1D Vicsek model

1D variant of the Vicsek model. Initialize agents on lines with random $x$ coordinate and random direction $\overrightarrow{e^i}=(1,0)$ (right) or $\overrightarrow{e}=(-1,0)$ (left). Agent color represents their intrinsic speed $v^i$, which is fixed per agent at a value uniformly sampled between $v_{\text{min}}$ and $v_{\text{min}}+\mathrm{\Delta }v$. Every step:

1. Update directions:
   • New direction of agent $i$ is the average direction of (same-line) neighbors $j$ within distance $R$.
2. Update positions:
   
   • Displacement is the direction $\overrightarrow{e^i}$ multiplied by the agents' speed $v^i$.
   • 1D addition: When the new position would place the agent inside the exclusion zone of a neighbor (and closer than the old position), it does not move during this step and has to wait for the neighbor to make space.