Branching Gravity Walk

A buried coffin, and thirty roots that walk downward around it under a gravity that keeps pulling them straight.

Above and below

The composition has a horizon and two different kinds of drawing on either side of it. Above is geometry: a dashed ground line and, in most presets, a bark-textured trunk running to the top edge. Below is growth, and whatever obstacle — if any — is buried in it.

DrawDashedLine(canvas, paint, TopH, 100);
foreach (var obs in Obstacles)
    obs.Draw(canvas, paint);

Everything is drawn through direct line calls to the canvas — one explicit segment at a time — which is why the whole piece reads as one continuous pen even where the subjects are unrelated.

Step 01

The setting, with no roots yet. When a trunk is present, sixty short marks scatter below the ground line as soil texture, placed by three chained coin flips that bias them towards the left wall, the right wall, or anywhere between:

if (rng.NextDouble() <= 0.25)       x = -SourceR;
else if (rng.NextDouble() <= 0.33)  x = SourceR - dd;
else                                x = -SourceR + (2f * SourceR - dd) * (float)rng.NextDouble();

A quarter cling to the left wall; of the rest, a third cling to the right; the remainder float. That three-way split is what stops the marks reading as uniform noise.

Thirty roots, evenly spread and not

float angle = 180f / (RootCount + 2f) * (1f + i + (float)rng.NextDouble() - 0.5f);

The angles divide a half-circle into RootCount + 2 slots and give root i slot i + 1 — so the fan is regular, and the two end slots are left empty so nothing grows horizontally along the surface. The rng.NextDouble() − 0.5 term then nudges each root by up to half a slot.

That is the difference between a fan and a diagram. Perfectly spaced roots look mechanical; a half-slot of jitter is enough to break the regularity while keeping the spread even.

Step 02

A quarter of the roots. Each begins within a unit or so of the coffin’s edge and grows away from it.

A root is a walk, not a curve

No root is planned. Each is a biased random walk: step forward a short distance, perturb the heading by a Gaussian, then pull the heading back towards straight down. Repeat until the length runs out, branching occasionally on the way.

The two forces are the whole character of the drawing. Without the jitter the roots would be straight lines; without the gravity they would wander off sideways and never descend. Together they produce the thing that reads as root rather than as crack: a line that is always going down and never going down directly.

The Gaussian is generated by Box–Muller rather than by summing uniforms:

return mu + sigma * MathF.Sqrt(-2f * MathF.Log(u)) * MathF.Cos(2f * MathF.PI * v);

Two uniforms in, one normal out — exact rather than approximate, which matters because it is the tail of that distribution that produces the occasional root that swings wide.

Step 03

Half.

Step 04

Three quarters. The roots part around the coffin — not because any of them tests for it, but because the ones aimed at it are deflected, and the gap that leaves is the coffin’s shape. Roots do not avoid each other at all: where two cross, they cross.

Step 05

All thirty.

Renderings

Rendering	Roots	Ink	Obstacle
Lime Roots	30	neon green on black	coffin
Chalk Veins	22	near-black on warm cream	coffin
Coral Tendrils	35	coral on near-black	coffin
Cobalt Veil	50	pale blue on near-black	coffin
Amber Drift	16	amber on near-black	coffin
Open Roots	45	teal on near-black	none
Wedge Block	25	gold on dark warm	single triangle
Stone Garden	35	pale cyan on near-black	five triangles
Slab	28	burnt orange on near-black	flat rectangle

Each has its own seed, so the renderings are independent growths. RootCount changes both the number of roots and the angular spacing between them, since the slot count is derived from it — so a denser rendering is not the same fan with more in it.

The obstacle a root encounters changes its visible path. A coffin creates a gap shaped like the buried object; a triangular wedge splits the curtain into two streams that curve around its slopes; a flat slab parts the roots left and right along a hard horizontal line; no obstacle at all lets each root wander freely until gravity alone decides where it lands.

Museum Frame

Lime Roots presented as a finished piece. A 100-pixel gallery mat in warm neutral gray surrounds the same 800 × 800 artwork on a 1000 × 1000 canvas, with a thin frame line at the mat boundary. The framing is a presentation layer over the unchanged generative design — the same seed, the same thirty roots, the same ink.

Origin

Inspired by the Turtletoy sketch at turtletoy.net/turtle/ad4a6ed109. The core biased-random-walk idea — step, jitter heading, let gravity pull back toward vertical — carries over directly, while the obstacle system and source configurations are new.

Determinism

One Random is created per draw, seeded from the preset, and consumed in a fixed order: the sixty soil marks first, then per root an angle jitter, a start position, and whatever the recursive growth needs. The generator is System.Random, which the project’s determinism policy flags as not guaranteed stable across .NET versions.

Progression 05

Variant 09

Gallery 01