Directed Morphic Tesselations
Five small browser demos: attention that reshapes a tiling, a line that has to stay whole across stacked slices, a lattice that fits itself to a photo, a vortex that can read that photo or draw a form of its own, and a round trip that reads a slice and draws it back from the mesh.
1. Attention morph
Move the pointer across the tiling. Nearby hexes lean along that motion, then ease back.
Hover directs the morph. Edges stay locked. This is a 2D attention demo, not the hairpin depth gate.
2. Hairpin across slices
Drag the stack. The line passes through every sheet and turns once underneath.
Drag to morph the sheets. The line threads every sheet and turns once at the bottom. Carried keeps it inside its tiles, pinned shows the check can fail. This is a toy line-consistency check across slices, not a trained model and not evidence of depth understanding.
3. Fit to a real image
A photo is blurred into slices, and a hex lattice fits each slice without opening an edge.
A photo you choose is processed in this browser and is not uploaded.
Click the photo to thread a line. Slices are blur levels of one photo, standing in for depth. The lattice fits each slice without opening any edges. The check tracks the clicked feature independently and asks whether it stays inside its carried tile. A toy check, not a trained model and not evidence of depth understanding.
Blur hairpins follow critical points as the blur increases (Koenderink 1984; Kuijper and Florack 1999). Those U-turns run across blur level, not depth. They are a self-consistency check of the lattice and the line on a real image, not a depth claim.
4. Attention vortex
The pointer is a signed center. Swirl rotates the lattice around it and fades with distance. Read checks that warp on a photo. Realize shades a blank lattice from the same warp, so the vortex draws a form. Hold still and the attended core sharpens step by step; the surround stays blurred, and plus/minus pairs there come back as the blur drops.
Read puts the vortex on blur levels of one photo and asks whether two tracked features stay inside their tiles. Realize uses no photo: tile area and rotation become tone, and the same closed-edge line is checked on that drawing. Hold still and the core sharpens one blur step at a time while the surround stays blurred; plus and minus pairs in that region come back as the blur drops. Human-like prefers a focused center that is strongest on the sheet you are pointing at and stays put while you hold still. Best for CV prefers the measured line, low distortion, no flips, and low cost. This is a toy. It does not compete with an image generator.
5. Strange loop: Read and Realize round trip
Play it forward. Each round refits the mesh to shrink the error against the photo. Gradient, the cap, and Attention change how much detail comes back.
The reconstruction is painted only from mesh parameters. Flat mode uses one color per tile. Gradient mode uses a linear color on each tile: a base and a slope in x and y, for each channel, nine numbers. No photo pixel is copied into that picture. Each round refits those parameters to shrink the error. The line score stays a constraint: a move that would push a held feature out of its tile is rejected. Adaptive refinement splits tiles that stay wrong. The cap is 480, 1000, or 2000 tiles, and the split budget on every fifth round is 8, 16, or 32. Attention spends three quarters of that budget inside a disk 2.3 hex radii across, the same core size as the vortex, and the rest outside. Click the photo to move that disk. The left plot is the round. The right plot is error against description size. This is a toy round trip, not a generator.
The citrus photo is processed in this browser and is not uploaded. Closed edges stay shared vertices. A move that would flip a tile is rejected.