"Every word has a geometric address that exists before any corpus is loaded. Language is geometry."
THE WORD is a standalone, browser-based visualizer designed to explore how different string-hashing algorithms distribute language across a 16-bit geometric address space (65,536 slots). By parsing plain text into custom deterministic tokens and processing them through mathematical ratios (like
- Zero Dependencies: 100% vanilla HTML, CSS, and JS. Runs entirely locally in your browser.
-
Drag-and-Drop Parsing: Drop any text or source code file (
.txt,.md,.rs,.py, etc.) into the corpus zone to instantly hash its vocabulary. - Real-Time Animation Transport: Scrub, play, and adjust sweep speed to visualize structural alignment ("snap points") as geometric variables shift.
-
Live Frame Statistics: Computes occupancy, hash collisions, maximum token density, Shannon entropy, and
$\phi$ -resonance in real time. - Dynamic Render Controls: Adjust point sizes, bloom/glow strengths, color palettes (Plasma, Inferno, Matrix, etc.), and mathematical bounds on the fly.
- One-Click Export: Easily save high-resolution PNG snapshots of any generated interference pattern.
- Coil Unwind (Archimedean Spiral): Maps the hash space into a coil. The "pitch" dynamically unwinds the spiral. As patterns overlap at tight pitches or separate into arms, you can spot geometric reinforcements and cancellations.
-
Sunflower Spiral (Golden Angle): Uses the Golden Angle (
$\approx 137.5^\circ$ ) to plot addresses naturally. Perfect for visualizing organic clumping and distribution efficiency. - XY Grid Sweep: Unrolls the 1D address space into a 2D matrix, sweeping the line-width parameter to look for rhythmic padding and modulo-based repetition structures.
- All Methods: A unified dashboard comparing the Sunflower projections of all 10 hashing methods side-by-side.
The visualizer implements 10 unique, byte-level processing methods built on top of a custom "Carousel Encoder" (which compresses characters into 5-bit integers):
- Original: Interleaved multiplication and division carousel.
-
Phi Ratio: Preserves the golden ratio (
$\phi \approx 1.618$ ) iteratively. -
Geometric Mean: A
$\phi$ -anchored square root aggregator. - Fib Index: Nearest-neighbor search within a precomputed Fibonacci lookup table.
-
Phi Knuth: Multiplicative hashing utilizing Knuth’s 32-bit golden integer (
2654435769). -
$\pi$ /$\phi$ Cross-Resonance: Cosine projections mapped across phase space. -
Silver Ratio: Driven by
$1 + \sqrt{2} \approx 2.414$ . -
Tribonacci: Driven by the tribonacci constant
$\approx 1.839$ . - Golden Spiral: Simple continuous angular rotation based on the golden angle.
-
Tau Circle:
$2\pi$ driven periodic phase wrapping.
There is no build step or installation required.
- Clone or download the repository.
- Open
GeometricHashVisualizer.htmlin any modern web browser. - Drag and drop a text file onto the left-hand panel.
- Hit Play and watch the coil unwind.
| Key | Action |
|---|---|
Space |
Play / Pause |
Left Arrow |
Previous Frame |
Right Arrow |
Next Frame |
Up Arrow |
Increase Playback Speed |
Down Arrow |
Decrease Playback Speed |
0 - 9 |
Quick-switch between the 10 hashing methods |
- Tokenization: The input text is cleaned (lowercase, alphanumeric) and split into distinct word strings.
- Carousel Encoder: Characters are compressed into bitwise seeds.
- Hashing: Every distinct word generates a deterministic float or integer sequence via the selected method, mapping the result to a strict
0 - 65,535slot address. - Counting: Frequencies are aggregated into a typed
Uint16Array. - Rendering: The index/slot is transformed into physical X/Y canvas coordinates via polar/geometric conversion formulas. Frequency governs the color intensity/palette mapping of each pixel.
MIT License. See LICENSE for more information.