Fractal Wave

[Paul Stdenis]

I have noticed what is called "the wave" at some sporting events.
A person participating in the wave will stand up briefly with their hands
up in the air if someone next to them has stood up briefly with their hands
up in the air. When someone starts the wave it usually spreads throughout
the stadium in a wave like pattern, hence the name.
I propose a a version of the wave with only slightly more complicated
rules which if done correctly will eventually result in a group of people
standing in a pattern commonly called the Sierpinski triangle, a fractal shape
named after Waclaw Sierpinski (1882-1969)
(For information on the Sierpinski triangle, see the book FRACTALS, CHAOS,
POWER LAWS by Manfred Schroeder)
I will now attempt to give thr rule for the "fractal wave"
for illustrative purposes, lets begin with a small section of seats
(box seats lets say) Each seat in this section will be labeled by row
and column, seat (1,1) being in the lower left hand corner (see below)

ROW 5 * * * * *
4 * * * * *
3 * * * * *
2 * * * * *
1 * * * * *
1 2 3 4 5 (* seats)

Each person sitting in their seat will be looking at the person
in front of them, the person to the right of them, and the person in front
of the person to the right of them. Each person will stand briefly
(with their hands in the air) if only one such person is standing.

For example the person sitting in seat (2,2) will look at the
behavior of the people in seats (1,1),(1,2) and (2,1). If person (1,1) is
standing and persons (2,1) and (1,2) are sitting, then person (2,2) will
stand briefly. Similarly if person (2,1) is standing and persons (1,1)
and (1,2) are sitting, or if person (1,2) is standing and persons
(1,1) and (2,1) are sitting, then person (2,2) will stand briefly.

The wave is started by person (1,1) standing briefly, here are the
first five "generations" illustrated, the "*" symbol means that a person
is standing.
Generation
1 2 3 4 5
5 5 5 5 5 * *
4 4 4 4 * * * * 4
3 3 3 * * 3 * * 3
2 2 * * 2 2 * * 2
1 * 1 * 1 * 1 * 1 *
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
The larger the section of seats the better the approximation
the Sierpinski triangle will be. Note each person stands once.
Timing would be important, one person out of sync early would result in
a heavily distorted image later on.
I think it would be nice to see this at some event, if anyone
knows anyone working in choreography at pep rallies etc, please pass
this idea on? Thanks,
Paul St. Denis