IFS with Memory

Romes

Here are the tables and corresponding graphs for these examples.
We saw address i contains a scaled copy of the whole shape if in the table all entries of the ith column are filled.
In the graph this condition is expressed as arrows lead from all four vertices to i.
In this case, we say vertex i is a rome. Remember "All roads lead to ... ."
The existence of a rome guarantees that the picture can be generated by an IFS without memory, although in some cases infinitely many transformations are needed.

Return to Romes.