Periodic vs. stochastic
Two families of lattice — one that repeats a unit cell, one that fills space without ever repeating.
Repeating cell, or random field.
A periodic lattice tiles a single unit cell through space: every region is identical, and the structure is defined by one cell plus a repeat rule. A stochastic lattice is generated from a random field and never exactly repeats, though it keeps a consistent statistical character — a typical pore size and connectivity.
The split is practical. Periodic lattices are predictable, easy to homogenize, and tunable cell by cell; stochastic lattices are more forgiving of orientation and load direction, distribute defects, and resemble natural porous materials like bone and foam.
Which tools sit where.
The periodic family is tpms, wave, and beam — surfaces and trusses from a repeating cell. The stochastic family is grain and noise — structures thresholded from spinodoid, reaction-diffusion, and procedural-noise fields. Both hand the same recipe to the rest of the pipeline.
Control, or robustness.
Choose periodic for exact control and clean tiling, and stochastic for isotropy-on-average, graceful failure, or a biological look. Many parts use both — a periodic core with a stochastic transition zone.