Murmurations are a mesmerizing display of synchronized movement by a flock of starlings. The birds fly in coordinated patterns, creating swirling, ever-changing shapes in the sky.

This behavior is thought to serve various purposes, such as confusing predators, sharing information, or simply as a form of social bonding.

• Alignment: Birds tend to match their velocity to the average velocity of their neighbors.
• Separation: Birds maintain a minimum distance from each other to avoid collisions.
• Cohesion: Birds are attracted towards the center of mass of their neighbors.

The model uses differential equations to calculate the position and velocity of each bird at each time step based on the alignment, separation, and cohesion rules.

• Click and drag (desktop) or touch and swipe (mobile) to attract the birds.
• The attraction force follows an inverse square law.
• Your gesture speed affects the birds' velocity.

• Use the "Number of Birds" slider to adjust the flock size.
• The "Simulation Speed" slider controls the simulation speed.
• Adjust alignment, separation, and cohesion with their respective sliders.
• Use preset buttons for tight, loose, or chaotic flocking.