Double pendulum · qwen3.6-flash
Simulate a chaotic double pendulum on a canvas using the correct equations of motion, drawing the arms and a colorful fading trail of the tip.
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Simulate a chaotic double pendulum on a canvas using the correct equations of motion, drawing the arms and a colorful fading trail of the tip.
thinking
The user wants a single-page web app that simulates a double pendulum with: 1. Correct physics equations of motion 2. Canvas rendering 3. Two arms drawn 4. A colorful fading trail of the tip 5. All in one index.html file 6. No external dependencies Let me write the double pendulum simulation using the Lagrangian-derived equations of motion: θ₁'' = (-g(2m₁+m₂)sin(θ₁) - m₂g sin(θ₁-2θ₂) - 2sin(θ₁-θ₂)m₂(θ₂'²L₂ + θ₁'²L₁cos(θ₁-θ₂))) / (L₁(2m₁+m₂-m₂cos(2θ₁-2θ₂))) θ₂'' = (2sin(θ₁-θ₂)(θ₁'²L₁(m₁+m₂) + g(m₁+m₂)cos(θ₁) + θ₂'²L₂m₂cos(θ₁-θ₂))) / (L₂(2m₁+m₂-m₂cos(2θ₁-2θ₂))) I'll use RK4 integration for accuracy. The trail will use HSL color cycling and fade out over time.
/index.html (7272 bytes)EROFS: read-only file system, open '/index.html'
thinking
The current working directory is /workspace, so I need to write to /workspace/index.html instead of /index.html.
/workspace/index.html (7271 bytes)Successfully wrote 7271 bytes to /workspace/index.html
thinking
The user wants me to verify the file exists and maybe provide a brief summary of what was built.
Done! Here's what I built in `/workspace/index.html`: **Double pendulum simulation** with: - **Exact Lagrangian equations of motion** — the classic coupled ODEs for two masses on two rigid rods - **RK4 integration** (4th-order Runge-Kutta) with 4 sub-steps per frame for numerical stability - **Colorful fading trail** of the tip (end bob) — hue shifts over time (HSL rainbow), with opacity fading from bright to ghostly - **Drawn pendulum arms & bobs** with connecting lines - **Motion blur effect** — the canvas background is re-drawn semi-transparently each frame, causing previous positions to naturally fade **Controls:** | Control | Effect | |---|---| | **Reset** | Back to rest initial condition | | **Pause / Resume** | Toggle simulation | | **Trail slider** | Trail length: 200–5000 points | | **Speed slider** | Simulation time scale: 1×–20× | | **g slider** | Gravity: 1–30 m/s² | No external resources — fully self-contained, runs sandboxed in any browser.
TAKE IT TO CODE
A single self-contained HTML file — copy it and open in any browser, or reuse the prompt with your own pi-agent run.
RUN
EVALUATION
Chaotic double pendulum with colorful fading trails animates continuously, filling into a dense radial pattern over time.
Vision grade · anthropic/claude-sonnet-5
MEASUREMENTS
Raw readings from the capture, not a verdict — the grade above is the only judgement. Percentages are how much of the screen changed; the measure under-reports sparse motion on a dark background.