Extended Data Fig. 2: Emergence of shape shifter within the multifarious assembly regime: weak non-reciprocal drive.

Four different structures of size 40 × 40 are encoded through reciprocal and non-reciprocal interactions as a sequence of length three. Strength of non-reciprocal interactions is set to λ = 10. In panel a each point is an average of error over 5 independent realizations of the system measured after 4 × 10⁶τ_s time steps. Different forms of self-assembly are obtained starting from the first structure as the initial seed. The square markers correspond to the points that undergo at least one shift. Shifts occur in the range of ε that respect the bounds \(\frac{2}{3}\varepsilon \approx {\lambda }_{\min }\le \lambda \le {\lambda }_{\max }\approx \varepsilon\). Increasing λ beyond the threshold value \({\lambda }_{\min }\) induces shifting between the structures and converts the multifarious assembly regime to a shape-shifting regime (square markers). Strong non-reciprocal drive for \(\lambda > {\lambda }_{\max }\) makes the initial seed unstable and results in a dilute dispersion. Grey dashed line shows the stability limit of the initial structure corresponding to the 2ε > − μ condition. The red dashed line is the convex hull of the points that correspond to error < 0.05 and have undergone at least one shift. Panels b and c are the same as a but for density and energy at the final configuration. The boundary between the states can be delineated using the three quantities error, density, and energy. d, Sample snapshots of the system at the end of the simulations for pairs of (μ, ε) values. Note that the liquid regime is extended and the liquid-chimera boundary is placed at higher ε.