Affine Map Keeps a Finite Ledger - Nonlinear Dynamics and Stability Step by Step

A finite map lesson begins with a seed, a rule, and checked states. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A map is a rule plus a seed

The seed is 0 and the checked rule sends it to one quarter.

x_{1}=\frac{x_{0}}{2}+\frac{1}{4}=\frac{1}{4}

The ledger stops at the pinned depth

The four displayed states are the seed, one quarter, three eighths, and seven sixteenths.

0\to\frac{1}{4}\to\frac{3}{8}\to\frac{7}{16}