Fixed Wave

A seed-based generative system for animated wave-equation compositions.

A catalogue of computational textile compositions for fashion, textile and surface design — algorithmically drawn, seed-documented, and ready for production.

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Overview

Fixed Wave is a generative design system rather than a single artwork. Each composition is a small grid of cells, one of which is a continuously oscillating source. The wave propagates outward from the source, reflecting off the fixed boundaries of the frame, until the grid fills with a slow, breathing pattern of interference.

The system is designed for:

• Fashion houses adapting physical ornament for apparel and accessories
• Textile studios developing repeat patterns and yardage
• Surface designers working across print, wallpaper, and interior applications

Every composition can be licensed, adapted, or commissioned to a brief.

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Concept

A wave, when it is simulated rather than drawn, becomes a physics — rippling, precise, quietly yours.

The wave — layered, oscillating, endlessly variable — has always carried the structure of ornament. From the geometric ripples of a Persian garden pool to the wave equation that governs sound and light, the physics of the wave is one of the oldest systems of mathematical beauty we have. Fixed Wave translates the wave equation into code. Each composition begins with an empty grid and unfolds through a finite-difference simulation driven by a single oscillating source, until the field fills with a slow pattern of interference.

The grid size, the wave speed, the source frequency, the source position, and the two-colour gradient palette are all derived from a single numeric seed.

Unlike most of the still volumes in this series, Fixed Wave's plate is animated. The wave equation needs to advance in time; the whole point of the composition is the slow ripple of the field. But the framed plate, the surfaces, the archive thumbnails, and the cover are all rendered as single static frames — the frame you would print.

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Features

• Seed-based generation — every composition is defined by a numeric seed and can be regenerated exactly
• Deterministic output — the same seed always produces the same composition at any given frame
• Wave-equation simulation — a finite-difference solution of the 2D wave equation, updated one step per frame
• Oscillating source — a single cell in the grid is driven by a sine function at a seed-defined frequency
• Fixed boundaries — the four edges of the grid are pinned to zero, producing the reflection that gives the composition its classic ripple pattern
• Two-colour gradient — the field is rendered by mapping each cell's amplitude into a linear gradient between two named colours
• Sixteen-colour palette — the palette is chosen from a fixed set of 16 named colours (Red, Blue, Cyan, Magenta, Olive, Beige, etc.)
• Live animated plate — the wave ripples continuously as the simulation advances
• Static catalogue — the framed plate, surfaces, and archive thumbnails are frozen single frames
• Adaptive surfaces — one seed applied across print, scarf, textile, and wall formats
• Archive — eight curated seeds available for immediate loading
• Download — export the current frame as a high-resolution PNG
• Keyboard shortcuts — R for new seed, S to save

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Project Structure

.
├── index.html          # Main catalogue page
├── images/
│   ├── fav.svg         # Favicon
│   ├── tote.png        # Mockup: tote bag
│   ├── tee.png         # Mockup: t-shirt
│   └── cushion.png     # Mockup: cushion
└── README.md

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How It Works

The Seed

A numeric seed (a large integer) initializes a deterministic pseudo-random generator. From this seed, the system derives:

• Start colour (from a palette of 16 named colours)
• End colour (a different colour from the same palette)
• Grid columns (10 to 160)
• Grid rows (columns − 5 to columns + 5)
• Time step dt (0.005 to 0.015)
• Wave speed c (scaled to the canvas)
• Source frequency (10 to 310)
• Source position (any interior cell of the grid)

Because the generator is deterministic, the same seed always produces the same composition — on any device, at any time.

The Wave Equation

Fixed Wave solves the 2D wave equation by finite differences:

∂²u/∂t² = c² (∂²u/∂x² + ∂²u/∂y²)

At every step, each interior cell is updated from its previous value and the values of its four neighbours:

next[i][j] = 2 · current[i][j] − prev[i][j]
           + coeff · (
               (current[i+1][j] + current[i−1][j] − 2·current[i][j]) / dx² +
               (current[i][j+1] + current[i][j−1] − 2·current[i][j]) / dy²
             )

where coeff = c² · dt². This is the classic explicit scheme for the wave equation: cheap to compute, and stable as long as c · dt is small enough.

