3. Simple rules generate complex behaviors

Preamble: Computer models/simulations with visual output are another one of the "changes in... technology [that] have changed our needs and capacities for mathematical thinking."

Preparation

• View https://www.youtube.com/watch?v=5h8WOWEqP6o on slime mold life cycle.
  (Although not described in the video, researchers have made models of the aggregation based on the rules: a) when food is short, send out a pulse of cAMP; b) when a pulse reaches you, send out a pulse yourself and then stop responding for a while to more pulses while you move in the direction the pulse came from.)
• View Steven Strogatz: The science of sync, https://www.ted.com/talks/steven_strogatz_on_sync
  (View only as far as you need to see how simple rules generate complex behaviors)

Goals

1. Understand differences between linear and non-linear dynamic models, in particular how simple rules can generate complex behaviors and small differences in initial conditions can yield large differences in outcomes
2. Apply social interpretation as a means to expose the restrictiveness that comes with using any quantitative tools

Activities
Game of Life (35 mins)

View and discuss video, "Introduction to Complex Systems: Patterns in Nature," https://www.youtube.com/watch?v=g5evD6AQeCQ, in relation to the second goal. (20 mins)

Plus-delta feedback on activity (5 mins)