Chaos in the Shift Map

leading bit of perturbation

number of bits to flip

1

2

All

initial condition

1

2

1

3

1

5

3

7

1

25

2

1

2

1

π

multiplier

2

3

2



π

use machine arithmetic

The shift map is a standard example of the sensitive dependence on initial conditions that is at the core of traditional chaos theory. This Demonstration illustrates this basic phenomenon, and shows that there is often more going on in the shift map.