The Source

A single cell of the grid — the "oscillating point" — is driven by a sine function on each step:

current[p.i][p.j] += sin(p.time · p.freq · 2π) · 450

This forces the source cell to move up and down over time. The energy from this motion propagates outward through the grid, reflecting off the fixed boundaries, and settling into a stable standing-wave pattern.

The Boundaries

The four edges of the grid — the first and last row, and the first and last column — are pinned to zero on every step. This produces a "fixed" or "Dirichlet" boundary condition: waves that reach the edge reflect back inward. The boundaries are what give Fixed Wave its characteristic rippled, mirror-symmetric composition.

The Colour

Each cell's amplitude is mapped into a linear gradient between two named colours:

Field value	Rendering
−450 (negative)	Start colour, low alpha
0 (rest)	Midpoint of the gradient, mid alpha
+450 (positive)	End colour, high alpha

The alpha channel also scales with the amplitude, so the wave reads as a soft, luminous field — the rest state fades into the background, and only the peaks stand out.

The Animation

Fixed Wave is one of the animated volumes in this series. The live plate:

• Advances the wave by one simulation step per frame
• Redraws the whole grid with the updated field
• Honors reduced motion — if prefers-reduced-motion: reduce, the plate renders a single frame and does not animate
• Pauses when hidden — when the tab is not visible, animation stops to save CPU
• Freezes for download — when you click Download, the animation pauses, the current frame is captured, then the animation resumes

The Surfaces

The same seed is rendered across four surface formats. These are static frames — they represent the print-ready composition.

Surface	Aspect	Material
Print	1 : 1	Cotton rag
Scarf	3 : 1	Twill silk
Textile	4 : 3	Fabric yardage
Wall	2 : 3	Wallpaper

Each surface uses the same underlying seed and structural logic — only the repeat, orientation, and scale change.

A Note on Warm-Up

The wave equation starts with every cell at zero. Without warm-up, the static surfaces would render as a flat empty field. So each static canvas runs 60 simulation steps before drawing, giving the wave time to propagate and settle into a visible pattern. The live plate runs 30 warm-up steps on init, and then continues advancing frame by frame.

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Usage

In the browser

1. Open index.html in any modern browser.
2. The Plate 001 composition ripples on its own.
3. Click New Seed to generate a new composition.
4. Click Download to save the current frame as a PNG.
5. Scroll to the Archive section and click any plate to load it into Plate 001.

Keyboard shortcuts

Key	Action
R	New seed
S	Save as PNG

Reproducing a composition

Each composition is identified by an 8-digit seed label displayed in the metadata panel. To reproduce a specific composition statically, note the seed and regenerate it programmatically:

const rng = new RandomGenerator(seed);
const features = buildFeatures(rng, canvasSize);
// Warm up the wave
const rectWidth = (canvasSize * features.scaleFactor) / features.cols;
const rectHeight = (canvasSize * features.scaleFactor) / features.rows;
for (let i = 0; i < 60; i++) updateWave(features, rectWidth, rectHeight);
renderComposition(canvas, features, false);

For an animated reproduction, use the same pattern with a requestAnimationFrame loop and call updateWave once per frame before redrawing.

