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Double Pendulum Art: reference guide
Open the Studio tab. The pendulums start running immediately and the trails will draw themselves.
Select a pendulum by clicking its name in the Pendulums list. The selected one is outlined in white on the canvas. All the Shape & Motion controls apply to the selected pendulum only.
Hit Clear to wipe trails and start fresh. Hit Save image when you like the design
| Command | Description |
|---|---|
| Pause / Play | Freeze or resume the simulation. Trails stay on screen; only new drawing stops. |
| Clear | Wipe all trails and reset the timer. Pendulums keep their current position and settings. |
| Reset all | Remove all pendulums and restore defaults. Shows a confirmation dialog first. |
| Move pivot | Toggle pivot drag mode. When on, drag a pendulum's anchor dot to reposition it. Simulation pauses during drag and resumes on release. |
| Hide / Show rods | Toggle the arm lines connecting pivot to balls. |
| Hide / Show balls | Toggle the circular bob indicators at the end of each arm. |
| Share | Generate a URL encoding all current settings. Opening it loads the exact same configuration. |
| Save image | Download the canvas as a full-resolution PNG. Choose trails only or include rods and balls. |
Multiple pendulums run simultaneously through the same physics. Each draws its own trail in its own color. Click a name to select it. Click × to delete it and clear its trail. + add pendulum creates a new one.
Applies to the selected pendulum only. Changing either angle resets that pendulum's velocity to zero and starts it from the new position.
| Parameter | Description |
|---|---|
| Angle 1 per pendulum |
Starting angle of the upper arm in degrees from vertical. 0° = straight down, 90° = right, 180° = straight up. |
| Angle 2 per pendulum |
Starting angle of the lower arm. Small differences in this value between pendulums cause large divergence in the resulting trails. |
| Length 1 per pendulum |
Upper arm length as a multiple of the base scale. |
| Length 2 per pendulum |
Lower arm length. Longer = wider, more dramatic trails. Shorter = tight spirals. |
| Mass 1 per pendulum |
Upper bob mass. Heavier upper bob makes the top arm dominate; lower arm follows more passively. |
| Mass 2 per pendulum |
Lower bob mass. Heavier lower bob increases chaos and spreads the trail further. |
| Opacity per pendulum |
Transparency of each trail segment. |
| Thickness per pendulum |
Width in pixels of each trail segment. |
These settings apply globally to all pendulums.
| Parameter | Description |
|---|---|
| Gravity global |
Gravitational constant. Higher = faster swinging. Earth real-world value is 9.8. |
| Speed global |
Simulation time multiplier. At 2× the pendulum moves twice as fast; physics stay accurate. |
| Damping global |
Energy loss per step. 0 = swings forever. Increase to make pendulums spiral inward and come to rest. |
| Fade global |
How quickly old trail segments disappear. Off = trails stay forever. Faster = comet-tail effect. |
| Blend global |
additive: overlapping areas glow brighter. normal: paints on top. multiply: overlaps get darker. |
Click any swatch to apply that color to the selected pendulum's trail. Use the color picker or type a hex code directly to set a custom color.
Check one or more pendulums, then click Erase to remove just those trails without stopping the simulation or deleting the pendulum.
| Input | Action |
|---|---|
| Scroll wheel | Zoom in/out centered on the cursor. |
| Click + drag | Pan the canvas. |
| + / − buttons | Zoom controls in the bottom-left corner. |
| ⌂ button | Reset to 100% zoom and center the view. |
Enable Move pivot in the toolbar. Each pendulum's anchor point becomes draggable. The simulation pauses while you drag and resumes on release.
| Action | Output |
|---|---|
| Save image | Full-resolution PNG download. Choose Art only (trails only) or With pendulum (includes rods and balls). |
| Share | URL encoding all pendulum settings. Opening it loads the exact same starting configuration. |
A generative art tool that runs entirely in your browser. The second bob's trail is the painting. No randomness, no noise, no tricks. Just a differential equation integrated forward until something beautiful happens.
A double pendulum has two rigid arms connected end to end, hanging from a fixed pivot. The full state at any moment is four numbers:
theta1: angle of arm 1 from verticaltheta2: angle of arm 2 from verticalomega1: angular velocity of arm 1omega2: angular velocity of arm 2Every frame, the second bob's position is computed and a line is drawn from its last position to its current one. Do that thousands of times and you get a painting.
The equations come from the Lagrangian (L = T − V), which is just a way of describing a system by its kinetic and potential energy instead of forces. Solving it gives you the angular acceleration of each arm at any point in time.
denom = 2*m1 + m2 - m2*cos(2*θ1 - 2*θ2)
α1 = [ -g*(2*m1+m2)*sin(θ1) - m2*g*sin(θ1-2*θ2)
- 2*sin(θ1-θ2)*m2*(ω2²*L2 + ω1²*L1*cos(θ1-θ2)) ]
/ (L1 * denom)
α2 = [ 2*sin(θ1-θ2)*(ω1²*L1*(m1+m2)
+ g*(m1+m2)*cos(θ1) + ω2²*L2*m2*cos(θ1-θ2)) ]
/ (L2 * (L2/L1) * denom)The same initial conditions always produce the same trail. Shift the starting angle by 0.001° and within seconds the two paths look nothing alike. This isn't a bug or a quirk of the simulation. It's a real property of the system, and it's why double pendulums are a classic example of chaos theory.
Everything runs locally in your browser.