NEW • Cross Section: 3D slices of 4D surfaces. Write an equation in x, y, z and p, then rotate the surface in 4D or slide the cutting plane along the fourth axis with P+/P−, and watch the section change shape. The 4D camera path works here too. • Precise ray marcher: removes the false "welds" that could join separate parts of high-degree equations. • Shell thickness is now a slider, saved with the surface. Existing shells may look thinner than before: raise the slider to restore their previous look. • Headlight: an optional light from the viewer, for cavities and the insides of tubes on ray-marched surfaces. • Backgrounds can now wrap around the scene as a sphere, cylinder or cube, turning with the camera. • The 4D step buttons show how far you have moved with each of them. IMPROVEMENTS AND FIXES • Surfaces and records save their full 4D state: equation, rotations and the position of the cutting plane. • Constants are no longer reset when a preset is loaded. • Switching between the 3D and Cross Section sub-tabs starts from a clean scene. • Equations that do not describe a surface are refused with a message instead of leaving an empty screen. • NEW clears the whole scene, and moving the view of an empty scene no longer asks you to save. • A camera path can now be written with a single coordinate. • Textures remember which library entry they come from, and Sync Focused Texture updates both surface and background textures without losing your colours and constants. • Applying a relief texture to a transparent surface no longer risks freezing the app.

New: Multi-mesh surfaces: build a surface from several independent grids, each with its own colour, texture and animation, and set per-mesh or global U/V domain limits to cut open individual grids or the whole figure. New button for an empty scene, distinct from restoring the default surface. Unsaved work is now protected: leaving a scene, switching tab, starting a new one or closing the app asks before discarding changes. Search across the whole manual from a single field, with page, occurrences and context. On-screen hints: presets, records and textures can show a short overlay explaining which sliders are live. Discrete constants and lower bounds in scripts: A := int(1,10) snaps a slider to whole numbers, A := min(1.0) keeps it above a floor. Constants A–F and S can now be used in the U/V/W limit fields, so the domain can follow a slider. A single Field of View slider in the renderer dock, replacing the two that competed for the same value. A notice when two parts of the scene claim the same constant, naming the letters still free. The status bar scrolls with a finger on mobile, so every button is reachable on a phone. Improvements: The equations module now applies as one, on Run: X/Y/Z/P, compositions, constraints, geodesic flow and the u/v/w domain no longer enter at different moments. Fixed a freeze when the preset library was kept in an iCloud folder. Fixed surfaces being clipped in Orthogonal projection. Fixed a hole in the background when flying inside a surface. A shader that fails to compile no longer clears the view. Records now keep their image texture and image background when reopened. Fixed the vertical profile of the Kerr funnel. The bundled preset library has been reviewed as a whole: clearer names, merged families, and every preset now states which constants are live.

New: New Field of View slider for both the 3D and 4D camera paths. New interior cutout for self-intersecting parametric surfaces. Cleaner interface: full-width tabs in Library and Equations docks. Seam-free default grid on closed surfaces. Improvements: Exported videos now faithfully match what's shown live on screen. Manually stopped animations stay stopped across other actions and exports. Loading a saved record now correctly restores camera view and motion. Improved transparency handling on mobile devices. Various minor fixes to save dialogs and path/equation editors.