  Two novel views are presented on the trapdoor channel. First, by deriving the
underlying iterated function system (IFS), it is shown that the trapdoor
channel with input blocks of length $n$ can be regarded as the $n$th element of
a sequence of shapes approximating a fractal. Second, an algorithm is presented
that fully characterizes the trapdoor channel and resembles the recursion of
generating all permutations of a given string. Subsequently, the problem of
maximizing a $n$-letter mutual information is considered. It is shown that
$\frac{1}{2}\log_2\left(\frac{5}{2}\right)\approx 0.6610$ bits per use is an
upper bound on the capacity of the trapdoor channel. This upper bound, which is
the tightest upper bound known proves that feedback increases capacity of the
trapdoor channel.
