The design domain is a lattice "ground structure": nodes on a 3D grid connected to every neighbor within one cell (axis, face-diagonal and body-diagonal links, 13 unique directions), each acting as a linear spring. This is the classic ground-structure approach to truss topology optimization.
Spring force: F = k · (‖xB − xA‖ − L0)
Stiffness: k = k0 · ρ(edge)^p (p = 3, SIMP-style penalization)
Strain energy: U = ½ · k · (‖xB − xA‖ − L0)²
Every frame the lattice is integrated forward with damped explicit dynamics (dynamic relaxation) — the load pulls the free nodes, the springs pull back, and viscous damping bleeds off kinetic energy until the shape settles into its static equilibrium, exactly like a physical model finding its resting deformation under load.
Periodically an evolutionary structural optimization step runs: every cell's sensitivity is the strain energy stored in the springs around it — cells carrying little strain energy are barely contributing to stiffness, so they are the first candidates to become void. The optimizer keeps exactly the top fraction of cells (by sensitivity) solid, ranked every step, and nudges that fraction toward your target by the evolution rate — this is a bi-directional scheme (BESO): raising the target regrows material in the highest-sensitivity void cells, lowering it removes more.
- Load magnitude — how hard the free end/midspan is pulled; higher load makes the surviving load path more visible.
- Target volume fraction — how much of the original block is allowed to remain once optimization converges.
- Evolution rate — how much volume fraction changes per optimization step (faster = coarser, more abrupt shapes).
Real engineering relevance: this is the same family of algorithm (SIMP / BESO) used by generative-design tools in Fusion 360, Altair Inspire and nTopology to grow aircraft brackets and 3D-printed lattices that use the least material for a given stiffness — the "rapid iteration" loop this article describes, run automatically thousands of times.