Simplexity
Materials and Teaching Checklist
Lesson Name: The Game of Life (Conway’s GoL)
Date to be taught: 10/17/2013
“I Can” Skills:
Last Time
Describe the principles behind one
dimensional Cellular Automata (1D CA).
Explore and explain different 1D CA
rules and their effect.
This Time
Describe the principles behind The Game
of Life (GoL).
Explore and explain different GoL initial
conditions (“colonies”) and their
evolution
Before the Lesson:
Copies to Make
Materials to Bring
-
During the Lesson:
Time
Section
(min)
Visuals to Make
Projector for laptop
1 page of quadrille/graph paper per
student
1 laptop for each pair of students
Internet connectivity for all laptops
I Say / Do
5
-
Hook
Next time
Differentiate between random behavior
and chaotic behavior. Describe and Give
examples.
Simulate chaotic behavior due to
different initial conditions.
Simulate unpredictable behavior due to
probability.
-
Teach-back on the rules for One Dimensional
Cellular Automata (1D CA) using the auto
generating Java applet:
http://www.employees.org/~hmark/courses/simplex
ity/CA%201D%20-%20auto%201.html
o Apply rules for a few
iterations/generations
Switch to 2 dimensions and the Game of Life:
Demonstrate a few patterns (initial populations)
using the applet http://www.ibiblio.org/lifepatterns/
Ask the students what
connections/relationships/similarities/differences
they see between the GoL and 1D CA
They Say / Do
Some interesting rules:
-
1D vs. 2D:
-
15
-
Mini
Lesson
-
Ask the students to explain the term
“neighborhood” in the case of 1D CA
Extend the definition to two dimensions, where
instead of looking at a cell and its 2 neighbors (on
the left and right), we look at its 8 neighbors all
around it in the two dimensional plane
Mention that GoL is looking at 8 cell
neighborhoods, but other games may look at 4 cells
(North, South, East, West), or a different number.
18, 22, 26, 30,45
54, 57,60,62,73,75,82,86
90,101,102,105, 109,110
121,126,131,135,…
More neighbors
Not necessarily more rules (1D CA has
7 cases per rule)
More possible movement on the 2D
grid
May have similar types of “boring”
and “interesting” behaviors
Answer the questions
-
-
Explain the rules for the GoL
(http://en.wikipedia.org/wiki/Conway%27s_Game_
of_Life):
o Any live cell with fewer than two live
neighbors dies, as if caused by underpopulation.
o Any live cell with two or three live
neighbors lives on to the next generation.
o Any live cell with more than three live
neighbors dies, as if by overcrowding.
o Any dead cell with exactly three live
neighbors becomes a live cell, as if by
reproduction.
Show a few examples on the board/graph paper.
Don’t show/explain the “glider” pattern (the
students will discover it in the next activity)
-
Each student will start with a “glider” and using the
quadrille/graph paper will create a few
generations by applying the rules of GoL
-
Each pair of students will use the GoL applet
http://www.employees.org/~hmark/courses/simplex
ity/Game%20of%20Life%201.html to verify the
pattern on their sheet of graph paper.
-
Using the applet
http://www.employees.org/~hmark/courses/simplex
ity/Game%20of%20Life%201.html each pair of
students will draw a population of 10 cells in a
vertical line in the center of the screen and generate
the patterns for a few generations.
o Does the colony “live forever”? (answer:
yes, it’s an oscillator)
o Since it’s oscillating, what is the cycle
length (period)? (answer: 15)
They will then run the applet to check their results
(the applet will mark any differences in red).
25
Activity 1
-
-
Using the same applet, ask the students to draw the
same 10 cell vertical line, and add 1 cell adjacent to
the 3rd cell from the bottom (either to the left or the
right of the line).
o
o
-
Running this population will result in a
“frozen” colony after 41 generations
How would the student define the colony?
Is the colony “alive” or “dead”?
Competition between pairs: Ask the students to
create another colony with a vertical 10 cell line and
a single additional cell adjacent to the line, to create
a colony that lives the longest. (Answer: the single
cell should be adjacent to the 5th cell from the
bottom)
Help with predicting the next generation
(evolution of the pattern)
Using the applet at http://www.ibiblio.org/lifepatterns/
15
-
Activity 2
Ask the students to open the “A-plus” colony, and
run it for a while, looking for patterns they’d like to
build on their own.
Then, each pair will pick a pattern and recreate it
either in http://www.ibiblio.org/lifepatterns/ or in
http://www.employees.org/~hmark/courses/simplex
ity/Game%20of%20Life%201.html
Using the applet for CA with different rules for 2D
(compared to GoL):
Minilesson
20
-
Instead of looking at 8 neighbors, there are games
that look at just 4. For example the Banks system
It can be used to build virtual computers and virtual
electronic circuits.
The rules are:
Summarize some ideas exhibiting the phenomenon of simple
rules leading to complex behavior
5
Exit Tix
Emphasize the role of rules
Remind students of our goals:
-
Dismiss
-
Identify and explain behaviors which may be
governed by simple rules, but exhibit complex
behaviors
Experiment with systems and simulations showing
these types of behavior
Create simulations of such systems/phenomena, and
demonstrate them
Thumbnails lesson timeline:
Students review some phenomena