Double pendulum · qwen3.6-27b
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.
transcript · 8 messages
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 chaotic double pendulum. I need to: 1. Implement the correct equations of motion for a double pendulum using Lagrangian mechanics 2. Draw the two arms on a canvas 3. Draw a colorful fading trail of the tip The equations of motion for a double pendulum (derived from the Lagrangian) are well-known. I'll use them directly: θ1'' = (-g(2m1+m2)sin(θ1) - m2*g*sin(θ1-2θ2) - 2sin(θ1-θ2)*m2*(θ2'^2*L2 + θ1'^2*L1*cos(θ1-θ2))) / (L1*(2m1+m2-m2*cos(2θ1-2θ2))) θ2'' = (2sin(θ1-θ2)*(θ1'^2*L1*(m1+m2) + g*(m1+m2)*cos(θ1) + θ2'^2*L2*m2*cos(θ1-θ2))) / (L2*(2m1+m2-m2*cos(2θ1-2θ2))) I'll use RK4 integration for accuracy. Let me write the complete HTML file.
/workspace/index.html (8018 bytes)Successfully wrote 8018 bytes to /workspace/index.html
thinking
Let me verify the file exists and looks correct.
{"command":"ls -la /workspace/index.html && head -5 /workspace/index.html && echo \"---\" && tail -5 /workspace/index.html"}-rw-r--r-- 1 node node 8018 Jul 31 03:00 /workspace/index.html <!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> --- loop(); </script> </body> </html>
thinking
The file is created successfully. Let me verify there are no external resources or CDNs used in the file.
{"command":"grep -iE 'http|cdn|external|@import|fetch|xmlhttp|axios' /workspace/index.html || echo \"No external resources found.\""}No external resources found.
thinking
Good, no external resources. The file is self-contained. Let me summarize what was built.
Done. `/workspace/index.html` is a fully self-contained double pendulum simulation. Here's what it does: **Physics** — Uses the full Lagrangian-derived equations of motion for a double pendulum with masses `M₁`, `M₂`, arm lengths `L₁`, `L₂`, integrated via **4th-order Runge-Kutta** with 8 sub-stepping iterations per frame for accuracy and stability. **Visuals** — On a dark canvas: - **Fading trail** of the tip bob with 3000+ stored points, using HSL color cycling so the path flows through a rainbow that shifts over time. Older points fade out with a quadratic alpha curve. - **Glow effect** on the tip bob via a radial gradient. - Two semi-transparent arms drawn with rounded line caps connecting the pivot → bob₁ → bob₂. - Motion blur via semi-transparent background fill each frame. **Interaction** — Click anywhere on the canvas to re-scatter with new random initial angles. The simulation is fully chaotic — tiny changes in starting conditions rapidly diverge into wildly different paths.
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
Animated double pendulum with colorful fading trail, but appears as multiple overlapping arms rather than a single clean pendulum.
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.