Numbers attract based on shared prime factors
Each particle represents a number. Particles attract each other based on shared prime factors. The more prime factors two numbers share, the stronger their attraction.
12 (2×2×3) and 18 (2×3×3) share two prime factors (2 and 3) so they attract strongly.
7 (prime) and 11 (prime) share no factors so they repel each other.
15 (3×5) and 20 (2×2×5) share one factor (5) so they have moderate attraction.