Your saved patterns appear here and as quick buttons under the Frequency controls. Until you mark a special, three starter examples are shown.
No patterns saved yet. In the Frequency view, press “Mark as Special” when you discover a design you love.
Main = bring that layer to the top and drive it with the big ‹ Hz › arrows. Top = jump it to the front. ▲▼ nudge one step. Slider = opacity. 🔒 lock freezes that layer’s Hz, colour, opacity and place in the stack — it will not shift when you add another layer. Adding a layer locks the one you just finished so the picture you liked stays put. Hide top / bottom. Auto Gen skips locked layers. Take picture now captures the same stack you see on screen.
Version 1.4.4
This studio turns pure frequency into visible geometry. Every value on the Hertz scale corresponds to a unique standing-wave pattern on a square plate — the classic Chladni figures first studied in the eighteenth century. As frequency changes, the nodal lines (where the plate is still) and the antinodal basins (where it moves) rearrange themselves. The luminous sand and the particles simply render that invisible vibration visible.
The pattern is a map of the frequency. Low tones open into broad, quiet chambers; mid-range tones weave balanced lattices; high tones draw fine, lace-like line art. Whether you sweep the slider, type an exact value, or open a Favorites card, the geometry that appears is the visual signature of that precise Hz.
A brief guide to the instruments of the studio.
Frequency — the heart of the instrument. Use the slider for continuous exploration, or type any exact value (from 1 Hz to the extreme ultrasonic) into the number field and press Enter. The geometry responds at once.
Intensity — governs how firmly the particles settle into the antinodal crevices. Raise it to fill the basins more completely; lower it for a lighter, more open field.
Colour language — selects the visual voice of the pattern. Spectrum, Aurora, Sakura, Nebula, Mode Hue, Gold and the others each lend a distinct atmosphere to the same underlying geometry. Plate tints the field behind the sand with the same colour list (Black is the studio default). Take picture still frames the export on a black boundary with a white outline.
Play Tone / Stop — when your device permits, a pure sine wave at the current frequency may be heard (within the audible range). The sound is optional; the pattern stands alone.
The checkboxes
Drive-point filter — conceals patterns whose centre is a node. On the default Waller − family that is almost every n ≠ m mode, which is mathematically correct: the minus combination is silent under a central drive. Turn on Waller + to see the twin figure that does ring at the centre; the filter then keeps modes whose centre is an antinode.
Waller + — same (n, m) and same Hertz, opposite combination sign. Off (default) keeps every pattern you already know. On draws the plus family used when a square plate is driven at its centre.
Compare overlay — ghosts the previous discrete mode in soft cyan, so the evolution of the geometry becomes visible as frequency changes.
Nodal lines — draws the zero-crossing boundaries in warm gold. These are the quiet edges of the standing wave — the classic Chladni lines themselves.
Density (high-freq) — at the highest orders the pattern grows extremely fine. This toggle softens the rendering so the dense lace remains legible rather than dissolving into noise.
Particles — shows or hides the swarm that fills the antinodal crevices (off by default). Turn them on to watch the basins fill.
3D — switches the square plate for a rotating cube of nodal surfaces. Drag on the cube to turn it; frequency still drives the geometry.
Frequency arrows (mobile) — the ‹ › buttons beside the Hz field step the current working frequency. Use the Step menu to choose how far each tap travels: Hair ×1.001, Ultra ×1.005, Fine ×1.02, Medium ×1.10, Coarse ×1.26, Next mode (the next discrete Chladni pair), multiply by 2 or 10, or jump a fixed Hertz amount (+1, +10, +100, +1 kHz, +10 kHz, +100 kHz, +1 MHz). At high frequencies a log multiply still covers a wide Hertz gap; lock a window or choose Next mode / +1 when you want neighbouring figures.
Range lock — From and To set a Hertz window. Lock window confines the slider and the arrows to that band so every millimetre on a phone is a small increment. Full scale returns the dial to 1 Hz … 4 × 1044 Hz. Band presets (Sub, Audible, Lab plate, Ultrasonic) fill From / To for you.
Radio scan — Scan ▶ walks the discrete plate modes whose n² + m² fall inside the current window. Each stop is a true Chladni eigenfunction, not a random blend (Auto Gen on the Layers tab remains the blender). Speed sets how long each mode is held. Seek pauses on clean figures — diagonal n = m modes, near-square pairs, primitive lattices, and even-diagonal modes whose centre can be driven. Continue resumes the sweep. Scan ⏹ keeps the mode you landed on.
Layers tab (2D only) — the live square pattern stays visible above the layer list. The Hertz slider, From / To scale, band presets and Lock window sit directly above the blend list and stay in sync with the Frequency tab. On a phone, Auto ▶ / ⏹ / Gen / ‹ / › sit just above the Hz line. Time and Shape stay with the blend tools below. Auto Gen draws new layer frequencies only from that From–To window. Shape (None, Random, Combination, Diamond, Circle, Square, Rectangle, Star, Cross) filters those modes. None clears the filter. Combination mixes families in one blend. Smart Gen scores discrete (n, m) modes in the window for that kinship and does not invent non-modal shapes. Press “+ Add Layer” to capture the current Frequency Hz and colour language. The layer you were working on is locked as you add the next one, so earlier patterns stay still. Press Main on an unlocked layer to bring it to the top and hand it the big Hz arrows. Press Top to jump it to the front without changing the editor target. Reorder one step with ▲▼, set opacity per layer, and use 🔒 / Lock all to freeze layers so they cannot slip. Unlock a layer first if you need to edit it again. “Edit base” returns the main controls to the Frequency pattern underneath. Take picture captures the exact stack on screen, including every visible frequency in the footer.
