Plants from grammars

The plants in this garden are not drawn. They are derived – from small grammars called Lindenmayer systems, invented in 1968 by the biologist Aristid Lindenmayer to describe how algae and plants grow.

A string that rewrites itself

An L-system starts with a short string, the axiom, and a set of rewriting rules. F means "draw a branch segment", [ and ] save and restore the position of a small turtle, +, & and / turn it in three dimensions, L places a leaf cluster. And A is an apex – a growing tip that the rules replace in every generation.

Here is the oak of this garden after zero, one and two rewrites:

Every A became a fork with two or three new branches, each ending in a new A. The string grows exponentially – after five rewrites the oak has several hundred segments.

Stochastic, so no two trees are alike

The rules are stochastic: an apex forks into two branches in some cases and three in others, and every angle is jittered a little. The random numbers come from a seed derived from the plant's id, so the same plant always grows into the same tree – on every computer, in the SVG and in 3D – while two oaks never look the same.

Growth levels: a new ring of branches per rain day

The trick that makes the garden grow is that every module remembers the generation it was born in. Because only apices are rewritten, generation n + 1 always contains generation n. So a plant can be shown at any level between zero and its last generation: segments born up to that level are visible, the newest ones grow in from the tip they sprang from, and the leaf tuft at the old tip shrinks away.

A plant's level comes from its stage – and its stage comes from the weather:

stage 6 / 110

stage 22 / 110

stage 44 / 110

stage 72 / 110

stage 110 / 110

This is literally what the brief asked for: plants that become more complex with every rain day, not just bigger.

stage 9 / 90

stage 27 / 90

stage 50 / 90

stage 72 / 90

stage 90 / 90

One skeleton, two pictures

The turtle works in 3D. The README picture is simply the front view of the skeleton; the website builds tapered tubes from the very same segments, sorted by the level they were born in, so a growth level is just a draw range on the GPU. The SVG and the 3D garden can never disagree about a single branch.