But between 15 Hz and about 60 Hz, the sound tends to be rather grating—possibly because this frequency range conflicts with that used for signals in the auditory nerve. … The picture below shows the extent to which such frequencies tend to be in the range that yield grating effects.

[Construction of] universal objects A more direct way to create a universal object is to set up, say, a 4D array in which two of the dimensions range respectively over possible 1D cellular automaton rules and over possible initial conditions, while the other two dimensions correspond to space and time in the evolution of each cellular automaton from each initial condition.

Cellular automaton art 2D cellular automata can be used to make a wide range of designs for rugs, wallpaper, and similar objects.

Implementation of general cellular automata With k colors and r neighbors on each side, a single step in the evolution of a general cellular automaton is given by CAStep[CARule[rule_List, k_, r_], a_List] := rule 〚 -1 - ListConvolve[k^Range[0, 2r], a, r + 1] 〛 where rule is obtained from a rule number num by IntegerDigits[num, k, k 2r + 1 ] .

For most types of systems (such as Turing machines) such non-deterministic versions do not ultimately allow any greater range of computations to be performed than deterministic ones.

It has been claimed that its frequencies are optimized for long-range transmission in the ocean, but this appears not to be the case.

And between these transitions there are usually ranges of parameter values that yield definite class 4 behavior.

My purpose in this chapter is to answer this question by looking at a wide range of different kinds of programs.

Such a mobile automaton must then itself be universal, since the universal cellular automaton that it emulates can in turn emulate a wide range of other systems, including all possible mobile automata.

Components for technology The Principle of Computational Equivalence suggests that a vast range of systems in nature can all ultimately be used to make computers.