⛅ Fractal Clouds 2 — Genuine fBm

Compare with v1 (Fractal Clouds): v1 builds each cloud from N random SWEllipse puffs. The ellipses have hard mathematical boundaries you can see at cloud edges — giving that slightly "cartoonish" look. v2 fixes all three root causes with new techniques.

Fix 1 — Genuine fractal shape: fBm

fBm (fractional Brownian motion) sums N octaves of Perlin noise, each at double the spatial frequency and (1/2)^H times the amplitude of the previous. Because it adds detail at every scale — large-scale shape from octave 1, medium lumps from octave 3, tiny edge turbulence from octave 5 — the cloud boundary is a true fractal isocurve. It looks statistically the same whether you zoom in or out, just like a real cloud silhouette.

Random candidate positions are scattered inside each cloud’s bounding ellipse (a Poisson-like scatter, not a regular grid — grids produced visible horizontal bands). A candidate becomes a puff only where fBm(x, y) × radial_mask > threshold. The threshold is the Cloud Cover slider; the number of cloud objects is the separate Cloud Count slider.

Fix 2 — No hard edges: radial gradient puffs

Each puff is drawn using drawingContext.createRadialGradient() — fully opaque at the center, smoothly fading to transparent at the edge radius. There are no solid fills and no SWEllipse outlines anywhere. Overlapping gradients blend together just like the water droplets in a real cloud merge into a continuous mass.

Fix 3 — Physical lighting: top-lit color model

Each puff is colored by its vertical position within the cloud. The top receives direct sunlight → near pure white (strong Mie forward-scattering). The bottom is in self-shadow → cool blue-gray (sky light scattered from below). This gradient is the single most important cue your eye uses to perceive a cloud as three-dimensional.

The Octaves slider — watch the fractal emerge

• 1 octave — smooth rounded blobs (single-scale, like v1)
• 2–3 octaves — cloud lobes start appearing
• 4–5 octaves — convincingly natural boundaries
• 6–7 octaves — wispy tendrils at every edge
• 8–9 octaves — maximum fractal detail

The Hurst Exponent H

• Low H (0.15–0.30) — high-frequency octaves contribute nearly as much as low-frequency ones → extremely jagged, turbulent edges
• Mid H (0.50–0.75) — balanced mix; typical cumulus
• High H (0.90–0.99) — high-frequency octaves fade out quickly → smooth, puffy fair-weather cumulus
• H = 0.75 — default; sweet spot for mid-latitude cumulus

Depth layers & parallax (same as v1)

• Far layer — upper sky, small, hazy opacity, slowest drift
• Mid layer — middle sky, medium size and speed
• Near layer — lower sky, large, bright, fastest drift

Cloud Count vs. Cloud Cover — two independent controls

These sliders control coverage at different levels of the system:

• Cloud Count (2–50) — the total number of cloud objects distributed across the three depth layers. Each object is an independent fBm-shaped mass that drifts at its own speed. More objects = more sky covered.
• Cloud Cover / Threshold (0.00–0.80) — the fBm density threshold inside each cloud object. Lower values accept more candidate puff positions, making each individual cloud denser and puffier. At 0.00 every candidate inside the bounding ellipse is accepted.

At a low threshold alone the sky can still look partly cloudy because only 12 cloud objects exist with gaps between them. Raising the count fills those gaps; lowering the threshold then packs each individual cloud solid.