benoît M vs BeautOfFractals

benoît M is a visual exploration of the Mandelbrot set — one of the most iconic and fascinating shapes in mathematics. Named in homage to Benoît Mandelbrot, who discovered this fractal-set named after him in 1979. The mathematician introduced the world to fractal geometry. This app lets you dive into a universe created from one deceptively simple formula: repeat z² + c, again and again. From that small rule emerge endless spirals, islands, valleys, coastlines, and self-similar structures that continue to reveal new detail as you zoom deeper. With real-time Metal rendering, benoît M turns fractal exploration into a smooth, visual experience. Pinch to zoom, pan to move, and double-tap to dive into interesting regions. Switch between classic Mandelbrot rendering and a beautiful pseudo-3D relief mode that gives the fractal a sculptural, almost metallic depth. Customize the look with image gradients, procedural palettes, inverted or flipped color styles, and adjustable iteration quality. When you find a scene worth keeping, export it as a square high-resolution PNG — up to 8K — directly to your Photo Library. Features: - Explore the Mandelbrot set interactively - Smooth Metal-based rendering - Classic Mandelbrot and pseudo-3D relief modes - Image-based and procedural color gradients - Adjustable iteration depth - Pinch, pan, and double-tap navigation - High-resolution PNG export: 2K and 8K - Saved app state, so you continue where you left off A compact tribute to Benoît Mandelbrot and the beauty of fractal geometry Whether you are fascinated by mathematics, generative art, abstract visuals, or simply beautiful patterns, benoît M invites you to explore infinity — one zoom at a time.

Beauty of Fractals turns mathematical structures into an immersive visual journey for iPhone and iPad. Explore the Mandelbrot set and a diverse collection of related fractals with natural touch navigation, fast Metal rendering, precise CPU deep zooms, expressive palettes and abstract rendering styles, iCloud-synced favorite spots, PNG export, and Apple Watch render mirroring. FEATURES - Explore Mandelbrot, Power of n (2-12), Julia, Burning Ship, Tricorn, Celtic, Newton, Kleinian, Mandelbrot Relief, Mandelbulb 3D, Mandelbox 3D, and Eight Rainbows - Navigate naturally with pinch-to-zoom and touch gestures - Use Automatic precision selection from fast interactive views through guarded Extreme Precision - Reveal selected Mandelbrot structures around 10^50x, with deeper views available as an experimental frontier - Render difficult deep zooms with adaptive reference anchors and coverage repair - Let the app choose an iteration budget from the center orbit plus a reserve, or select up to 250,000 iterations manually - Save and revisit precise favorite spots with thumbnails, palette, quality, mode, and effective iteration counts - Sync favorites through iCloud across iPhone, iPad, and Mac - See render progress, final previews, and the current zoom on Apple Watch - Create abstract worlds with Metallic Dreams, Embossed Metal, Guilloché, Spheroid Glass, Quantum Glass, Quantum Traps, and Orbital Waves - Shape each new style with its dedicated touch control - Choose from additional expressive color palettes, including Aurora, Auric, Pearl, Rainbows, and Deep Current - Export PNG images recalculated locally for the selected output size - Collapse the controls for an unobstructed view of the fractal - Follow longer calculations with clear render status and diagnostics Beauty of Fractals is designed for exploration. There are no accounts, advertisements, analytics, or tracking. Rendering and export happen locally on your device. Optional iCloud sync and Apple Watch communication use Apple system services.