Difference in Digit Sequences by Changing Initial Conditions

perturbation degree

25

steps

44

constant c

3

2

This Demonstration allows one to browse through difference diagrams for the digit sequences of iterated maps produced by a small change in the initial conditions. Some digit sequences of iterated maps show sensitive dependence on initial conditions, others do not.

The iterated maps are of the form

x→{cx}

where

c

is the "constant" value in the Demonstration and

{·}

is the fractional part function. "Perturbation degree" refers to where in the initial condition the perturbation originally occurs. Black cells represent locations where the perturbed iterate differs from the original.