Start with a vector $x\in\mathbb{R}^{n}$, and a vector-valued function $f:\mathbb{R}^{n}\mapsto\mathbb{R}^{n}$.


Given some $k\in\mathbb{Z}^{+}$, what are elegant ways to produce the table of convolutes?

{x, f(x), f(f(x)), f(f(f(x))), ..., f^{k}(x)}

Say $ k = 6 $,

NestList[f, x, 6]
{x, f[x], f[f[x]], f[f[f[x]]], f[f[f[f[x]]]], f[f[f[f[f[x]]]]], f[f[f[f[f[f[x]]]]]]}

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