But a finite version in which one looks at results after a limited number of steps is similar to my concept of a universal object.

In most sequential substitution systems there is more than one possible replacement that can in principle apply at a particular step, so the order in which the replacements are tried matters.

But one can also set up substitution systems that are based on subdividing other geometrical figures, as shown below.

Note that processes such as cellular automaton evolution do not yield networks whose properties are particularly close to those of purely random ones.

Studying natural selection From the basic description of natural selection one might have thought that it would correspond to a unique simple program.

Successive approximations to this number are given by Fibonacci[n - 2]/Fibonacci[n] , so that elements numbered Fibonacci[n] (i.e. 1, 2, 3, 5, 8, 13, ...) will be the ones that come closest to being a whole number of turns apart, and thus to being lined up on the stem.

These rules correspond to the moves invented by James Alexander in 1923 in connection with transforming one knot into another.

[Generating] random networks One way to generate the connections for a "completely random" trivalent network with n nodes is just to apply a random permutation: RandomNetwork[n_?

To a good approximation this distance is proportional to the logarithm of the frequency, and going up one octave in frequency corresponds to moving roughly 3.5 mm. … Presumably related is also the fact that it is typically much easier to make realistic sound effects than realistic visual ones.

One might have thought that this would imply in reverse that to an observer moving with the object the whole infinite future of the outside universe would in effect seem to go by in a finite time. … For example, it was shown in 1990 that close encounters in a system of 5 idealized point masses can lead to infinite accelerations which cause one mass to be able to go infinitely far in a finite time.