= Iterative spreadsheet calculation
A different interpretation can treat cyclic <spreadsheet formulas> as simultaneous equations and seek a <fixed point> by repeated numerical updates. This requires an explicit update rule, initial values and stopping condition. It is not automatically the meaning of a <spreadsheet formula>. In particular, a <directed cycle> alone tells us neither whether a <fixed point> exists nor whether a chosen update rule approaches it.
Two original toy examples make the distinction exact. The cyclic pair `X1=Y1+1`, `Y1=X1+1` has no solution over the <real numbers>: substitution gives $X1=X1+2$. For `X1=Y1`, `Y1=X1`, every equal pair is a <fixed point>, so there is no unique answer. Simultaneously updating both <spreadsheet cells> from the previous pair gives $(x_{n+1},y_{n+1})=(y_n,x_n)$. Starting at $(0,1)$ produces the <periodic sequence> $(0,1),(1,0),(0,1),\ldots$, which does not approach a <fixed point>. Updating `X1` first and immediately using its new value for `Y1` instead gives $(1,1)$ in one sweep. That difference follows from the specified rules, not from a claim about any current spreadsheet product. Numerical iteration can be useful for a deliberately chosen model with a justification such as the <contraction mapping theorem>; ordinary acyclic <spreadsheet dependency evaluation> already has its answer from prerequisite order.
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