**Figures for the heart example.** **Top-left**: The Young diagram \(\lambda^0\) considered in the heart example. **Top-right:** The frozen boundary curve of the corresponding liquid region. **Bottom (from left to right):** a uniform random tableau of shape \(\lambda_N\) with \(N=130000\) boxes displayed as a discrete surface in a 3D space (brown is used for small values of the surface and blue for large ones); the corresponding bead processes \(M_{\lambda_N}\); the corresponding height function \(H_{\lambda_N}\).