Computational Complexity of the Logistic Map

control parameter μ

3.7

initial condition

x

0

0.2

iteration steps N

200

output precision p

6

This Demonstration shows the computational space complexity needed to exactly compute the iteration of the logistic equation

x

n+1

=μ

x

n

(1-

x

n

). The initial value of the iteration is

x

0

, with

N

, the number of iterations performed, and

μ

, the bifurcation parameter for the logistic map. Each value

x

n

of the orbit,

n=0,…,N

, is computed up to relative error of

-p

10

.