Phase-Field Studio — Interactive Materials Simulation Turn your device into a computational materials science workbench. Phase-Field Studio brings real-time phase-field simulations to iOS — explore microstructure evolution, pattern formation, and fracture mechanics with intuitive touch controls and live visualization. WHAT IS PHASE-FIELD MODELING? Phase-field methods replace sharp interfaces with smooth order parameters evolving under variational free-energy principles. This framework unifies a broad class of phenomena — from alloy solidification to biological tissue growth — under one computational paradigm. SIMULATIONS INCLUDED * Cahn-Hilliard (FFT) — Spinodal decomposition via spectral methods. A uniform mixture spontaneously separates into coexisting phases. * Anisotropic Cahn-Hilliard — Directional phase separation where crystallographic anisotropy reshapes domains into faceted structures. * Grain Growth (Allen-Cahn) — Polycrystalline coarsening with curvature-driven boundary migration and random Voronoi microstructures. * Coupled Allen-Cahn / Cahn-Hilliard — Simultaneous ordering and compositional separation producing complex multiphase microstructures. * Dendritic Growth — Anisotropic solidification with thermal diffusion controlling dendrite tip shape and side-branching. * Sintering — Powder consolidation via surface-energy-driven diffusion with neck formation and pore shrinkage. * Swift-Hohenberg — Spontaneous pattern formation: stripes, spots, and labyrinthine structures from a single control parameter. * Complex Ginzburg-Landau — Spiral wave dynamics and oscillatory media near a Hopf bifurcation. * Cell Dynamics — Collective cell migration governed by order parameters, substrate friction, and intercellular adhesion. * Chemotaxis Cahn-Hilliard — Phase separation coupled with chemotactic signaling that biases domain morphology. * Phase Fracture (AT1) — Variational fracture mechanics: energy minimization regularizes sharp cracks into a smooth damage field with irreversibility. FEATURES * Real-Time On-Device — All simulations compute locally. No server, no network. * Interactive Parameters — Adjust constants, resolution, and initial conditions with responsive sliders. * Live Visualization — Continuous color-mapped rendering of evolving fields. * Educational Panels — Governing equations, physical background, and parameter guides for every simulation. * Themes — Dark, light, and custom color themes. WHO IS IT FOR? Materials science students, researchers, educators, computational scientists, and anyone curious about how complex patterns emerge from simple equations. No programming required — pick a simulation, adjust the parameters, and watch the physics unfold.