I'm a Wolfram science summer school instructor, so I'm in a position to see the kinds of trends there are towards NKS-style methods. It's slow, but definitely there. Some of it is directly inspired, some of it is 'convergent evolution'.
Here's a very high-level and eclectic list of themes and specific research directions I can remember off-hand: agent-based modeling in economics and operational research, game theory automata in evolutionary biology, lattice gas methods in fluid dynamics, tessellation-based approaches to solving PDAs, L-systems in architectural design, logic automata for programming array-based computers, cellular automata-based PRNGs for stream ciphers, program search for finding lock-free concurrent algorithms, rBMs as used in deep learning.
In fact, I used an exhaustive NKS-style search the other day to find novel data query primitives (i.e. what other functions live in the type-signature space that MapReduce occupies?).
Here's a very high-level and eclectic list of themes and specific research directions I can remember off-hand: agent-based modeling in economics and operational research, game theory automata in evolutionary biology, lattice gas methods in fluid dynamics, tessellation-based approaches to solving PDAs, L-systems in architectural design, logic automata for programming array-based computers, cellular automata-based PRNGs for stream ciphers, program search for finding lock-free concurrent algorithms, rBMs as used in deep learning.
In fact, I used an exhaustive NKS-style search the other day to find novel data query primitives (i.e. what other functions live in the type-signature space that MapReduce occupies?).