SWIsland Recursion Saga

Stage 8 inherits everything from Stage 7 — the same recursive island growth, the same SWIsland and Coordinates classes, the same controls. It adds one new feature: after all islands are placed you can press 🌊 Apply Fractal Coastline to redraw them with organic, realistic borders instead of blocky grid edges.

Two phases inside SWFractalIsland.js

How roughness is controlled

The displacement scale shrinks each iteration using the Hurst exponent H:

Multiplying by |AB| (edge length) keeps the roughness visually consistent: long edges get bigger absolute bumps, short ones get smaller ones — so every part of the coastline looks equally jagged.

Seeded PRNG — why random but reproducible?

SWFractalIsland uses a Linear Congruential Generator (LCG) instead of Math.random():

Each island gets a unique seed: seed + islandIndex × 7919 (7919 is prime — keeps seeds well-spread). This means clicking the button twice with the same roughness and passes still gives a different coastline (new random seed each click), but the same seed always produces the exact same shape — useful for reproducible demos.

Why outline extraction is safe for these islands

A polygon outline algorithm can fail at a pinch point — a grid corner where two diagonally opposite cells are island but the other two diagonal neighbors are not, creating an ambiguous branching vertex.

Our island growth algorithm prevents this: every cell is added by orthogonal adjacency, and SWIsland.isValidExpansion() requires all 8 neighbors of a new cell to be either water or this island. Together these rules guarantee that if two cells in a finished island touch diagonally, at least one of the two “rook” cells (sharing an edge with both) is also in the island — so no pinch points are possible.

Controls — Stage 8 additions

• Roughness — 0.10 (gentle, rolling hills) to 0.80 (sharp, jagged cliffs). 0.45 is a good natural default.
• Subdivision passes — each pass doubles the vertex count and adds a finer level of detail. 3 passes gives 8× the original vertices (good for most island sizes); 5 passes can give thousands of vertices for very large islands.
• 🌊 Apply Fractal Coastline — enabled only when at least one island has been placed. Clicking again generates a fresh random coastline with the same settings.
• Reset / Clear — both return to the normal grid view and disable the button until the next run completes.

Inherited from Stage 7 (unchanged)

• Full island growth algorithm inside SWIsland.grow().
• All 8-direction diagonal separation rules.
• Auto-placed seeds, BFS reachability pre-check, step-count safety limit.
• Candidate hint overlay, backtrack flashes, recursion log.
• Ocean pits, sprinkle, speed slider, randomize toggle.
• SWIsland.toString() logged on island completion.