IFS with Memory

Horizintal, Vertical, and Diagonal Line Pair Answers

The vertical line determined by T1 and T3 and the vertical line determined by T2 and T4 are additive.

The diagonal line determined by T1 and T4 and the diagonal line determined by T2 and T3 are additive.

What about the vertical line determined by T2 and T4, and the horizontal line determined by T3 and T4? Are these lines additive? They are not, and the reason is clear: both lines share the transformation T4. The part of the vertical line in the square with address 4 is scaled and copied to the square with address 34, and then to the cascade of smaller squares with longer addresses 334, 434, 3334, 4334, 3434, 4434, and so on. Similarly, the part of the horizonal line in the square with address 4 is scaled and copied to the square with address 24, and then to the cascade of smaller squares with longer addresses 224, 424, 2224, 4224, 2424, 4424, and so on.