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Uzumaki

Interactive mathematical art across six platforms from shared algorithms

Cross-platform spiral visualization app for Web, iOS, iPadOS, macOS, and watchOS. Generate mesmerizing animated spirals from ten mathematical algorithms with real-time customization.

React 19 TypeScript Swift 6 SwiftUI Canvas API Web Workers PWA SIMD

View on GitHub Live Demo

Architecture

flowchart LR
    subgraph Web["Web Platform"]
        A[React 19]
        B[Canvas API]
        C[Web Workers]
    end
    subgraph Apple["Apple Platforms"]
        D[SwiftUI]
        E[Canvas]
        F[SIMD]
    end
    subgraph Core["Shared Algorithms"]
        G[Spiral Math]
    end
    subgraph Deploy["Deployment"]
        H[iOS]
        I[iPadOS]
        J[macOS]
        K[watchOS]
        L[PWA]
    end
    A --> B
    B --> C
    C --> G
    D --> E
    E --> F
    F --> G
    G --> H
    G --> I
    G --> J
    G --> K
    G --> L

The Problem

Mathematical spirals appear throughout nature and art, but experiencing their beauty requires either specialized software or deep mathematical knowledge. Existing spiral generators are either too simplistic with limited algorithms, or too complex requiring extensive parameter tuning. None offer a truly cross-platform experience from web browser to wearable device.

The Solution

Built a unified spiral visualization platform spanning five Apple platforms plus the web. Ten spiral algorithms from Archimedean to Curlicue render with consistent behavior across all platforms. Web Workers with TypedArrays power smooth 60fps animations on the web, while SIMD optimization handles the same workload on Apple devices. Shareable URLs encode spiral configurations for instant sharing.

The Results

Ten mathematically accurate spiral algorithms
Six platforms: Web, iOS, iPadOS, macOS, watchOS, and PWA
60fps animation with Web Worker parallelization
Shareable configuration URLs for any spiral state
iOS 26 Liquid Glass design preparation
watchOS complications for glanceable spiral art

Spiral Types

Platforms

Color Presets

60fps

Animation

Uzumaki is an interactive spiral visualization app that renders ten mathematical spiral algorithms across web and Apple platforms. From the elegant Fibonacci golden spiral to the chaotic Uzumaki pattern, each algorithm produces mesmerizing animated artwork.

Spiral Gallery

Uzumaki spiral animation demo showing color transitions and spiral types

Fibonacci Aurora

Vogel Sunflower

Uzumaki Neon

$Curlicue Matrix fractal$ Curlicue Matrix

Available Platforms

iOS

watchOS

macOS

App Store Web App Source

Spiral Algorithms

Each spiral follows a specific mathematical formula in polar coordinates:

Spiral	Formula	Natural Examples
Fibonacci	r = a * phi^(2*theta/PI)	Nautilus shells, galaxies
Vogel	theta = n * 137.5 deg	Sunflower seeds, pinecones
Archimedean	r = a + b * theta	Watch springs, coiled rope
Fermat	r = a * sqrt(theta)	Optical lenses
Logarithmic	r = a * e^(b*theta)	Hurricane formations
Curlicue	phi = 2PIphi*n^2	Fractal art

Technical Implementation

The web app uses Web Workers with TypedArrays for parallel spiral generation:

function generateSpiralTyped(params: SpiralParams): TypedSpiralPoints {
  const points = createTypedPoints(numSteps);
  const rotation = time * spinRate;

  for (let i = 0; i < numSteps; i++) {
    const theta = i * stepSize + rotation;
    const r = calculateRadius(i * stepSize, params);
    setPoint(points, i, r * Math.cos(theta), r * Math.sin(theta));
  }
  return points;
}

The Swift implementation uses SIMD for vectorized math operations, achieving the same 60fps performance on Apple devices.

Platform Features

Web/PWA: Shareable URLs, keyboard shortcuts, PNG export
iOS/iPadOS: Pinch-to-zoom, pan gestures, full-screen mode
macOS: Menu bar integration, keyboard shortcuts
watchOS: Digital Crown zoom, swipe navigation, complications