Bicomplex numbers have zero divisors, but an exact linear change of basis separates the quadratic iteration into two independent complex maps. The evaluation record retains both factor records; a point is bounded precisely when both factors are bounded.
The four-dimensional object is a Cartesian product in its natural coordinates. Returning to the visible bicomplex basis and taking an affine 3D section makes that product appear as an oblique interlocking structure—the same product-and-slice logic used throughout the library.
The named pairs are landmarks rather than separate formulas. Each complex factor has its own real and imaginary parameter, so the controls traverse a continuous four-real-dimensional family. Changing one factor can alter only one side of the exact product while the other remains fixed, making the origin of each visible feature easier to test.
Ray-marched mode evaluates the factorized field adaptively for every visible fragment. Its step count is a per-ray ceiling rather than a voxel resolution, and cyan/magenta indicates which complex factor controls the local outside distance. The separate 256-probe line is a 4×4×4×4 CPU-versus-GPU record check rather than displayed geometry.
The diagnostic mesh evaluates a declared grid such as 38³ = 54,872 points. “Escaped” means at least one factor exceeded the escape radius within the iteration budget; “still bounded in both factors” is its finite-depth complement. Marching tetrahedra place approximate boundary triangles between neighboring classifications and retain the source samples.
The factorization and product law are exact statements. The ray marcher uses the proven product-metric distance estimator with a conservative step factor; its terminal epsilon and finite iteration budget remain numerical presentation choices. The alternative mesh remains explicitly approximate, with its source grid, factor payloads, and source-cell provenance available for inspection.