Starfish Living Crystal: Odd Elasticity & Chiral Matter Simulator

LATTICE INTERACTION CANVAS Click & drag to poke/shear embryo vertices

Clockwise Spin (Cilia Torque)

Odd Transverse Force & Stress Flow

Hexagonal Living Coordination

Preset:

Chiral Spin Frequency (Hz)1.4 Hz

Odd Elastic Modulus (K_odd)8.5

Odd Elasticity Tensor [K_ij]

In active chiral crystals, K_odd ≠ 0 breaks Maxwell-Betti reciprocity: K_xy ≠ K_yx. Transverse strain creates perpendicular stress!

K_xx = 12.0
Young's bulk

K_xy = +8.5
+K_odd chiral

K_yx = -8.5
-K_odd non-recip

K_yy = 12.0
Young's bulk

Cycle Work (∮ σ : dε): +14.2 mJ

Hexatic Order (ψ₆): 0.89 (Crystalline)

Total Chiral Vorticity: +51.8 rad/s

Reciprocity Violation: ΔK = 17.0

Rigorous distinction between laboratory proof and open biological hypotheses:

Empirically Proved

Hypothesized Function