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 $f(1) =
b$.