sound · headphones
The Pulse
Listen as two nearby tones create a steady pulse. Wear headphones: each ear gets its own tone, and the pulse forms between them.
Hear the pulseSound · pattern · nature
Find the shape of your nature.
Simple rules. Unexpected beauty. Explore the patterns, then consider what makes something unmistakably itself.
Tap anywhere to send a wave.
pattern number
1618
φ 1.6180339887 golden angle 137.507764° shape (3,5) → (5,8)
The number sets where the waves start and how they're tuned. The same number always sets up the same pattern; it keeps moving, and your taps change it.
0°
Try this first
The Groove.
Stripes grow on their own from two virtual chemicals, then drift and fold around each other. Draw a line through them and watch them bend around it. Switch on glow, make the stripes fine, and save the picture when you love it.
Draw on itHow it works
Sound makes shapes.
On a vibrating plate, sand moves away from the parts that shake and gathers along the lines that stay still. Change the vibration, and a different pattern can appear. Ernst Chladni made these figures famous in 1787 by drawing a violin bow along sand-covered metal plates.
This plate is a mathematical visualization inspired by his experiments, not a model of a real metal plate. It blends five idealized vibration patterns, each strongest at its own pitch, and thousands of virtual sand grains drift toward wherever the blend holds still. The moving pattern at the top of the page is built the same way: waves spread from eight points and mix with a plate pattern, and the bright lines mark where they cancel.
210.1 Hz
Slide to change the pitch. Near five pitches a pattern locks in; between them, the sand stays loose.
Plays the current pitch through your speaker.
Sand gathers wherever the plate holds still.
Explore the math
Each of the five patterns uses the classic textbook approximation for a square plate:
ψ = cos(nπx)·cos(mπy) ± cos(mπx)·cos(nπy)
The sand gathers where ψ = 0. The animated plate slowly shifts between the + and − forms, so a pattern can change shape while the pitch stays put.
Each pattern's pitch comes from one rule:
f(n,m) = (n² + m²) × 6.18 Hz
| Pattern | n² + m² | Pitch |
|---|---|---|
| (1,2) | 5 | 30.90 Hz |
| (2,3) | 13 | 80.34 Hz |
| (3,5) | 34 | 210.12 Hz |
| (5,8) | 89 | 550.02 Hz |
| (8,13) | 233 | 1439.94 Hz |
Each pair is two neighboring Fibonacci numbers, and for those pairs n² + m² is also a Fibonacci number. That follows from the pairs this model uses; real plates have no preferred Fibonacci frequencies. The 6.18 Hz is this model's scale factor, chosen to echo the golden ratio, not a physical constant.
Each pattern responds most strongly at its own pitch and fades as you move away. The pitch slider covers 21 to 1,597 Hz on a logarithmic scale and snaps to a pattern within about 6% of its pitch.
Waves and atoms
Wave mathematics also helps us understand atoms. Electrons are described by wavefunctions that tell us where they're likely to be found. Those patterns help explain how atoms form bonds.
Your nature
Your nature has a signature.
A pattern takes shape from the rules behind it. That offers a useful way to think about identity.
For a person or a business, start with what's already true: what you care about, how you work, and what people can depend on you for.
Let that shape how you show up.
Further reading: "ghost in the machine", a two-act story about a body deciding what counts as itself.
Keep exploring
Experiments.
Five experiments in sound, motion, and pattern. Still evolving.
3D · particles
The Cube
Watch 34,000 particles drift through a slowly turning cube toward the quiet spots of a three-dimensional wave pattern, or gather on a glowing gyroid lattice. Drag to turn it, and pick its colors.
Explore the cubemotion · golden angle
The Vortex
Steer a glowing whirlpool and pick its colors. Change its speed, move its center, or reverse its direction. Its 2,584 particles are spaced by the golden angle.
Steer the vortexpattern · Turing
The Groove
Two virtual chemicals react and spread at different speeds, and stripes form on their own: a Turing pattern. Each stripe is drawn in three bands from fourteen color palettes, and a slow drift keeps them traveling and folding around each other.
Grow the stripeschemistry · new
The Skull
Adam Gurley's own AdamsLocal skull, with three virtual chemicals living in its shadows. Each one feeds on the next, like rock, paper, scissors, so their waves chase each other into spirals. Tap to stir in more, or save a picture.
Meet the skull
sound · waves · new
GhostSandbox LIVE
A poster you can play. Tune a real tone and watch its wave, add a second wave to see the two add up or cancel out, and walk between two speakers to find the loud and quiet spots. Sound starts only when you tap.
Enter the fieldFree downloads
Take one home.
Eight patterns to keep, print, or share. Free for personal use.
Want to use a pattern for a business, product, or website? Just ask: adam@adamslocal.net.
Questions
Common questions.
- Is this a real physics simulation?
- No. The plate is a mathematical visualization inspired by Chladni's sand experiments. It's built to show the idea clearly, not to reproduce a real metal plate. Explore the math shows exactly how it works.
- Why the golden ratio?
- It's a design choice for this project, not a law of nature. The golden ratio, about 1.618, sets the page's spacing and type sizes, the eight wave sources step around by the golden angle (about 137.5°), and their wave sizes grow in powers of it. One rule, used everywhere, to see how a single principle shapes a whole design.
- What is the Φ that appears when I tap?
- Φ (phi) is the symbol for the golden ratio. It's our signature: it appears where you tap, then fades.
- Does sound play on its own?
- No. Sound starts only when you press a sound button, such as "Hear this tone" or "Hear the pulse," and the same button stops it.
- Can I use these images?
- Yes, for personal use: wallpapers, prints, and your own social profiles. For a business, product, or website, email adam@adamslocal.net first.