1.G. The Random IFS Algorithm

Randomness

So how can we make a random sequence?

To make the explanation easier, we'll consider only random sequences of 0s and 1s.

To make an infinite random sequence of 0s and 1s, toss a coin infinitely many times.

Each time a heads comes up, put a 1 in the sequence. Each times tails comes up, put a 0 in the sequence.

So if the coin toss started out

heads, heads, tails, heads, tails, tails, tails, heads

the random sequence would start

11010001

Of course, computers don't toss coins, but rather generate pseudorandom numbers.

One method starts with the time on your computer's clock, multiplies by a large number, divides by another large number, and takes the remainder.

In an early investigation of the logistic map, Ulam and von Neumann used iterates of x_n+1 = 4x_n(1 - x_n).

In Mathematica, random numbers are generated by the outputs of the cellular automaton with rule .

Return to Randomness.