recurrence-relations #

Visualizes the pipeline from a linear homogeneous constant-coefficient recurrence to its characteristic polynomial P(r), then shows how roots (and multiplicity) map to solution terms r^n and n^j r^n. A built-in example with a repeated root (r=1, multiplicity 2) demonstrates why the general solution gains an extra n factor, and interactive sliders let you change initial conditions x0 and x1 to see how they uniquely determine the linear-combination coefficients (c0, c1) and the resulting sequence values.

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Solving algorithm time recurrences (e.g., divide-and-conquer) using characteristic roots
02.Analyzing linear feedback shift registers and discrete-time systems
03.Deriving closed forms for sequences in combinatorics and counting problems

technical notes #

Pure Canvas2D, green-on-black blocky UI with snapped coordinates. Animation cycles through stages (recurrence -> P(r) -> roots -> general solution) over ~4.2s with easing-based reveals and a sweeping cursor over r and n. Optional interactivity: pointer events on the canvas adjust two sliders for initial conditions; coefficients are computed from the displayed recurrence with a repeated root.

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