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Note that by prepending suitable i[r] instructions one can effectively set up initial conditions with arbitrary values in registers.

Note (a) for The Notion of Numbers

In antiquity however most systems for writing numbers were like the Roman one and not based on digit sequences.

Note (a) for The Emergence of Order

But in rule 126, black cells always tend to appear in pairs, while in rule 182, every white cell tends to be surrounded by black ones.

Note (d) for Sensitivity to Initial Conditions

Properties [of difference patterns] In rule 126, the outer edges of the region of change always expand by exactly one cell per step.

Note (d) for Systems of Limited Size and Class 2 Behavior

In particular, if a state of a cellular automaton has a certain spatial period, given by the minimum positive m for which RotateLeft[list, m]  list , then this state can never evolve to one with a larger spatial period.

Note (e) for Randomness from the Environment

Electronic randomness Since the 1940s a steady stream of electronic devices for producing randomness have been invented, with no single one ever becoming widely used.

Note (b) for Randomness from the Environment

But to avoid having a particular program give exactly the same random sequence every time it is run, one usually starts from a seed chosen on the basis of some random feature of the environment.

Note (a) for The Problem of Satisfying Constraints

Larger objects normally come to the top (as with mixed nuts, popcorn or pebbles and sand), essentially because the smaller ones more easily fall through interstices.

Note (f) for Fundamental Issues in Biology

One might expect that biological evolution would have had obvious effects on proteins.

Note (c) for Ultimate Models for the Universe

This principle has worked well in physics, where it has often proven to be the case, for example, that out of all possible terms in an equation the only ones that actually occur are the very simplest.