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sequences #

Visualizes a sequence as an indexed ordered list (n → a_n). The animation steps through terms and highlights the rule that generates the next term: arithmetic sequences add a constant difference d each step, while geometric sequences multiply by a constant ratio r each step. Recurrence and explicit formulas are shown side-by-side to connect “process” and “closed form.”

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

• 01.Modeling linear growth like saving a fixed amount each week (arithmetic)
• 02.Modeling exponential growth/decay like doubling bacteria or compound interest (geometric)
• 03.Recognizing patterns in data streams and predicting the next value from constant difference/ratio

technical notes #

Time-based stepping animates from a_n to a_{n+1} with eased interpolation. The visualization alternates modes every ~2.1s (arithmetic/geometric) and uses snapped coordinates for a blocky grid aesthetic. Pure Canvas 2D API; responsive scaling via scale = min(w,h)/baseSize.

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