⛰ Fractal Mountains — Build Mode

This version adds a Detail Level slider so you can see exactly how Midpoint Displacement constructs a fractal mountain range one subdivision pass at a time.

What each pass does

1. Pass 0 — No displacement yet. Each mountain layer is just two endpoints at the same height — a flat horizon. You see 4 flat colored bands stacked on each other.
2. Pass 1 — One midpoint is added to each segment and randomly pushed up or down. You get the first gentle wave in each band.
3. Pass 2 — Both halves of the pass-1 result each get their own midpoint. Now you have 4 segments per layer, each with a smaller displacement.
4. Pass k — 2^k segments, 2^k+1 points, 2×2^k triangles per layer.
5. Pass 8 — 256 segments, 257 points on the nearest layer. Full fractal detail — 1152 triangles across all 4 layers.

Why the coarse and fine versions match up

Midpoint Displacement is hierarchically nested: it only ever adds new points between existing ones, never moving them. Because p5.js's random is seeded, running with 3 passes gives you the exact same first-level structure as running with 8 passes — the extra passes just reveal midpoints that were always mathematically "there". This is the self-similarity property of fractals.

The triangle count formula

At detail level k, each layer contributes 2 × 2k triangles (two per quad, 2^k quads). Each layer caps at its own maximum (far/mid at 7, near at 8, fg at 6) so the total grows from 8 (at pass 0) to 1152 (at pass 8).

Controls

• Detail Level slider — drags through 0–8 passes; the info box updates the exact point and triangle counts in real time.
• Animate Build — resets to pass 0 and auto-steps forward every 700 ms so you watch the scene assemble itself.
• Roughness Bias — shifts the Hurst exponent globally (smoother or jaggier).
• New Seed — a different seed gives a completely different landscape (but the same building process applies).
• Factory Reset — returns to seed 42, day, full detail, neutral roughness.