Morphon vs Fractal Atlas

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.

Fractals are patterns that never run out of detail. Fractal Atlas lets you fly into them with your fingers. ZOOM DEEPER THAN YOU'D BELIEVE Pinch into the Mandelbrot set and keep going, trillions of times closer, with the picture staying sharp the whole way. The Sierpinski carpet and gasket and the Apollonian gasket go deeper still, about a quadrillion times. SURPRISE ME Tap the die to fly to one of 107 named places, from Seahorse Valley to a fleet of burning ships. On the Sierpinski carpet and gasket, it takes you on a spiral dive. Or browse every place in the Places sheet and dive to the one you pick. NO MATHS REQUIRED Just pinch, drag and twist. The info card tells you in plain words how far you've zoomed and where you are, with a scale bar like a map's. The technical readout is there if you want it. SEE TWO WORLDS AT ONCE Dual view pairs a Mandelbrot with its Julia set. Drag across one and the other follows. Pick a famous Julia set and see exactly where in the Mandelbrot it comes from. 27 FRACTALS AND PATTERNS Mandelbrot, Burning Ship, Tricorn, Celtic, Multibrot, Phoenix, Julia sets, Newton's method, Nova, Sierpinski carpet and gasket, Apollonian gasket, Koch snowflake, Pythagoras tree, Hexaflake, Dragon, Hilbert and Gosper curves, Barnsley fern, Sierpinski pentagon and more. Every one supports pan, zoom and two-finger rotation. Press play and the Koch snowflake, Pythagoras tree, Hexaflake and the dragon, Hilbert, Gosper and arrowhead curves grow and shrink by themselves, and on the Barnsley fern, Sierpinski pentagon and triangle, Lévy C curve and Vicsek fractal, play replays the chaos game one dot at a time, in a run of about 15 seconds. Share a link after a run and it plays the same run. YOUR COLORS On the Mandelbrot family and the Julia sets, pick a Look: Edge glow, Stripes, Bands, Orbs, Rays or Relief. Then choose from twelve colormaps, from Inferno and Viridis to Classic and Fire, tune Repeat and Shift, and set how much detail to compute. SHARE ANY VIEW Save a still to Photos or send a link. Anyone you send it to lands on your exact spot, in the app or in their browser. PRIVATE BY DESIGN No ads, no account, no tracking.