Planar slices and 3D cutaways

Loading

Complete 17th prefix generation · red f₀(K), blue f₁(K)

Decompressing numerical mesh data…

Drag to orbit · Scroll to zoom ·

Parameter slice and cutting surface

3D contextSection

2D parameter plane

Drag outside the unit disk · Arrow keys: 0.01; Shift: 0.001.
Both chart lifts are marked in 3D.Selected parameter

Re(c)

Im(c)

Continue with this parameter in 4D → Contact-search depth

What this displays. Actual sampled IFS parameters and genuine clipping of the resulting mesh. Every radial sample was tested independently; no radial monotonicity was assumed. Colour is a finite address code, not a topological classification. Dark grey is unresolved. The 3D display uses fixed meshes (angular stride 2; section stride 4). The 2D planes retain all 1,025 × 320 samples. Clipping and camera motion preserve mesh detail.

Coordinate chart. a = exp(i(α−γ))/ρ, b = exp(−i(α+γ))/ρ. X = (4+ρ cos α) cos γ; Y = ρ sin α; Z = (4+ρ cos α) sin γ. The angular chart is a double cover: (α,γ) and (α+π,γ+π) describe the same pair. The radial domain shown begins at ρ = 1.025.