Surface Explorer vs Fractal Navigator

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.

Navigate through living mathematics. Fractal Navigator turns motion into exploration: tilt your iPhone to explore through the Mandelbrot set as it zooms ever deeper, bend a growing fern to see its repeating pattern, and watch the dragon curve copy itself fold by fold. THREE WORLDS • Mandelbrot — tilt to steer, auto-zoom to dive. Four color palettes. Bookmark the places you find. • Garden — a fern grown live from the same L-system rules botanists use to model real plants. Tilt the phone and wind blows through it. Shake for a new plant. • Fractal Curves — the dragon curve and Sierpinski arrowhead reveal themselves fold by fold. A build-it-yourself challenge lets you fold the curve on your own. LEARN AS YOU FLY Wonder cards surface the ideas behind what you're seeing — self-similarity, infinite boundaries, how simple rules grow complex shapes. A museum mode keeps the experience running hands-free for exhibits and classrooms. BRING YOUR OTHER DEVICES (OPTIONAL) Everything works with just your iPhone. Add AirPods and your head steers too. Add Apple Watch and the crown grows the garden while wrist tilt reshapes the plant. No account. No ads. Nothing collected — bookmarks stay on your device.