Lets consider linear cellular automata with Wolfram rule 90

Elementary cellular automata is essentially string of two symbols, lets call them 0 and 1, equipped with rules (and starting configuration, of course)

Rule takes symbol in the position, as well as left and right neighbors. Ie – when calculating symbol of the cell, we should consider 3 cells, cell to the left, cell itself and cell to the right.

Ie – suppose we have set of rules(*):
`111 - 0`
`110 - 1`
`101 - 0`
`100 - 1`
`011 - 1`
`010 - 0`
`001 - 1`
`000 - 0`

Or graphically:

So if we have 10011 for starting configuration, calculation goes like this(from top to bottom):

 1 0 0 1 1 (0) 1 1 1 (1) (1) 1 0 0 (1)

(italics) means that we dont know which symbol is to the left and right to the starting configuration, for simplicity I consider here absent symbols to be 0s (ie …00000100110000…)

Now, what is 90, which is called Wolfram rule.

It is obvious, that  3 cells define state, and since we have two symbols, all possible combinations are , and since we have two possible symbols for each combination – rule of CA can be expressed as (0,2⁸=256) number.

90 in binary would be (*), which is enough to describe elementary ca behavior.