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.
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.
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. Useful when you wish to see only those modes that would respond strongly to a central drive.
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) — step back and forth through the preset frequencies beside the Hz field.
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.
Thin-plate flexure (Kirchhoff): relative natural frequencies scale as n² + m². The program selects the integer pair (n, m) whose n² + m² is closest to the spectral index set by the Hz control.
Mode shape (exact zero set drawn on the plate):
n ≠ m: u = cos(nπx) cos(mπy) − cos(mπx) cos(nπy)
n = m: u = cos(nπx) cos(nπy)
The first form is the classical Rayleigh–Waller combination used for free-edge Chladni figures. The second is the non-vanishing diagonal mode when n = m. Once (n, m) is fixed, the nodal lines are the exact mathematical zeros of that function.
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 mode, the drawn pattern is the exact nodal set of the analytical eigenfunction above. Frequency ranking follows the correct power law for that model (plate: n²+m²; cube wave: √(n²+m²+p²)).
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.