benoît M vs Morphon

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.

Sixty-three simulations from real physics, chemistry, and mathematics — running entirely on your device's GPU. Touch them. Pinch into a Mandelbrot set. Inject a vortex. Drag a magnet and watch a fractal basin re-paint. Drop pebbles into a pool and watch the waves bounce off the walls. Nothing is pre-recorded; everything you see is computed from the underlying equations as you watch. WHAT'S INSIDE • Fractals — Mandelbrot, Julia, Burning Ship, Newton, IFS chaos game, and ten construction fractals (Koch snowflake, Hilbert curve, Apollonian gasket, and more) that build up one iteration per second • Cellular Automata — Conway's Game of Life, Lenia, Brian's Brain, Forest Fire, neural CA • Reaction-Diffusion — Gray-Scott, Belousov-Zhabotinsky, Turing morphogenesis (square + hex lattice) • Fluid Dynamics — incompressible Stable Fluids, shallow water, Kelvin-Helmholtz instability with optional vortex shedding past a cylinder, non-Newtonian oobleck • Wave Phenomena — Chladni plates, Faraday waves, cymatics, animated underwater caustics • Chaos — Lorenz / Rössler / Halvorsen attractors, magnetic-pendulum fractal basins, Hénon-Heiles • Phase Transitions — Ising, XY-model, Potts, Kuramoto oscillators, percolation, bubble foam coarsening • Field & Flow — Perlin noise, curl-noise, flow fields, paint-your-own velocity fields • Growth — crystal nucleation, L-systems, real DBM Lichtenberg lightning, differential growth • Collective Behaviour — slime-mould Physarum, Boids flocking • Plus granular sand, cloth, sandpiles, Schelling segregation, small-world networks, and more INTERACTION Every simulation responds to touch in a way that's specific to it. Drag to inject dye into a fluid; pinch to zoom into a fractal; flip spins in the Ising model; drag the magnets in the Magnetic Pendulum and watch the basin re-paint. Multi-touch is supported throughout. KEEP YOUR ART Save stills (PNG) and short loops (MP4) directly to Photos, share to social, or just sit back and watch. Six color palettes including viridis, magma, plasma, and turbo apply across every simulation. NO ACCOUNTS, NO ADS, NO TRACKING Morphon collects no data, runs no analytics, and connects to no servers. Whatever you make stays on your device. UNIVERSAL & OPTIMISED Built for iPhone and iPad. Targets 60 fps on every supported device with thermal-aware downshift on older hardware. Pencil-aware on iPad: pressure and tilt drive simulation parameters where it makes sense. Open it. Touch it. The math does the rest.