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MoMath Hackathon 2018: Vortex Pool

  • Project category: Math Square
  • Team members:
    • Azeem Bande-Ali
    • Steven Gomez
    • Kathryn Grunewald
    • Danny Guo

The Math

In fluid dynamics, a vortex is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of boats, or the winds surrounding a tornado or dust devil.

Each User controls the position of an idealized point vortex on the screen. Each vortex induces an angular velocity given by


Where Γ is the strength of each vortex and r is the location of the user or vortex. At any given point the particles react to the influence of every vortex and the constant free stream flow.

The Submission

Our math square behavior visually simulates the effects of multiple vortexes on a moving field of particles (which could represent water, wind, etc.).

Vortexes can merge when they get close enough, creating an extra-large vortex that produces a noticeably stronger force.

Vortexes can spin in either a clockwise or counterclockwise direction.

Each particle has a trailing line behind it, and the length of the line represents the velocity of the particle. This makes it particularly clear when a particle speeds up when it gets close to the vortex.

We also added rainbow colors to the particles to make the visual effects more obvious.

We think kids will enjoy this behavior because they can stand in the middle of the field, creating their own vortex and allowing them to experiment with how they can affect the flow of particles.

Additional Notes

The entire behavior is in vortex-pool.js.


Run $ npm install to install dependencies.

Run $ npm run build to build vortex-pool.js.

You can also run $ npm run build:watch to automatically rebuild when you change source files.

Create a symlink to vortex-pool.js in the behs directory in the Math Square directory.