Figure 1

Formation of an extended tubular network by fusion and growth of microplasmodia on agar. The time is given in hours and minutes (hh:mm). The networks’ skeletons are overlaid on top of bright field images. The largest network component is colored in red. Around 6.7 hours (06:40) the largest component grows to the size of the whole system and percolates most of the structure. The sequence is available as a movie [21].Reuse & Permissions

Figure 2

Definition of link degrees. The probability of a node with link degree $k$ is denoted by $p_k$. Nodes with two links have no biological significance and are omitted. Nodes with a link degree higher than four rarely occur and can be neglected.Reuse & Permissions

Figure 3

Left axis: Distribution of link degrees $p_k$ for $k<5$ as a function of time $t$ ($p_0$ red, $p_1$ green, $p_3$ blue, $p_4$ yellow) corresponding to the sequence shown in Fig. 1. Right axis: The ratio $p_0/p_3$ (black) drives the percolation transition at $p_0/p_3=2$ (dashed horizontal line). In this particular example, the network percolates at $t=6.7$ h (dashed vertical line).Reuse & Permissions

Figure 4

Panel A: Fraction $S(q)$ of all nodes included in the largest connected network component as a function of the ratio $q=p_0/p_3$ in a semilogarithmic plot. The solid line depicts the theoretical value [Eq. (2)]. The percolation is visible as a sharp increase of $S=1-u$ from zero at $p_0/p_3=2$. The gray dots correspond to 48 experimental trajectories, while the dashed line shows the median. The black markers correspond to one particular trajectory of a vascular network assembly of endothelial cells [17, 21]. Panel B: Average link degree as a function of the ratio $p_0/p_3$ for the data sets shown in panel A. Near the percolation transition at $(⟨k⟩,p_0/p_3)=(1,2)$ the data collapse onto a line with slope $-1/6$, see inset [Eq. (5)].Reuse & Permissions