Surface Explorer vs FrankenSim

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.

Carry a working numerical laboratory on your iPhone, iPad, or Mac. FrankenSim contains forty-three native experiments drawn from the FrankenSim Rust workspace. Each one runs a real local kernel and pairs the result with an interactive visualization and a concise account of what was computed. Explore heat diffusion, spectral waves, Lorenz dynamics, Gray-Scott reaction diffusion, fluid flow, smoke, topology optimization, signed-distance geometry, isosurfaces, Gaussian-process optimization, randomized linear algebra, symplectic orbits, computational geometry, interval-certified fractals, and more. The library is organized from foundations through deep experiments, end-to-end campaigns, and three larger flagships. Evidence labels distinguish a computed result from an illustration, approximation, bound, or certified conclusion. The theory atlas explains the equations and numerical ideas behind the displays. Every experiment runs on the device. FrankenSim has no account, advertising, tracking, cloud compute, or required network connection.