Current research involves computational exploration into novel bicontinuous foam geometry produced by a Gray-Scott reaction-diffusion system—the same class of mathematical process that generates the structures found in trabecular bone, coral, and lung tissue.

To the best of our knowledge, no prior system implements bidirectional Gray-Scott cellular automata coupling in three dimensions with periodic boundary conditions to produce tileable, fabricatable porous geometry. This work investigates that possibility and the resulting geometric capabilities.

The system produces three distinct tiling families.

 

Face-Pair Family

Tiles are generated in matched pairs: the right face of tile A is the exact boundary of tile A′'s left face. These tiles have a specific neighbour and cannot be freely rotated, yet every interior remains geometrically unique. No two tiles in the family share the same internal structure. The joint between them was not fitted after the fact; both halves of the boundary existed independently before the tiles were ever placed together, and the bicontinuous network emerges continuously across the interface.

 

P1 Tileability

A single tile whose opposing faces are identical to the faces they will meet. This is achieved through periodic boundary conditions during simulation, which drive opposite faces toward the same boundary profile at convergence. When placed in a straight run without rotation, the interior morphology continues uninterrupted across every joint, reading as a single continuous object rather than an assembly. No pairing, no ordering, no gaps.

 

C4 Crystallographic Rotation

The same P1 tile can be rotated in 90-degree increments—either tile-by-tile within a row or row-by-row throughout an assembly. The joints remain closed while the foam orientation shifts across each boundary, producing a richer geometric field from a single tile. Orientation itself becomes a design parameter capable of encoding position and pattern.

These capabilities have been confirmed through direct measurement. Face-match scores of 99% or greater have been recorded on all three axes across multiple tile generations. Tiles placed in physical adjacency—without welding, merging, or post-processing—exhibit continuous foam morphology across the joint as though the assembly were generated as a single object. The same tile, rotated by 90 degrees, produces a closed joint through the same mechanism.

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Together, these three tiling families enable seamless filling of arbitrary and irregular volumes. The stochastic interior ensures that no two assemblies are identical, while the boundary geometry guarantees exact mating between components.

A Grasshopper plugin is currently in development to bring this system directly into parametric design workflows.

Potential applications range from architectural panels and acoustic surfaces to thermal management structures, lightweight engineering components, filtration media, and biomedical scaffolds.

Patent Pending — May 2026