For Students · Bifurcation Diagram
Bifurcation Diagram for a loan payoff
Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a loan payoff live below — adjust the inputs and watch it respond, right in your browser.
Bifurcation DiagramLive
logistic map · route to chaos
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The logistic map xₙ₊₁ = r·xₙ(1−xₙ) doubles its period again and again as r grows, then dissolves into chaos near r ≈ 3.57 — with windows of order inside.
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Mapr·x(1−x)
Chaos onsetr ≈ 3.57
Feigenbaum δ4.669
Governing equation
Reading this result: Past r ≈ 3.57 the branches blur into chaos, yet pale vertical windows remain where periodic order suddenly returns.
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Frequently asked questions
- Is this good for students?
- Yes — this version of "Bifurcation Diagram for a loan payoff" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
- Do I need to install anything?
- No. It runs in any modern browser, free, with no account required.