How do we conclude that the "Sierpinski
dust" (that is, the part that has not been removed) has zero
area?
The Chaos game - generating fractals using random movement! (p. 447)
Once again, simple rules lead to complex
objects. This time, however, we don't proceed
methodically, but rather haphazardly - and yet we still
produce the complex images!
Chaos is roughly defined as "sensitive dependence on
initial conditions", but what this means is that if you start at two different
points in a system (for example, in weather you might be thinking of a
state of three variables, temperature, barometric pressure, and wind
speed), very close to each other but distinct, then eventually the system will
produce wildly different behaviors (even those the starting conditions were
extremely close).
