generating-functions #

Cycles through three linked views: (1) encoding a sequence a_n as an ordinary generating function A(x)=∑a_n x^n, (2) extracting a specific coefficient [x^n]A(x)=a_n with an animated scanner, and (3) showing how algebra on generating functions corresponds to sequence operations (index shift via x^k and convolution via the Cauchy product).

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Solve counting problems by translating combinatorial constructions into algebraic equations in A(x).
02.Derive and solve linear recurrences with constant coefficients using rational generating functions.
03.Compute sequence convolutions (e.g., ways to combine independent choices) via multiplication of generating functions.

technical notes #

Uses a 3-scene time loop (~3.2s each). All geometry snaps to a 4px grid for a blocky aesthetic. Animations use time-based phases and the provided cubic ease(). No external state; pure Canvas 2D drawing with lightweight shapes and monospace text.

← regularization joint-distributions →