The polynomial law is err(k) = C/(1 + αk)p, so its error decreases monotonically from err(0) = C. Choose whether the approximation fills one, two, or three rows; the number of displayed digits adapts automatically to the available width. The correct-digit count is computed directly from the model error as floor(-log10(err(k))) and is independent of the display window. When the iteration count exceeds the plotted horizon, the x-axis doubles automatically. When the error falls below the plotted range, the log-scale y-range doubles downward automatically.