Discrete map · 1D · dim 1
PWLCM (piecewise-linear chaotic map)
A workhorse of chaos-based cryptography: simple, fast, uniform invariant density, large positive Lyapunov exponent, and parameter p easy to use as a key.
Equations
x_{n+1} = x_n / p if 0 < x_n ≤ p
= (x_n − p) / (0.5 − p) if p < x_n ≤ 0.5
= symmetric for x_n > 0.5At a glance
| Parameters | p ∈ (0, 0.5) |
|---|---|
| Chaotic for | always |
| Lyapunov exponent | λ = − [p log p + (0.5 − p) log(0.5 − p)] · 2 |
| History | Widely used in chaos cryptography since the 1990s. |
Try it
Open the interactive playground at /tools/cobweb.