Self-Similar Map Explorer

The Coylean map has a deterministic substitution structure: each 4×4 section, identified by its (down, right) input code, always expands to the same 2×2 block of child sections at the next order. This makes the map an infinite fractal that can be explored to arbitrary depth using a finite lookup table of 34 rules.

The Substitution Rule

Of the 64 possible (down, right) code pairs, only 34 are reachable from the V₇₇ seed. Each reachable code maps to a fixed 2×2 block. Interior borders show where Coylean segments cross the child-section boundary. Codes are grouped by D4 orbit — e (identity), sᵥ (mirror), sₕ (flip), r² (180°).

Reachable Codes

The 34 codes that appear in the map. Highlighted codes have letter assignments from the glyph catalog.

H Substitution Rule

The horizontal-seniority (H) map uses right-wins-ties priority. Under backslash reflection, Vd,r → Hr,d. Each reachable code maps to a fixed 2×2 block, parallel to the V-grid rules above.

H Reachable Codes

Codes reachable under horizontal seniority. Highlighted codes have letter assignments (backslash-reflected from the V-grid catalog).

Universe View

The Coylean map extends to the full plane with a 2×2 quadrant seed. The standard map (F) occupies the bottom-right; the other three quadrants are J, M, and J×sh.

Level 0 — Order 5 (8×8)

Interactive Explorer

Click any section to zoom in. The substitution table generates child sections on demand — no limit to zoom depth. The path is remembered so you can zoom back out.

Adjacent sections share a boundary but their dots are computed independently from each section's input code. When dots at a shared boundary are misaligned (one filled, one hollow), this reveals the transition state — the signal changes as it crosses from one section to the next.

Note: a small gap appears where black boundary segments meet at section corners. This is a rendering artifact from the section-gap layout — to be addressed in a future update.

Level 0 — Order 5 (8×8)