- Exams (Temporarily) Returned (you've got to give them back!)
- Add 5 to your raw score, then divide by 80.
- Some of you obviously didn't practice your Game of Life!
- New assignment:
Mon 3/22 Chaos - Read section 6.5
- Homework pp. 498, #19-24; due Mon, 3/29
- Chaos is roughly defined as
sensitive dependence on initial conditions, but what this means is that if you start at two different points in a system (for example, in weather you might be thinking of a state of three variables, temperature, barometric pressure, and wind speed), very close to each other but distinct, then eventually the system will produce wildly different behaviors (even those for which the starting conditions were extremely close). - To see what this means, let's start by trying out the exercises using the calculator in section 6.5.
- Let's talk about the logistic map:
(our authors use this in their discussion of the Verhulst Model for Population growth). This will lead us back to fractals, as well as to the new idea of cobwebbing.
- Some links to an important real world example: The Lorenz Equations
- The Lorenz attractor in 3-D
(here's a local copy)
- Make your own butterfly! (here's a local copy)
- The Lorenz attractor in 3-D
(here's a local copy)
- Cobwebbing - another example (#5 and 6), using a "tent function"