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Technical Notes

• No build step. The system is a single HTML file with inline CSS and JavaScript.
• No dependencies. All drawing is done with the native Canvas 2D API.
• Deterministic. The RandomGenerator class uses a xorshift-based PRNG seeded by an integer, so identical seeds produce identical outputs.
• Animation isolated to the plate. Only the live Plate 001 uses requestAnimationFrame. All other canvases render a single frame and stop.
• Feature isolation. Cover, framed plate, surfaces, and archive thumbnails each derive their own feature set from their own local RNG, without disturbing the main plate's state.
• Stable simulation. The wave-speed / time-step ratio is bounded so the finite-difference scheme stays stable. No runaway oscillation.
• Fixed boundaries. The four edges of the grid are pinned to zero on every step, producing the reflection that gives Fixed Wave its classic interference pattern.
• Warm-up on static renders. The framed plate, surfaces, archive thumbnails, and cover all run 60 simulation steps before drawing, so the wave is visible in the first frame.
• Cleanup on visibility change. Animation pauses when the tab is hidden, and restarts cleanly when it returns.
• Responsive. The layout adapts from large desktop down to very small mobile devices (tested at 360px viewport width).
• Accessible. Supports prefers-reduced-motion. Pinch-zoom is enabled.

Browser support

Tested in current versions of:

• Chrome / Edge
• Firefox
• Safari (desktop and iOS)

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Licensing

All Fixed Wave compositions are seed-documented and available for licensing across textile, surface, and print applications.

• Standard licenses cover single-product production runs.
• Commercial use, custom editions, or exclusive rights are available on request.

Each license is issued against a specific seed ID. Regeneration of the same seed produces the identical composition — ensuring reproducibility between artist, studio, and manufacturer.

For licensing enquiries: reyhanehdaneshdoost@gmail.com

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Commission

Fixed Wave is a generative design system, not a fixed artwork. It can be adapted for specific briefs:

Service	Description
Licensing	Existing seeds from the archive, licensed for production use
Commission	New compositions designed to your palette, repeat, and product
Systems	A private generative tool built for your studio's ongoing use

To begin a conversation: reyhanehdaneshdoost@gmail.com

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Series

Fixed Wave is part of a computational textile series. Each volume approaches ornament from a different structural angle:

Volume	Structure	Motion
Girih 1	Islamic geometric	Static
Arachne	Rotating rings	Static
Baroque Me Baby	Baroque frames	Static
Bezier 1	Concentric curves	Static
Bezier 2	Single rotating curve	Animated (plate)
Brownian Graphe	Graph networks	Animated + interactive
Celestial Grove	Recursive branch trees	Static
ChaotiColor	Cellular automata	Static
Citrus Mosaic	Arc-and-triangle tiles	Static
Crazy Knight Curve	Knight's-tour smooth path	Static
Crazy Knight Line	Knight's-tour gradient	Static
Crazy Letter	Framed wavy lines	Static
cyPollock	Scattered branch field	Static
Digital Pollen	Noise-driven texture	Static
Draconic Fractals	Tiled dragon curve	Static
Dreamscape Watercolors	Layered watercolor blooms	Static
Elliott Waves	Financial chart	Static
Ellipses	Concentric elliptical rings	Static
Enigma Sudoku	Playable 9×9 puzzle	Interactive (plate)
Ephemeral Whirls	Wandering looper field	Static
Eyes	Layered iris portrait	Static
Fibonacci Fourier	Harmonic line field	Animated (plate)
Fixed Wave	Wave-equation field	Animated (plate)

The series is designed as a coherent whole — same page structure, same seed logic, same licensing and commission terms — so that each volume can be presented individually or as part of a larger body of work.

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Credits

• Design & Generative System — Reyhaneh Daneshdoost
• Typefaces — Cormorant Garamond · DM Mono
• Platform — Reyrove Studio
• Edition — Fixed Wave, Autumn 2026

On AI tools

Where technical obstacles were encountered, AI tools were used for debugging and code optimization. Every structural, aesthetic, and conceptual decision remained the artist's own.

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Links

• Website — reyrove.github.io
• Instagram — @rey._.rove
• LinkedIn — Reyhaneh Daneshdoost
• X — @reyrove

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© Fixed Wave · All compositions reproducible by seed · Computational Textile Design