The
Lesson of Cellular Automata
Kazumi Yamada
Faculty of Education and Human Sciences
Niigata University
Japan
Abstract
The lesson of cellular automata
The mathematics of a discrete system like a cellular automaton is suitable
for training the mathematical thinking method and logical thinking capability
which are not in traditional mathematics education. In the introductory
contents of the mathematics of a discrete system, since the object to
investigate is finite, junior high school students can learn mathematics
applying a trialanderror method by drawing figures on paper. However,
they should come to feel difficulty and a limit for pursuing, while drawing
figures. After all, they probably will become necessary to experiment
using computers. For example, when they investigate change of cells of
the Game of Life, which is a special case of a twodimensional cellular
automaton, using papers containing grids , since time is taken too much,
computers are needed.
Usefulness of a lesson of the mathematics of a discrete system
The mathematics of a discrete system has the very deep back. In addition,
even if it is introductory contents which can be understood to them, it
has very rich contents. By learning a cellular automaton and a fractal,
they understand that the complicated phenomenon of nature is acquired
by repeating simple modification repeatedly. As a result, their view to
a natural phenomenon is changed gradually. Moreover, they meet with the
mathematics not using a formula, and are surprised.
