Morphon vs BeautOfFractals

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.

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.