Riley limit-set explorer

Explore the boundary orbit of X(z) = z + 1 and Y(z) = z / (ρz + 1).

ρ = 0.0 + 2.0im · depth 8 · 8748 words · 8748 finite points · 0.078 s

Scroll to zoom; drag to pan. Colours show the average word-prefix label in each pixel. Colours use three-letter prefixes. Drag the ρ marker to update the sample. Dragging, keyboard controls, and numeric submissions are constrained to the nonnegative quadrant on or above the approximate boundary. Reset restores the initial parameter and view.

Each sample enumerates a complete level of freely reduced words from the seed z = 0. Repeated points are retained; points at infinity in the displayed chart are omitted.