4D Fractal Explorer

Flat Flame and Solid restart after an edit settles. With 4D or Balloon geometry, changes apply the next time you enter that renderer. Surface restarts without resetting the view; an unsupported change returns to Points.

Emitter shapes and Surface → Shape trap use the same built-in library and Custom shape composer for different purposes.

A ring of mirror spheres inverts a seed shape repeatedly, shrinking a copy into each gap. Turned on, it replaces the transforms as the scene's subject; they return when it is turned off. A 3D arrangement makes a 3D scene, a 4D arrangement a native 4D one; Depth sets how many inversions deep the copies go.

Glass needs a solid with an interior, and an IFS attractor is infinitely thin dust. Surface then renders the solid your maps build, the shape the transmission walks through. Author Glass on a map to see it. Against a dark backdrop, light a checker floor behind the object; the glass presets and starters arrive with one.

Enable Combine systems under Systems to add an isolated block, then tune the links between its transforms here. Leak controls make broad changes; the matrix provides precise control.

These controls color the Points view. Each other renderer has its own Scene color section.

Balloon changes are immediate in Points and Solid. They restart Flame. In Surface, on/off and palette changes restart the render; size and tint stay live.

In Points, opening this section shows labeled Key and Rim disks with arrows pointing out of the emitting face; adjust position, aim and disk radius below. In 4D, lights stay in the displayed 3D space as the scene rotates or slices. Close the section to hide the guides; saved images and thumbnails omit them.

Set Order to at least 2-fold, then choose XW, YW, or ZW—or raise Twist above 0. A change between 3D and 4D regenerates Points before another renderer can use it.

Every link's step rotates the orbit point by a fixed angle and shifts it, so the chain's escape set bends as a rigid whole — the "rotation applied to point p" recipe, generalized past the twisted Menger carve.

The classic Menger sponge carve with a fixed rotation applied to the query point between levels — the exact construction the twisted-sponge presets approximate. A w turn or offset lifts it to the 4D hyper-Menger.

A prism of mirrors and spheres, tiled by inverting in its faces; the drawn set is the limit of that tiling. A finite inversion sphere closes it into a quasi-sphere; without one the set runs off unbounded (a terrain).

A reflection group folds space into its fixed chamber and repeats the chamber's fractal piece; the mirrored lattice repeats it in x and z (and w in 4D) across a bounded window. The content clip trims the piece without reshaping the chamber; a clip that admits nothing is reported, never replaced by the untiled attractor.

System B is an affine-only snapshot. Depth controls how many randomly chosen B maps bend each plotted point after the main system.