Homomorphism Marker Field · interactive demo
Be the camera
A camera sees only a small patch of this pattern. From one cross-shaped glimpse, segment h and segment v , it works out exactly where it is and how it is turned. Drag on the field to move the camera, then watch the decoder. Switch on majority vote and add errors to see how a larger patch survives misread cells.
The printed field
Field
n = 6 · 16 × 16
n = 8 · 50 × 50
n = 8 · 58 × 58, longest sequence
What the camera sees, and how it decodes
Decode with
One cross
Majority vote
Misread random cells:
5 %
10 %
20 %
No errors
one cross segment h segment v
read apply D found in gives
D(y)j = yj ⊕ yj+1 ignores complements, so it does not matter whether a row of the field is B or its complement. Because the sequence S is orientable, the four lists X, XR , Y, YR never share a window, so each segment has exactly one place. In majority-vote mode every run of n + 1 cells along a row or column of the patch votes for where the patch starts, and the most popular answer wins (a simplified version of the paper's voting). The 58 × 58 field uses a 108-bit maximum-length sequence found in this project, instead of the 92 bits of the paper's Theorem 1. Based on Z. Mao et al., Homomorphism Marker Field , Measurement 261 (2026) 119631. Demo for the poster by Muhammad Junaid Khalid, COMP 5112, Lakehead University.