Original Math Notes
All Seasons
Season 5
Episode 504: Thirty-Six Hours
False-color recording of bugbots using info-chemo-taxis to follow scent sources moving in circles
Scene 23:
The termites morph OVER the bots -- we see both at the same
time, doing the same activities -- moving as a swarm. Their
radio communications are delineated by radiating lines.

                    CHARLIE (cont'd)
          These bots employ info-taxis, a
          spatial search algorithm in which
          agents repeatedly update guesses of
          an object's location.

Garbage Collection by Ants »

Assume there are many tiny pieces of garbage scattered on a 2D square space, where many ants are wandering to forage randomly. Each ant individual behaves according to the following very simple rules when it comes to a place where there is some garbage. 1. If the ant is holding a piece of garbage, it drops it off there. 2. If the ant isn't holding any garbage, it picks up a piece of garbage there.
Scene 25:
   
Charlie removes the leader bot.  The remaining bots stop,
rotate, then line up behind a new leader, go back to work.

                    CHARLIE
          They figure out the next best leader,
          and keep going.  Much more robust --
          and cooperative -- in hostile
          environments than people.
          (indicating laptop screen)
          Each bot creates a model of its local
          environment, networks it, and we get
          a collective picture.

3D Boid Model »

The Boid model is a famous multi-agent model that was invented by Craig Reynolds. Each Boid is an agent following three simple rules: (1) Align with other neighbors; (2) Try to be close to neighbors; (3) Avoid collision with other neighbors. These rules can make the flock of Boids reproduce the behaviors of real bird flocks or fish schools.
Scene 59:
                    CHARLIE (ON RADIO)
            (realizing)
          Dammit --
            (to Colby)
          Colby, are you counting in meters?

                    COLBY (ON RADIO)
          That's the problem -- I counted in
          yards.  Let me backtrack, do it right.

                    DON
          Go easy.

                    CHARLIE
          Do you want the calculations in
          yards?

Length Units of Measurement »

Visualizing just how large a unit is can be difficult. Displayed here are a few real-world examples of the size of some units of measurement.
 
Wolfram: Creators of Mathematica, Leaders in Math & Computation
Wolfram|Alpha