A cobweb plot turns iteration of the map into a staircase of ledger points bouncing between the curve y = f(x) and the diagonal y = x, visualizing whether the sequence converges, cycles, or runs off. The geometry is exact only for the stated map rule and iteration points in the ideal discrete-map model. Real systems add continuous dynamics, noise, unmodeled feedback, finite sampling, parameter uncertainty, and source-traceability limits.
A cobweb diagram is source-bound geometry, not a free sketch. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Cobweb points come from the ledger
The plotted states are the seed, one quarter, three eighths, and seven sixteenths.
0,41,83,167
The step segments are checked geometry
There are 4 source points and 6 checked cobweb segments.