LIFE:
a game that imitates real life.

This simulation is based on a game invented by mathematician John Horton Conway. Conway’s Game of Life is an example of “cellular automation” where all cells’ behavior on the grid are determined by a set of rules. The game board represents a community and each cell represents a community member. All members follow certain rules.

The rules are simple.
1. If a cell has too many (meaning 4 or more) neighbors the cell dies because of overcrowding.
2. If the cell is too lonely (meaning one or less neighbors), it also dies.
3. The last rule of the game is that if a cell has the right environment (meaning exactly three neighbors) a baby cell will be born.

This applet also has an added feature to make it easy to see the age of the cell – the color fades form red to blue (red being young cell and blue an older cell)

As you play, try using “step” instead of start and stop – it slows the action down.

Then complete this HW

For Monday:

1) Finish your solution to the Gossip Problem.  Include several diagrams and explain the formula and HOW it works.

2) Practice folding and flying planes.  Pick two that are quite different fliers to use for comparison when we study data.  Here’s a site I’ve used that has good instructions.  Try the rapier, the floating plane, the flying fish, the dart or any others that interest you.

The Gossip Problem:

If everyone has a unique “secret” and shares every “secret” they know with someone whenever they have a conversation, what is the fewest number of conversations that must happen for any number of people to share all their secrets with each other?

Use a vertex-edge graph and one paragraph of explanation for your solution.  Remember: you are looking for a pattern/rule, not for a particular number.  I would recommend starting with a small number of people and working your way up to at least 10.

Today we used the bridges of New York City to explore Hamiltonian and Euler paths.  Use the worksheet from class to find paths and, if possible, circuits for each vertex-edge graph.  (Due after the break).

Here some fun examples of paths and circuits you can solve online if you would like to test yourself. (Click the link and then scroll down – you can try to solve each graph in either Euler or Hamiltonian mode).

This week’s assignment:

Write one page (1.5 spaced, times new roman or helvetica) about how the faces, vertices and edges are related to each other in a vertex/edge graph.  Include the formula we found in class.  Explain why this formula is true.  Use examples in your explanation.  Your one page should be at least half writing, though (not all diagrams).  You can do your diagrams by hand or use the drawing toolbar in pages or word if you feel adventurous :)

Also, you will be handing in the assignment that was due this Monday at the same time, so make sure it is your best, as we discussed this week.