Definie a function ComplexityFunction $(w,n)$ that computes the complexity function given in definition $4\mathrm{.}1$ on the sequence $w$ for the subword length $n.$Define a function TopologicalEntropy$($w$)$ that computes the topological entropy of $w.$

Use matlab

Definition $4\mathrm{.}1$ For a given sequence $w,$ the complexity function $p_w$:$NN$ is

defined as the number of different n$-$length subwords $($with overlaps$)$ that appear

in $w.$ That is$,$

$p_w(n)=|\{u$:$|u|=n$ and $u$ appears $as$ a subword $ofw\}|.$

Definition $4\mathrm{.}2$ Let $w$ be a finite sequence of length $|w|$ on the alphabet $A,$ let

$n$ be the unique integer such that

Then for $w_1^{4^n+n-1}$ the first $4^n+n-1$ letters of $w,$ the topological entropy of $w$

is defined as

$H_{\text{t}\text{o}\text{p}}(w)=\frac{lo{g}_4(p_{w_1^{4n}+n-1}(n))}{n}.$