstrate a 98.7% template mismatch with standard continuous chirplets — meaning if this structure exists in the data, current pipelines cannot find it. The equation z² + c has been visible since 1980. The lens to see what it actually is has been missing. This paper is the lens.