Science Advances

Supplementary Materials

The PDFset includes:

  • Fig. S1. Stable solution defined for the speeding force and the turning force.
  • Fig. S2. Derivatives of simple discontinuous function.
  • Fig. S3. Interaction strength in 2D and 3D.
  • Fig. S4. Effects of the terms of Eq. 3 (main text) on a focal observer according to the relative position the other disk (blue).

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Other Supplementary Material for this manuscript includes the following:

  • Movie S1 (.mp4 format). Dynamics observed in the model for N = 50 individuals polarized on a line perpendicular to the movement ( α11=β11=12.5BL, α0 = 0.2, and β0 = 0.01).
  • Movie S2 (.mp4 format). Dynamics observed in the model for N = 50 individuals polarized in a circular shape ( α11=β11=12.5BL, α0 = 0.5, and β0 = 0.1).
  • Movie S3 (.mp4 format). Dynamics observed in the model for N = 50 individuals rotating; no preferred direction is chosen here, so individuals are turning in both directions at the same time ( α11=β11=12.5BL, α0 = 0.1, and β0 = 0.02).
  • Movie S4 (.mp4 format). Dynamics observed in the model for N = 50 individuals swarm behavior where individuals are moving freely in the swarm ( α11=β11=12.5BL, α0 = 0.5, and β0 = 1).
  • Movie S5 (.mp4 format). Dynamics observed in the model for N = 50 individuals crystal-like configuration ( α11=β11=12.5BL, α0 = 0.1, and β0 = 10).
  • Movie S6 (.mp4 format). Dynamics observed in the model for N = 50 individuals tube-like configuration ( α11=β11=5BL, α0 = 0.5, and β0 = 1).

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