- Homework for 4.7 is due
- New assignment:
Mon 3/1 Fractals and Dynamics - Read 6.3
- Problems pp. 421-, #1, 5, 8, 9, 12-15 (due 3/15)
- Final Fourth Dimensional Cube summary:
Name Dimension # of Vertices # of Edges # of Faces # of 3D Faces Dot 0 1 0 0 0 Segment 1 2 1 0 0 Square 2 4 4 1 0 Cube 3 8 12 6 1 Hypercube 4 16 32 24 8 And the general rule is this: if we're looking at a certain type
, and the type
one dimension below it, then the rule is:
- Take a few minutes to examine the gallery of fractals in section
6.1
What do you think of the gallery? Mathematics or Art? - What do you suppose mathematicians mean by dynamic models?
- How many people do you suppose will be on the earth a hundred years from now?
- Start Somewhere (collect data!)
- Apply a process and get a result
- Apply the same process to that result to get a new result
- Apply the same process to the new result to get a newew result
- Repeat patiently and persistently, forever.
- Start Somewhere (collect data!)
- Why are simple rules that result in complex phenomena important?
Here's an important example that affects our educational
system these days....
- Some people doubt the "theory of evolution", because they don't believe that simple rules can result in the complexity we see around us.
- If scientists can demonstrate that complex phenomena can arise from simple phenomena, then that argument holds less water.
- An introduction to the Game of Life:
- Is generally played on an infinite checkerboard, or on a world that wraps back around on itself.
- The rules are:
- A living square will remain alive in the next generation if exactly two or three of the adjoining eight squares are alive in this generation; otherwise, it will die.
- A dead square will come to life if exactly three of its adjoining eight squares are alive; otherwise, it will remain dead.
- Create your own creatures!
- Can you think of one that will lead to extinction?
- Can you think of one that will lead to a stable pattern?
