Feigenbaum Explorer

An interactive browser-based explorer for the logistic map and its period-doubling route to chaos.

Originally written as a Python/matplotlib animation. Converted to this interactive tool by Claude Code.

Live at: https://feigenbaum.pedroqueiroz.workers.dev

What it shows

• Cobweb diagram — visualises the iteration of f(x) = r·x·(1−x) as a staircase between the parabola and the diagonal y = x. Segments are drawn at low opacity so frequently-visited regions glow brighter.
• Bifurcation diagram — the classic Feigenbaum diagram showing which x-values the orbit settles on for each r ∈ [2.5, 4.0].
• Teal attractor dots — when the orbit is periodic (not chaotic), dots mark the exact cycle points on the parabola.
• Horizontal guides — dashed teal lines connect the attractor y-values across both charts when in a periodic window.

Controls

• Drag the blue line on the bifurcation diagram to set r (cursor changes to ↔ near the line).
• Increment buttons — fine-tune r in steps of ±0.1 down to ±0.0000001.
• URL — the current r value is stored in ?r=, so any state can be bookmarked or shared.

Tech Stack

• Frontend: Vanilla JavaScript + Canvas 2D API, no dependencies
• Hosting: Cloudflare Workers (serves static HTML)

Deployment

npm install -g wrangler
npx wrangler login
npx wrangler deploy