Double pendulum · qwen3.8-27b
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 · 18 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
Create an index.html containing a double pendulum simulation using the standard Lagrangian equations of motion, and implement a fading trail using a semi-transparent overlay or a trail array with color changes (hue). Self-contained.
/tmp/ws/index.html (7668 bytes)Successfully wrote 7668 bytes to /tmp/ws/index.html
thinking
(Internal note) Quick check: verify the file exists. A quick node check for syntax errors is also possible. No problem — should I try running a quick node syntax check on the script? Optional. Quickly checking whether index.html exists should be enough.
{"command":"ls -la /tmp/ws/index.html && node -e \"\nconst html = require('fs').readFileSync('/tmp/ws/index.html','utf8');\nconst m = html.m-rw-r--r--. 1 node node 7724 Aug 15 13:52 /tmp/ws/index.html <anonymous_script>:7 const canvas = ({getElementById:()=>({addEventListener:()=>{}})})..getElementById("c"); ^ SyntaxError: Unexpected token '.' at new Function (<anonymous>) at [eval]:4:1 at runScriptInThisContext (node:internal/vm:219:10) at node:internal/process/execution:451:12 at [eval]-wrapper:6:24 at runScriptInContext (node:internal/process/execution:449:60) at evalFunction (node:internal/process/execution:283:30) at evalTypeScript (node:internal/process/execution:295:3) at node:internal/main/eval_string:71:3 Node.js v24.18.1
thinking
My sloppy substitution caused the check to fail (it replaced "document" including the occurrence inside "document.getElementById"). Let me use a proper stub and redo the check.
The check script had a bad substitution, not the file. Let me verify properly with a stub:
{"command":"node -e \"\nconst fs = require('fs');\nconst html = fs.readFileSync('/tmp/ws/index.html','utf8');\nconst js = html.match(/<scrip<anonymous_script>:23 hue = 0; ^ ReferenceError: Cannot access 'hue' before initialization at reset (eval at <anonymous> ([eval]:10:1), <anonymous>:23:9) at eval (eval at <anonymous> ([eval]:10:1), <anonymous>:26:3) at eval (eval at <anonymous> ([eval]:10:1), <anonymous>:197:3) at [eval]:10:103 at runScriptInThisContext (node:internal/vm:219:10) at node:internal/process/execution:451:12 at [eval]-wrapper:6:24 at runScriptInContext (node:internal/process/execution:449:60) at evalFunction (node:internal/process/execution:283:30) at evalTypeScript (node:internal/process/execution:295:3) Node.js v24.18.1 Command exited with code 1
thinking
A bug actually exists: `reset()` is being called before `hue` and `trail` are declared (since `let hue` comes later, the TDZ error applies). Fix: hoist the declaration of `trail` and `hue` above `reset()`, or move `let hue = 0; trail = []` up. The simplest way is to move the declarations of `hue`/`trail` above `reset()`.
Caught a real bug: `reset()` is called before `hue`/`trail` are declared (temporal dead zone). Fixing:
{"path":"/tmp/ws/index.html","edits":[{"oldText":" // State: angles from vertical (down), angular velocities\n let th1, th2, w1, w2;\n\n Successfully replaced 2 block(s) in /tmp/ws/index.html.
thinking
Also, `pivot` is used in bobPositions before being declared later — bobPositions is only called after resize() has set pivot, so no problem. However, the `let pivot` declaration is currently placed after the step/derivatives definitions — bobPositions is called inside frame() and inside drag handlers, both of which execute after resize(). OK. Re-running the tests.
{"command":"node -e \"\nconst fs = require('fs');\nconst html = fs.readFileSync('/tmp/ws/index.html','utf8');\nconst js = html.match(/<scrip<anonymous_script>:85 canvas.style.width = innerWidth + "px"; ^ TypeError: Cannot set properties of undefined (setting 'width') at resize (eval at <anonymous> ([eval]:11:15), <anonymous>:85:24) at eval (eval at <anonymous> ([eval]:11:15), <anonymous>:91:3) at eval (eval at <anonymous> ([eval]:11:15), <anonymous>:197:3) at [eval]:12:1 at runScriptInThisContext (node:internal/vm:219:10) at node:internal/process/execution:451:12 at [eval]-wrapper:6:24 at runScriptInContext (node:internal/process/execution:449:60) at evalFunction (node:internal/process/execution:283:30) at evalTypeScript (node:internal/process/execution:295:3) Node.js v24.18.1 Command exited with code 1
thinking
My stub is missing `style` on the canvas element — that's a problem with the test harness, not a bug in the file. I'll add `style: {}` to the stub.
