Double pendulum · qwen3.7-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.
transcript · 6 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 HTML file that simulates a chaotic double pendulum with: 1. Correct equations of motion for a double pendulum 2. Canvas rendering showing the two arms 3. A colorful fading trail of the tip position I need to implement: - The physics: double pendulum using Lagrangian mechanics, giving coupled ODEs solved via RK4 - The visualization: canvas with arms drawn as lines, and a trail that fades over time with color cycling (HSL hue rotation) Let me write this all in one index.html file. The equations of motion for a double pendulum (with equal lengths L1=L2=L and equal masses m1=m2=m): θ1'' = (-g(2m1+m2)sin(θ1) - m2*g*sin(θ1-2θ2) - 2*sin(θ1-θ2)*m2*(θ2'^2*L2 + θ1'^2*L1*cos(θ1-θ2))) / (L1*(2m1+m2-m2*cos(2θ1-2θ2))) θ2'' = (2*sin(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 Runge-Kutta 4th order for integration. For the trail, I'll store recent positions and draw them with decreasing opacity and cycling HSL color. Let me build this.
/tmp/ws/index.html (9444 bytes)Successfully wrote 9444 bytes to /tmp/ws/index.html
thinking
Let me verify the file was written correctly.
{"command":"wc -l /tmp/ws/index.html && head -3 /tmp/ws/index.html && echo \"---\" && tail -3 /tmp/ws/index.html"}354 /tmp/ws/index.html <!DOCTYPE html> <html lang="en"> <head> --- </script> </body> </html>
thinking
The file is written correctly. Let me provide a summary of what's in it.
Done — `/tmp/ws/index.html` (354 lines, fully self-contained). Here's what it includes: **Physics** — Correct double-pendulum equations of motion derived from the Lagrangian, integrated with 4th-order Runge-Kutta (RK4) using 8 substeps per frame for stability. **Rendering:** - Two arms drawn as grey lines (pivot → mass1 → mass2/tip) - Glowing pivot point and shaded circular masses - The tip emits a color-cycling glow dot - A **rainbow fading trail** of the tip position stored as HSL-colored segments with opacity proportional to recency **Controls:** - Sliders for initial θ₁, θ₂, arm length, and trail length - Reset button to reinitialize - Drag on the canvas to reposition the pivot mid-simulation - Scroll wheel interaction area reserved
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
Double pendulum sim with physics-driven chaotic motion and colorful fading trails; drag/wheel reposition pivot and zoom.
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.