Double pendulum · muse-spark-1.3
Output generated Cost / run $0.0779 Runtime 60.7s
Prompt for this run
Build a planar double-pendulum simulation on a canvas with a colorful fading trail at the lower bob. Use HTML, CSS, and JavaScript as needed. Write it to `index.html` in the current working directory using your file tools. Inline your own CSS and JavaScript. Do not use external assets, CDNs, or network requests. No third-party libraries are provided. Required behavior: - Model two point masses connected by massless rigid rods under gravity, without damping or external driving. Use the coupled equations of motion rather than independent sine-wave animations. - Use equal masses and rod lengths, gravity of 9.81 in consistent simulation units, initial angles of 120 and -10 degrees measured from downward vertical, and zero initial angular velocities. - Draw a fixed pivot, both rods and bobs, and a bounded fading trail of the lower bob. Keep both rod lengths constant and the pendulum visible. - Provide Pause/Resume and Reset. Reset restores the stated initial conditions and clears the trail. - Use a numerically stable integration scheme and time step so ordinary playback does not explode or freeze. Verify: Sample the pendulum at several moments to inspect coupled motion, connected rods, and the lower-bob trail. Pause and resume to check the motion control, then reset and confirm that the starting pose and cleared trail return.
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
METRICS
Transcript · 15 messages
Build a planar double-pendulum simulation on a canvas with a colorful fading trail at the lower bob. Use HTML, CSS, and JavaScript as needed. Write it to `index.html` in the current working directory using your file tools. Inline your own CSS and JavaScript. Do not use external assets, CDNs, or network requests. No third-party libraries are provided. Required behavior: - Model two point masses connected by massless rigid rods under gravity, without damping or external driving. Use the coupled equations of motion rather than independent sine-wave animations. - Use equal masses and rod lengths, gravity of 9.81 in consistent simulation units, initial angles of 120 and -10 degrees measured from downward vertical, and zero initial angular velocities. - Draw a fixed pivot, both rods and bobs, and a bounded fading trail of the lower bob. Keep both rod lengths constant and the pendulum visible. - Provide Pause/Resume and Reset. Reset restores the stated initial conditions and clears the trail. - Use a numerically stable integration scheme and time step so ordinary playback does not explode or freeze. Verify: Sample the pendulum at several moments to inspect coupled motion, connected rods, and the lower-bob trail. Pause and resume to check the motion control, then reset and confirm that the starting pose and cleared trail return.
thinking
Deriving double pendulum equations and planning RK4 integration with rendering and controls for a single-file HTML simulation.
Building your double-pendulum with coupled physics and a glowing trail — writing the app now.
index.html (9890 bytes)Successfully wrote to index.html
thinking
File written — now I'll verify motion, trail, and controls in the browser.
{"action":"reload"}Frame 1, +0ms
[Browser image supplied to model]
{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Planar Double Pendulum\nCoupled equations of motion · RK4 integration · m1=m2, L1=L2, g=9.81 · θ1=120°, θ2=−10°\nPause\nReset\nt = 0.12 s θ1 = 116.1° θ2 = -11.7° trail = 7\npivot\nupper bob (m1)\nlower bob (m2) + fading trail\nAngles measured from downward vertical.","images":"attached"}
thinking
Initial frame looks correct — now sampling motion and testing the controls.
{"action":"motion"}Frame 1, +0ms
[Browser image supplied to model]
Frame 2, +578ms
[Browser image supplied to model]
Frame 3, +1145ms
[Browser image supplied to model]
Frame 4, +1705ms
[Browser image supplied to model]
{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Planar Double Pendulum\nCoupled equations of motion · RK4 integration · m1=m2, L1=L2, g=9.81 · θ1=120°, θ2=−10°\nPause\nReset\nt = 7.42 s θ1 = -56.0° θ2 = -96.5° trail = 443\npivot\nupper bob (m1)\nlower bob (m2) + fading trail\nAngles measured from downward vertical.","images":"attached"}
thinking
Chaotic coupled motion and the fading trail check out — now I'll confirm pause and reset.
{"action":"click","x":210,"y":100}Frame 1, +0ms
[Browser image supplied to model]
{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Planar Double Pendulum\nCoupled equations of motion · RK4 integration · m1=m2, L1=L2, g=9.81 · θ1=120°, θ2=−10°\nResume\nReset\nt = 11.15 s θ1 = -14.0° θ2 = 53.3° trail = 667 ⏸ paused\npivot\nupper bob (m1)\nlower bob (m2) + fading trail\nAngles measured from downward vertical.","images":"attached"}
thinking
{"action":"click","x":210,"y":100}Frame 1, +0ms
[Browser image supplied to model]
{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Planar Double Pendulum\nCoupled equations of motion · RK4 integration · m1=m2, L1=L2, g=9.81 · θ1=120°, θ2=−10°\nPause\nReset\nt = 11.23 s θ1 = -11.0° θ2 = 84.9° trail = 672\npivot\nupper bob (m1)\nlower bob (m2) + fading trail\nAngles measured from downward vertical.","images":"attached"}
thinking
{"action":"click","x":311,"y":100}Frame 1, +0ms
[Browser image supplied to model]
{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Planar Double Pendulum\nCoupled equations of motion · RK4 integration · m1=m2, L1=L2, g=9.81 · θ1=120°, θ2=−10°\nPause\nReset\nt = 0.07 s θ1 = 118.7° θ2 = -10.6° trail = 5\npivot\nupper bob (m1)\nlower bob (m2) + fading trail\nAngles measured from downward vertical.","images":"attached"}
thinking
All checks passed. `index.html` is saved. **What was verified in-browser:** - **Initial pose:** θ1≈119–120°, θ2≈−10°, pivot + 2 connected rods + 2 bobs visible. - **Coupled motion:** motion strip showed non-periodic chaotic swinging (θ sweeping through e.g. −47°/194°, −16°/128°, 67°/−54°, −47°/−109°), rods stayed connected and lengths constant, pendulum stayed in view without exploding. - **Trail:** colorful fading polyline at lower bob, growing to ~400–670 points, fading alpha/width by age, hue cycling. - **Pause:** clicked Pause → button became Resume, readout froze at t=11.15s with "paused". - **Resume:** clicked Resume → time advanced (11.18s+), button back to Pause. - **Reset:** clicked Reset → t≈0.02s, θ1≈119.9°, θ2≈−10°, trail cleared to ~2 points, starting pose returned. **Remaining unverified:** long-run (>minutes) energy drift and exact pixel rod-length constancy were not numerically measured — integration is RK4 with ~2ms substeps, clamped frame dt, which showed no instability in testing.