Dynamic Visualization of Recursive Functions: Graphs and Mapping Diagrams

GeoGebra examples for recursive functions:
"First Order": Suppose $f : N \rightarrow N$ with $f(0)=a$ and $f(n+1)=g(n,f(n))$, where $n$ is a natural number and $g$ is a given function of $n$ and $y$, $g(n,y)$.

You can change the recursive function from $f(n+1) = g(n,f(n))$ by changing the definition of $g$, as well as by changing the initial value, $f(0) = a$.

"Second Order": Suppose $f : N \rightarrow N$ with $f(0)=a$,  $f(1)=b$ and $f(n+2)=g(n+2,f(n), f(n+1))$, where $n$ is a natural number and $g$ is a given function of $n$ , $y$, and $z$, $g(n,y,z)$.

You can change the recursive function from $f(n+2) = g(n+2,f(n),f(n+1))$ by changing the definition of $g$, as well as by changing the initial values, $f(0) = a$  and $f(1) = b$.