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For unless one has a realistic understanding of how important something is, it is very difficult to place or absorb it.
But sometimes one needs infinite collections of such individual axioms, and in the main text these are represented by axiom schemas given as Mathematica patterns involving objects like x_ .
In studying specific instances of objects like groups one often represents elements as products of constants or generators, and then for example specifies the group by giving relations between these products.
Multiples of irrational numbers
Instead of powers one can consider successive multiples Mod[h n, 1] of a number h .
Negative bases
Given a suitable list of digits from 0 to k - 1 one can obtain any positive or negative number using FromDigits[list, -k] .
Neighbor-dependent [2D] substitution systems
Given a list of individual replacement rules such as {{_, 1}, {0, 1}} {{1, 0}, {1, 1}} , each step in the evolution shown corresponds to
Flatten2D[Partition[list, {2, 2}, 1, -1] /. rule]
One can consider rules in which some replacements lead to subdivision of elements but others do not.
1D cellular automata
In a cellular automaton with k colors and r neighbors, configurations that are left invariant after t steps of evolution according to the cellular automaton rule are exactly the ones which contain only those length 2r + 1 blocks in which the center cell is the same before and after the evolution.
A cellular automaton model can be made by allowing particles with more than one possible energy: the average particle energy in a region corresponds to fluid temperature.
But even in this case there is no real progression in which one travels backwards in time.
In a more direct analogy to actual physical systems, one would consider instead a very large number of cells, then compute the density in a single state of the system by averaging over regions that contain many cells but are nevertheless small compared to the size of the whole system.