When a frequency moves you, press Mark as Special. It is saved on your device and appears under Favorites, ready to be revisited.
Think of a square trampoline, or a clear box of air you can “ring” like a bell. When you drive it at a steady rate — measured in hertz (Hz), cycles per second — it settles into a preferred shape of motion. Some regions bounce hard; some stay quiet.
This studio draws the quiet places (nodes). On a flat plate they look like lines and webs. Inside a cube they look like sheets and chambers. Change the Hz, and a different natural shape is selected, so the quiet map changes.
A useful analogy: turning a radio dial. Each station locks onto a different channel. Here each frequency locks onto a different vibration “station,” and the picture is a map of that channel’s still zones — not a photograph of a real metal plate in a lab, but a faithful drawing of the ideal mode the math assigns to that Hz.
The frequency control runs from 1 Hz up to 4 × 1044 Hz — that is the number:
400,000,000,000,000,000,000,000,000,000,000,000,000,000,000 Hz
In words: four, followed by forty-four zeros. That is an extreme, exploratory range — far beyond everyday sound or laboratory plate tests — so you can keep climbing the mathematical ladder of modes without the software running out of headroom.
On the flat plate (2D), higher and higher modes pack more and more nodal lines into the same square. Past a certain point those lines become finer than a single pixel. The screen then shows a dense mesh that barely seems to move, even though the underlying mode indices are still advancing.
In 3D, the same climb adds structure in depth: new nodal surfaces fold through the volume of the cube. When you rotate the cube, those sheets catch the light at different angles, so the pattern keeps looking different all the way toward the top of the dial — even when the 2D view has already become a near-uniform lace.
So: 2D is limited by the resolution of a flat picture; 3D still reveals new geometry because the mode is filling a whole volume, not only a plane.
A thin plate can vibrate in many shapes. Each stable shape is a mode. Still places are nodes; moving places are antinodes. On a real Chladni plate, sand gathers on the nodes. This studio draws those geometries from a clear mathematical rule.
A real free square plate has no closed-form Kirchhoff eigenfunctions. This studio uses the classical Rayleigh–Waller cosine model that Chladni tables and teaching texts use to classify the figures. Thin-plate flexure frequencies scale as n² + m² (Kirchhoff / biharmonic: ω ∝ k²). The program selects the integer pair (n, m) whose n² + m² is closest to the spectral index set by the Hz control. Absolute hertz are an index, not a lab calibration.
Mode shape (the zeros drawn on the plate are the exact zeros of this function):
n ≠ m, Waller − (default): u = cos(nπx) cos(mπy) − cos(mπx) cos(nπy)
n ≠ m, Waller + : u = cos(nπx) cos(mπy) + cos(mπx) cos(nπy)
n = m: u = cos(nπx) cos(nπy)
The two signs are the two degenerate combinations that share the same n² + m². The minus family has a node at the centre, so it does not ring under a central drive. The plus family does. Cosine (not sine) is the free-edge qualitative family: edges are antinodes. Sand in the picture is drawn where |u| is near zero — true nodes. Particles, when enabled, climb the antinodes; that overlay is artistic, not how laboratory sand behaves.
What this model is not: a Ritz / finite-element free-plate solution. Lowest laboratory modes (especially figures that need an index 0, such as a single pair of diagonals) are only partly represented. Higher (n, m) Waller figures match the textbook Chladni catalog closely. Indices start at 1, so the Hz → pattern map stays stable with earlier versions of this studio.
Standing waves in a unit cube with free-face (Neumann) boundary conditions. Eigenfunctions separate exactly:
u = cos(nπx) cos(mπy) cos(pπz), n,m,p = 0,1,2,… (not all zero)
Wave-equation frequencies satisfy f ∝ √(n² + m² + p²). The studio matches that spectral law when mapping Hz to (n, m, p). Drawn surfaces are where |u| ≈ 0 — the true nodal surfaces of that eigenfunction.
Absolute hertz still depend on plate size, thickness, stiffness, and density (2D), or on wave speed and cavity size (3D). Here Hz is a consistent index into the ideal spectrum, not a calibrated lab reading of a particular specimen. Real systems also have damping and imperfect boundaries; this studio shows pure ideal modes so geometry stays clear.
Higher-dimensional views extend the same separated-cosine idea for exploration; 2D plate and 3D cube are the scientifically primary models.
Bottom line. For each selected (n, m), the drawn sand is the exact nodal set of the Rayleigh–Waller function above — not a photograph of a particular metal plate. Frequency ranking follows the correct power law for that model (plate flexure: n²+m²; cube Helmholtz: √(n²+m²+p²)). Toggle Waller + to see the centre-drive twin of the same frequency.
Four-dimensional standing-wave geometry. Modes are labeled (n, m, p, q). What you see is a projection of nodal structure from a unit hypercube into the plane. Frequency is shared with the Frequency tab — set Hz there, then open 4D to view it in four dimensions.
Diamond H Designs
Designed by: Michael Christopher Crichton Haws
Grok assisted
Patron(s): Archangel Gabriel + St Eligius
Ave Maria · Deus Vult · JMJ
Chladni patterns · Modal geometry · Artistic vibration
Dedicated to C+K+D
“The heavens shew forth the glory of God, and the firmament declareth the work of his hands.”
— Psalm 18:2, Douay-Rheims 1899 American Edition (DRA)
Disclaimer. This dashboard is a conceptual and artistic exploration of modal geometry and frequency-to-pattern mapping. It is not a scientific instrument, laboratory measurement, or engineering tool. Patterns are illustrative simplifications of standing-wave ideas and should not be taken as precise physical predictions or claims of technical, medical, or industrial accuracy.