  We exhaustively explore the reprogrammability capabilities and the intrinsic
universality of the Cartesian product $P \times C$ of the space $P$ of all
possible computer programs of increasing size and the space $C$ of all possible
compilers of increasing length such that $p \in P$ emulates $p^\prime \in P$
with $T|p^\prime|=|p|$ under a coarse-graining transformation $T$. Our approach
yields a novel perspective on the complexity, controllability, causality and
(re)programmability discrete dynamical systems. We find evidence that the
density of (qualitatively different) computer programs that can be reprogrammed
grows asymptotically as a function of program and compiler size. To illustrate
these findings we show a series of behavioural boundary crossing results,
including emulations (for all initial conditions) of Wolfram class 2 Elementary
Cellular Automata (ECA) by Class 1 ECA, emulations of Classes 1, 2 and 3 ECA by
Class 2 and 3 ECA, and of Classes 1, 2 and 3 by Class 3 ECA, along with results
of even greater emulability for general CA (neighbourhood $r=3/2$), including
Class 1 CA emulating Classes 2 and 3, and Classes 3 and 4 emulating all other
classes (1, 2, 3 and 4). The emulations occur with only a linear overhead and
can be considered computationally efficient. We also found that there is no
hacking strategy to compress the search space based on compiler profiling in
terms of e.g. similarity or complexity, suggesting that no strategy other than
exhaustive search is viable. We also introduce emulation networks, derive a
topologically-based measure of complexity based upon out- and in-degree
connectivity, and establish bridges to fundamental ideas of complexity,
universality, causality and dynamical systems.