That's a missing `style` property in my test stub, not the file. Fixing the harness:
{"command":"node -e \"\nconst fs = require('fs');\nconst html = fs.readFileSync('/tmp/ws/index.html','utf8');\nconst js = html.match(/<scrip300 frames simulated OK
thinking
Also, do a simple sanity check on energy stability too — run the integrator in isolation and verify that the energy remains roughly conserved. Quick check: extract the derivative functions. Optional, but it can be done quickly. I'll just do a simple standalone check of the physics behavior.
Runs cleanly. One more sanity check — verify the integrator conserves energy (proof the equations of motion are correct):
{"command":"node -e \"\n// Energy-conservation check of the physics (mirrors index.html exactly)\nconst m1=10,m2=10,L1=140,L2=140,g=9.81*30,E0= 371087.536 E(t)= -1236060.000 relative drift after 600s: 4.33e+2%
thinking
The energy is dropping massively... but that's because I'm applying damping DAMP=0.9999 to the velocity every substep — 8 substeps per frame, 60fps, 600 seconds: 0.9999^(8*60*600) = 0.9999^288000 ≈ e^-28.8 ≈ 3e-13. So the velocity decays to nearly zero, and the energy is basically just potential energy only. Is this an expected result from the damping, not integrator error? In fact, the potential energy at the hanging position = -g*(m1*L1 + m2*(L1+L2))... with L in pixels, g=294.3: -294.3*10*(140+420) = -294.3*2600 ≈ -765,180. Hmm, E(t) = -1,236,060, which is even lower than that. Let me calculate: m1*g*L1 + m2*g*(L1+L2) = 294.3*10*(140 + 420) = 2943*560 = 1,648,080. So the minimum potential energy is -1,648,080. E(t) = -1,236,060, which is between the minimum potential and the initial value. It's plausible for a damped system that's slowly still moving. To verify the integrator's accuracy, it's better to test with DAMP=1.
That drift is from the intentional damping. Let me verify the integrator itself with no damping:
{"command":"node -e \"\nconst m1=10,m2=10,L1=140,L2=140,g=9.81*30,DAMP=1.0;\nlet th1=Math.PI/2*1.1, th2=Math.PI/2*1.4, w1=0, w2=0;\nfunctionundamped, 600s: relative energy drift = 3.75e-6%
thinking
The integrator is accurate (a 4e-8 relative drift over a chaotic 600 seconds of simulation). Done. The final file exists.
Done. `index.html` is in place at `/tmp/ws/index.html` — a fully self-contained double pendulum simulation. **Physics** — the exact Lagrangian equations of motion for a double pendulum: - θ₁″ and θ₂″ computed from the standard closed-form expressions (with the `2m₁ + m₂ − m₂cos(2θ₁−2θ₂)` denominator) - Integrated with **RK4 at 8 substeps/frame** — verified to conserve total energy to ~4×10⁻⁸ relative drift over 600 simulated seconds, confirming the equations are correct - Tiny optional air damping (0.9999) for realism **Rendering** - Canvas sized to the window (DPR-aware), with both arms drawn from the pivot - **Colorful fading trail**: 900-point history of the second bob, where each segment's hue cycles (rainbow trail) and its alpha fades as a power curve toward the oldest points, with width tapering from 1→3 px - Bobs rendered with radial gradients and a hue-matched glow; the bobs and trail colors continuously cycle through the spectrum **Interactions** - Drag near the second bob to reposition it (velocities zeroed, trail cleared) - Reset button restores the initial conditions - Touch support included No external resources — everything (CSS, JS, rendering) is inline in the one file.
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 with chaotic motion and colorful fading tip trails animates smoothly; keys/click had little distinct effect but simulation runs continuously.
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.