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 ( α1−1=β1−1=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 ( α1−1=β1−1=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 ( α1−1=β1−1=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 ( α1−1=β1−1=12.5BL, α₀ = 0.5, and β₀ = 1).
• Movie S5 (.mp4 format). Dynamics observed in the model for N = 50 individuals crystal-like configuration ( α1−1=β1−1=12.5BL, α₀ = 0.1, and β₀ = 10).
• Movie S6 (.mp4 format). Dynamics observed in the model for N = 50 individuals tube-like configuration ( α1−1=β1−1=5BL, α₀ = 0.5, and β₀ = 1).