Fujii, Hokusai: theculturetrip.com
With respect to language in general, the grammar for a language is
the set of rules that operate on the elements in a sentence. With
respect to a programming language, this grammar has been sort of
formalised in Lisp with the use of S-expressions inside the lambda
However, there is no simple grammar or re-writing ruleset for a
multi-dimensional sequence, MDS. In a effort to define a simple
grammar for MDS's we're attempting to use re-writing rules for
a simple sequences inside of loops. Loops, of course, contain
the iteration or recursive constructs inside a computer program.
The analogy of comparing loops to geometric polytopes is in the
possibility that using loops on rewriting sequences will reduce
dimensionality and increase order. Another advantage, maybe a
necessity, in using loops, is the setting of initial conditions
and adjusting dynamic mutable variables and functions when
propagating the computations.
The picture below is an illustration of this.
The formalism for this method of analysis is contained in the notion
of rewriting systems. The Church-Turing Lambda Calculus also
contains the notion of rewriting rules. Finite state machines
used in production systems are fundamentally the dynamic elements
of rewriting rulesets.
The construction of a self-aware kind of machine, I think, depends
innately on a feed back system built inside of the recursive loop.
This is the idea in 3Lisp, and the recursive tower of
Brian Smith. [1, 2]
 Reflection and Sentantics in Lisp, Brian Cantwell Smith, 1984.
 The Mystery of the Tower Revealed, Mitchell Wand and Daniel