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Examples range from tulip bulbs in the mid-1630s to railroads in the mid-1800s to internet businesses in the late 1990s.
With odd n the same turns out to be true for sequences Exp[2 π Mod[Range[n] 2 , n]/n] —a fact used in the design of acoustic diffusers (see page 1183 ). … It is also flat for maximal length LFSR sequences (see page 1084 ) and for sequences JacobiSymbol[Range[0, p - 1], p] with prime p (see page 870 ).
Patterns generated by rules of the type shown on the previous page , with a range of choices for the weights of cells at distances 2 and 3.
EvenQ] := Partition[ Fold[Insert[#1, #2, Random[Integer, Length[#1]] + 1] &, {}, Floor[Range[1, n + 2/3, 1/3]]], 2]
Networks obtained in this way are usually connected, but will almost always contain self-loops and multiple edges.
Quadratic residue sequences Mod[Range[n] 2 , n] (see page 1081 ) are used to give profiles for acoustic diffusers that operate uniformly over a range of frequencies.
But by doing Nest[s, Range[52], 26] one ends up with a simple reversal of the original deck, as in the pictures below.
The purpose of this chapter , however, is to investigate a range of systems that are based on numbers, and to see how their behavior compares with what we have found in other kinds of systems.
For what I have found is that with the new kind of science I have developed it suddenly becomes possible to make progress on a remarkable range of fundamental issues that have never successfully been addressed by any of the existing sciences before.
But while we have discussed a whole range of different kinds of underlying rules, we have for the most part considered only the simplest possible initial conditions—so that for example we have usually started with just a single black cell.
The diversity of these spectra is quite striking: some have simple nested forms dominated by a few isolated peaks at specific frequencies, while others have quite complex forms that cover large ranges of frequencies.