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Notations [for logical primitives]
Among those in current use are (highlighted ones are supported directly in Mathematica):
The grouping of terms is normally inferred from precedence of operators (typically ordered , ¬ , ⊼ , ∧ , ⊻ , ⊽ , ∨ , ), or explicitly indicated by parentheses, function brackets, or sometimes nested underbars or dots.
Dimensionality of networks
As discussed on page 479 , if a sufficiently large network has a d -dimensional form, then by following r connections in succession from a given node, one should reach about r d distinct nodes.
And one feature of the simple branching processes I describe is that for purely mathematical reasons, their rules always produce structures that are of limited size.
But one way to see the properties of the rule is to use nested initial conditions, obtained for example from substitution systems of the kind we discussed on page 82 .
For there appears to be an irreversible increase in randomness as one goes down successive panels on the page.
The JPEG method of image compression uses an approach similar to the one shown here, though with basic forms that have continuous levels of gray, rather than just black and white.
[Universal] tag systems
Marvin Minsky showed in 1961 that one-element-dependence tag systems (see page 670 ) can be universal.
At a practical level, the one-dimensional character of data from radio signals makes it difficult for us to apply our visual systems—which remain our most powerful general-purpose analysis tools.
Eastern religions have however normally tended to take a different view, and to consider humans as just one of many elements that make up the universe as a whole.
Undecidability in Mathematica
In choosing functions to build into Mathematica I tried to avoid ones that would often encounter undecidability.