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🌌 Overview

Time on the clock is not flat.

This project reimagines time as a single, unbroken 1D space curve winding through a 3D helical torus ($S^1 \times S^1$). The entire 24-hour cycle is mapped into 24 continuous macro-loops, ensuring every unique moment occupies an exact, non-overlapping coordinate in 3D space.

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📐 Spatial Perspectives & Recursive Geometry

• Torus View (24h Macro): Displays the full 24-hour cycle across the helical ring, revealing the depth of the 24 poloidal loops wrapping around the torus tube.
• Recursive Micro-Spirals (Seconds Flow): Minutes and seconds follow the exact same toroidal logic. Seconds form micro-helices nested seamlessly within the minute coils, eliminating discrete mechanical "ticks" in favor of continuous 3D flow.

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☀️ Dynamic Solar Synchronization

• IP-Based Solar Tracking: Detects your approximate location to calculate precise astronomical sunrise and sunset times in real time.
• Celestial Wire Markers: Exact sunrise and sunset coordinates are anchored directly onto the 3D helical wire. Hovering over either marker reveals the astronomical time.
• Atmospheric Tone Shift: The environmental palette continuously shifts from warm solar daylight to deep Aurora Borealis night skies as the active time spark crosses the solar threshold.

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🕹️ Interactive Controls

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📐 Mathematical Formulation

The macro wire is parameterized as a closed $(p, q) = (1, 24)$ helical curve embedded on the surface of a torus with major radius $R$ and minor radius $r$:

$$\begin{aligned} \theta(t) &= 2\pi t \ \phi(t) &= 24 \cdot 2\pi t \ x(t) &= (R + r \cos \phi) \cos \theta \ y(t) &= r \sin \phi \ z(t) &= (R + r \cos \phi) \sin \theta \end{aligned}$$

where $t \in [0, 1)$ represents the fractional progression of the 24-hour solar day. The micro-spiral of seconds introduces a second nested perturbation along the Frenet–Serret frame of the curve.

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🛠️ Local Development

# Clone the repository
git clone https://github.com/nimabeh/helical-time.git

# Navigate into project directory
cd helical-time

# Install dependencies
npm install

# Start local Vite development server
npm run dev

# Build production bundle
npm run build