Figure 1

The six geometric types that permit analytical solutions in a single dendritic cable. The geometric ratios \(F(X)\) (in blue) were computed as listed in Table 1 with \(L=1.5\) and \(\kappa=\pi/3\), except the Sinusoidal case with \(L=0.15\) and \(\kappa=\pi /2.7\). The dendritic radii (in red) were obtained numerically by solving Eq. (8) for \(r(x)\). For plotting purposes, we assume \(F(0)=r(0)=1\), and scale the x-coordinate by a factor of 10, where all coordinates and parameters are in arbitrary units