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Rail

A fungeoid in which the control flow does not move freely through the program space, as in Befunge and others, but is modelled as a train running on a railway.

RecurseMe by Zzo38

A Brainf***-like language in which the main means of control flow is to call the whole program as a subroutine of itself.

REDGREEN by Chris Pressey

A two-dimensional cellular automaton using various symbols representing everyday objects.  It includes elements from Life and WireWorld.

reMorse by Ryan Kusnery

Pronounced with the emphasis on the first syllable.  A tiny language resembling Morse code, with four basic instructions to work with a set of 16 operations.  Although the documentation states early on that the language is Turing complete, it later admits that this is not quite so.

RUBE by Chris Pressey

An automaton named after Rube Goldberg, a creator of funny cartoon machines.  (Hang on, I thought that was Heath Robinson!)  The predecessor to REDGREEN, but not a true cellular automaton.  It works with a 'warehouse' paradigm based upon movement of data.