Double pendulum · deepseek-v4.1-flash
Output generated Cost / run $0.0035 Runtime 83.1s
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 · 25 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
Let me build a double pendulum simulation. I'll write the index.html file with proper physics. Equations of motion for double pendulum with equal masses m and lengths L: θ1'' = (-3g sinθ1 - g sin(θ1-2θ2) - 2 sin(θ1-θ2)(θ2'^2 L + θ1'^2 L cos(θ1-θ2))) / (L(3 - cos(2θ1-2θ2))) θ2'' = (2 sin(θ1-θ2)(2θ1'^2 L + 2g cosθ1 + θ2'^2 L cos(θ1-θ2))) / (L(3 - cos(2θ1-2θ2))) Let me use RK4 integration with small dt. Let me write it. Angles measured from downward vertical. Positions: x1 = L sinθ1, y1 = L cosθ1 (y downward positive? let's use screen coords) x2 = x1 + L sinθ2, y2 = y1 + L cosθ2 Initialize θ1 = 120°, θ2 = -10°. Let me code. I'll implement RK4 on state [θ1, ω1, θ2, ω2]. Trail: store points, bounded array, fade with age. Draw on a separate offscreen canvas or with alpha. Let me write.
{"command":"ls -la"}total 12 drwx------ 3 node node 4096 Oct 29 01:29 . drwxrwxrwt 8 root root 4096 Oct 29 01:29 .. drwxr-xr-x 3 node node 4096 Oct 29 01:29 .home
thinking
Let me write index.html.
index.html (10577 bytes)Successfully wrote to index.html
thinking
I have a typo: `background: linear-gradient(180deg,#2b3purple,#22call);` — that's invalid CSS but has a following valid declaration. Let me remove it.
{"path":"index.html","edits":[{"oldText":" background: linear-gradient(180deg,#2b3purple,#22call);\n background: #253048;","newText":"Successfully replaced 1 block(s) in index.html.
{"action":"reload"}Frame 1, +1ms
[Browser image supplied to model]
{"console":[],"dom":"Pause\nReset\nrunning\nt = 0.06 s θ₁ = 118.8° θ₂ = -10.5° bob2 = (0.69, 0.50) m","images":"attached"}
thinking
Let me check the motion over time.
Initial pose correct. Let me sample motion and check trail development.
{"command":"sleep 2"}(no output)
{"action":"inspect"}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"Pause\nReset\nrunning\nt = 2.66 s θ₁ = -22.5° θ₂ = 167.4° bob2 = (-0.17, -0.05) m","images":"attached"}
thinking
The simulation looks great — colorful fading trail, coupled chaotic motion, rods connected. Now test pause/resume and reset. Let me pause via click. The pause button is at approx (62, 41).
Coupled chaotic motion and colorful fading trail working. Now test Pause/Resume and Reset.
{"action":"click","x":62,"y":41}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"Resume\nReset\npaused\nt = 3.91 s θ₁ = 86.1° θ₂ = 369.6° bob2 = (1.16, 1.05) m","images":"attached"}
thinking
Paused, θ₂ = 369.6° which means it's wrapping — the angle is just unbounded, that's normal. Let me verify pause actually freezes: wait and check state unchanged. Let me check simTime again.
Pause confirmed. Let me verify state is frozen, then resume.
{"command":"sleep 1.5"}(no output)
{"action":"inspect"}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"Resume\nReset\npaused\nt = 3.91 s θ₁ = 86.1° θ₂ = 369.6° bob2 = (1.16, 1.05) m","images":"attached"}
thinking
Frozen. Now resume then reset.
Frozen correctly. Now Resume, then Reset.
{"action":"click","x":62,"y":41}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"Pause\nReset\nrunning\nt = 3.94 s θ₁ = 90.4° θ₂ = 370.2° bob2 = (1.18, 0.98) m","images":"attached"}
{"action":"click","x":141,"y":41}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"Pause\nReset\nrunning\nt = 0.02 s θ₁ = 119.8° θ₂ = -10.1° bob2 = (0.69, 0.49) m","images":"attached"}
thinking
Reset restores initial angles 120°, -10°, clears trail, simTime 0. The upper bob appears at (0.69, 0.49) wait that's bob2. Let me verify the pose matches initial: θ1=120°, θ2=-10°. Upper bob at sin120=0.866, cos120=-0.5 → to the left and up relative to pivot. Yes image shows upper bob left/up. Lower bob from there + θ2=-10: x=0.866+sin(-10)=0.866-0.17=0.69, y=-0.5+cos(-10)=-0.5+0.98=0.48. Matches (0.69,0.49). Trail cleared. Everything works. Also check no console errors — none reported. Verify no network requests: all inline. Good. One concern: DPR and canvas.H = Math.min(availH-40, max(...)) — fine. I could check long-run stability but time budget. The RK4 with dt=0.0005 and 16 substeps per frame at 60fps = 8ms sim/frame, real-time. Stable. Done. Report.
All required behaviors verified. Final file is at `/tmp/job-5LZHNd/index.html`. ## What I checked (in-browser) - **Initial pose**: On load/reset, θ₁ = 120°, θ₂ = -10°, zero angular velocities; pivot at top, upper bob up-left, lower bob hanging near-vertically below it. Matches hand-computed position (0.69, 0.49) m. - **Coupled motion**: Sampled at ~0.06 s, ~2.66 s, ~3.91 s — angles evolve chaotically (θ₁ 118.8°→−22.5°→86.1°, θ₂ −10.5°→167.4°→369.6°), confirming the two DOF are dynamically coupled rather than independent sines. - **Rods & bobs**: Screenshots show a fixed pivot, both rods joined end-to-end, and both bobs; rod lengths stay constant throughout. - **Trail**: Lower bob leaves a bounded, rainbow-hued fading trail that accumulates and clips at `MAX_TRAIL`. - **Pause/Resume**: Pause froze both sim time (3.91 s) and bob position across a 1.5 s wait; Resume advanced again. - **Reset**: Restored the 120°/−10° pose, zeroed sim time, and cleared the trail back to empty. - **Console**: No errors/warnings; no external resources (all CSS/JS inline). ## Implementation notes - Full coupled double-pendulum EOMs (equal masses/lengths, g = 9.81), integrated with **RK4** at dt = 0.0005 s × 16 substeps/frame (~8 ms sim per frame, real-time), with a frame-gap clamp to avoid blow-ups. - `window.__pendulum` exposes state/trail for inspection. ## Unverified / remaining - Very long-run energy conservation and behavior after many minutes (only a few seconds were sampled). - Responsive layout on window resize/mobile was implemented but not interactively resized. - Touch input and keyboard shortcuts (Space/R) were implemented but not exercised.