FIGURE 4.

Left: geodesics (white) joining multiple points with ${\mathbf{x}}_1$. Contour plots of $\mathbf{x}\mapsto {\nabla }_{{\mathbf{x}}_1}\delta \left({\mathbf{x}}_1,\mathbf{x}\right)\cdot \mathbf{n}$ (middle) and $\mathbf{x}\mapsto \left|{\nabla }_{{\mathbf{x}}_1}\delta \left({\mathbf{x}}_1,\mathbf{x}\right)\cdot \mathbf{n}\right|$ (right) for fixed $\mathbf{n}\in {\mathbb{S}}^{d-1}$. Moving a single EAS in the direction $\mathbf{n}$ alters the activation times $\delta \left({\mathbf{x}}_1,\mathbf{x}\right)$ as shown. In contrast, splitting in the same direction $\mathbf{n}$ is similar to simultaneously moving a source point in both directions, and keeping only the shorter geodesic (right)