Double pendulum · mimo-v2.5-pro
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 · 4 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. Use the correct Lagrangian mechanics equations for a double pendulum 2. Draw it on a canvas 3. Show the arms 4. Show a colorful fading trail of the tip Let me build this. The double pendulum equations of motion from the Lagrangian are: For a double pendulum with masses m1, m2, lengths L1, L2, angles θ1, θ2: 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 RK4 for integration and create a beautiful visualization with a colorful fading trail. Let me create this as a self-contained index.html.
/workspace/index.html (8460 bytes)Successfully wrote 8460 bytes to /workspace/index.html
thinking
The file has been created. Let me verify it's there.
The double pendulum simulation is ready at `/workspace/index.html`. Here's what it includes: **Physics** - Correct Lagrangian-derived equations of motion for the double pendulum (two coupled nonlinear ODEs) - 4th-order Runge-Kutta integrator for accuracy with a 5ms timestep - Configurable damping torque **Visualization** - Canvas-based rendering with semi-transparent overlay for subtle motion blur - Two arms drawn with rounded caps, pivot point, and gradient-lit masses - A **colorful fading trail** of the tip mass — the hue cycles continuously through the rainbow, older points are thinner and more transparent, and a glow effect follows the tip **Controls** | Button | Action | |--------|--------| | **Reset** | Randomizes initial angles and clears the trail | | **Pause/Resume** | Toggles the simulation | | **Clear Trail** | Erases the trail only | | **Speed slider** | 0.1× – 5× simulation speed | | **Damping slider** | Adds friction to watch energy dissipate | Open the file in a browser — no network or dependencies needed. The chaotic sensitivity to initial conditions means each Reset produces a completely different dance pattern.
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 animates continuously with colorful fading trails; inputs may perturb it but effect unclear, mostly self-running.
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.