Make Chirps vs Surface Explorer

This educational app displays gravitational wave chirps created by mergers of massive black holes in several different ways, giving users an intuitive understanding of these exotic disturbances of space-time itself produced by cataclysmic events in distant galaxies. FEATURES: • Simulation: Experience the intricate behavior of gravitational waves through physics simulation of inspiralling black holes that merge to form a final black hole which then “shakes off” its excess energy. • Visualizations: See the essence of gravitational waves via waveform plots, frequency evolutions, and spectrograms, to understand the patterns and how they depend on black hole masses. • Auditory Experience: Listen closely as you hear the evolution of gravitational waves, detecting the characteristic increase in time in strength and frequency. Try varying masses to see how pitch is affected. • Dynamic Animations: Witness the captivating dance of black holes in collision animations. Explore the propagation of these waves through space-time with mesmerizing spiral animations. • Educational Insights: Gain a comprehensive understanding of gravitational waves and the pioneering work of LIGO through informative text pages, enhancing your knowledge of these cosmic phenomena. COMPATIBILITY Compatible with iPhone and iPad, iOS 16 or later. ACKNOWLEDGEMENT Supported by the National Science Foundation with grant PHY-2110181.

Surface Explorer is a high-performance visualizer for intricate mathematical surfaces — 2D manifolds embedded in three- or four-dimensional space, and 3D slices of four-dimensional hypersurfaces — bringing abstract geometry to life with real-time GPU rendering. KEY FEATURES • Cross Section — slice four-dimensional hypersurfaces and watch their 3D sections change shape as you rotate them in 4D or slide the cutting plane along the fourth axis, even along a 4D camera path. • Ray Marching Engine — real-time rendering of implicit surfaces and signed-distance fields, with procedural displacement, transparency, adjustable shells, and a precise mode for high-degree equations. • Multi-Mesh Surfaces — build figures from several independent grids, set with a single field or a script, each with its own color, transparency, texture, image and domain. • Solid Curve — write a curve in 3D or 4D and see the tube drawn around it, with adjustable thickness; several tubes from a script. • Surface Borders — add a tube along the edges of a parametric surface, with its own color, texture and thickness. • Geodesic Flow — explore intrinsic geometry on curved manifolds (S³, H²×R, SL(2,R) and more), integrating geodesics from initial conditions. • 4D Spatial Exploration — dedicated controls for hyperspatial rotation (Omega, Phi, Psi), projection, and 3D and 4D camera paths. • 4D Lighting Models — Directional, Observer, and Slice lighting designed for hyperspace. • Dynamic GLSL Scripting — write custom shaders for procedural textures and surface logic in the built-in editor. • Backgrounds — images and procedural effects, fixed on screen or wrapped around the scene as a sphere, cylinder or cube. • Audio-Visual Synthesis — synchronize geometric parameters with a mathematical sound synthesizer. • Video Recording — capture your explorations directly in the app and save them to your device. A library of ready-made presets ships with the app, from classic parametric surfaces to black-hole ergospheres, curved-space tori and slices of the 3-torus, together with a searchable built-in manual. Built with Qt and Metal for smooth, native performance on iPhone and iPad.