An interactive spiral visualization app for Web, iOS, iPadOS, macOS, tvOS, and watchOS.

Try it live at uzumaki.app

• 10 spiral types: Archimedean, Fibonacci, Fermat, Logarithmic, Hyperbolic, Lituus, Theodorus, Vogel, Uzumaki, and Curlicue
• Real-time animation with adjustable speed
• 10 color presets with gradient support
• Line style options: Solid, Dashed, Dotted, Glow, Points, and Triangles
• Variable line thickness for dynamic visuals
• Theme options: Dark, Black, Gradient, and Matching backgrounds
• Curated presets for interesting spiral configurations
• Pan and zoom controls
• Export to PNG
• Shareable URLs with encoded parameters
• Keyboard shortcuts for quick control
• Progressive Web App (PWA) support
• iOS 26 / macOS 26 Liquid Glass design support
• Web Workers with TypedArray optimization for smooth performance

Fibonacci Aurora	Uzumaki Neon
Vogel Sunflower	Logarithmic Ocean
Fermat Fire	Curlicue Matrix
Theodorus Retro	Lituus Candy

Experience Uzumaki on the big screen with Apple TV. Navigate using the Siri Remote, explore curated presets from the Top Shelf, and enjoy 4K visuals.

Rainbow	Aurora	Sunset	Ocean
Fire	Neon	Candy	Matrix

Each spiral type follows a specific mathematical formula. Most use polar coordinates where r is the radius and theta is the angle.

Archimedean Spiral r = a + b * theta Constant spacing between turns. Named after Archimedes who first described it circa 225 BC.	Fibonacci (Golden) Spiral r = a * phi^(2 * theta / pi) Self-similar spiral based on the golden ratio. Found in nautilus shells and galaxies.
Fermat Spiral r = a * sqrt(theta) Parabolic spiral where area swept is proportional to angle. Used in optics.	Logarithmic Spiral r = a * e^(b * theta) Self-similar at any scale. Also called equiangular spiral. Seen in hurricanes.
Hyperbolic Spiral r = a / theta Approaches a point asymptotically. The inverse of the Archimedean spiral.	Lituus Spiral r = a / sqrt(theta) Named for its trumpet-like shape (lituus = Roman curved trumpet).

Spiral of Theodorus angle_n = sum(arctan(1 / sqrt(k))) for k=1..n Constructed from right triangles with hypotenuse sqrt(n). Demonstrates irrationality of square roots.	Vogel Spiral (Phyllotaxis) theta_n = n * 137.5 deg, r_n = c * sqrt(n) Models sunflower seed arrangement. Uses golden angle for optimal packing.
Curlicue Fractal phi_n = 2 * pi * s * n^2 Where s is irrational (phi). Cumulative angle sums create fractal patterns.	Uzumaki Spiral Custom chaotic formula Inspired by the manga. Time-varying amplitude with sinusoidal modulation.

• Node.js 18+
• npm or yarn

cd web
npm install

npm run dev

npm run build

npm run preview

A native SwiftUI implementation with the same features as the web app, plus platform-specific optimizations.

• macOS 14.0+
• Xcode 16+ (for development)
• Swift 6.0+
• iOS 17.0+ / iPadOS 17.0+ / tvOS 17.0+ / watchOS 10.0+

Using Swift Package Manager:

cd apple
swift build
swift run Uzumaki

Or open in Xcode:

cd apple
open Package.swift

Then select the Uzumaki scheme and run (Cmd+R).

cd apple
swift test

• Native SwiftUI Canvas rendering
• SIMD-optimized spiral generation
• All 10 spiral types from the web app
• All 10 color presets
• Play/pause animation with TimelineView
• Pinch-to-zoom and pan gestures
• PNG export
• Keyboard shortcuts (Space, R, E)
• macOS menu bar integration
• iOS 26 / macOS 26 Liquid Glass effects with backward compatibility
• iPadOS menu toggle for full-screen experience

• Siri Remote gesture support (swipe, click, play/pause)
• Focus-based navigation optimized for TV
• Top Shelf integration with curated spiral previews
• 4K display support for stunning visuals
• Game Controller support

• Digital Crown zoom control with haptic feedback
• Swipe gestures for preset navigation
• Tap to play/pause, double-tap to reset zoom
• Long press for settings
• Watch face complications (circular, corner, rectangular, inline)

• React 19
• TypeScript
• Vite
• Canvas API

• Swift 6
• SwiftUI
• Swift Package Manager
• SIMD for optimized math

MIT

Made with ❤️ by Cameron Rye