The table below gives all repeating Rule 30 patterns that have been found
by various methods by increasing width. Till width 30 this has been done
by an algorithm that simply tried every possible pattern, seeing if it
will repeat. Most solutions above this size have been found by an
algorithm which tries to find a pattern that fits in a given box.
I discovered this algorithm on January 9, 2005
and later perfected it a little more. Below there is also a table
that gives the patterns by increasing area.