*2.1. Logistic Mapping*

Chaos refers to the seemingly random and irregular movement that occurs in a nondeterministic system. It originates from nonlinear dynamic systems. Logistic mapping is one of the most famous chaotic mappings due to its simple expression and excellent performance [37–39]. Its expression form is as Equation (1).

$$y\_{n+1} = \mu \times y\_n \times (1 - y\_n),\tag{1}$$

where *n* = 0, 1, 2, 3, ... and *y* belongs to 0 and 1. The system control parameter *μ* is the constant and *μ* ∈ (0, 4]. When 3.569945672 ··· < *μ* ≤ 4 and the final sequence value belongs to [0, 1], the logistic sequence *yn* is in the state of chaos. The function has the characteristics of aperiodic and sensitive dependence to the initial condition. Logistic mapping is simple without losing the complex characteristics of the chaos, so it is usually used on image encryption.
