L-System Tree Generator

How the L-System Tree Generator works

L-system tree generator: what to know first

Lindenmayer invented these systems in 1968 to describe how algae cells divide, and they turned out to draw convincing plants with almost no code. Each preset is an axiom, the starting string, and one or two rules that say what each letter becomes. The Fractal tree preset starts from X and uses X → F+[[X]−X]−F[−FX]+X and F → FF. After five iterations that is a string of several thousand characters.

Reading the string, F draws a segment, + and − turn by the branch angle, and [ and ] save and restore the turtle's position and heading. The brackets are what make it a tree: every time the turtle finishes a side branch it pops back to the fork and carries on with the trunk. Letters with no drawing meaning, like X, only exist to carry the growth rule.

Iterations is how many times the rules are applied. Each one adds a level of branching and roughly doubles the detail; six or seven gives a full canopy but the string grows fast, so the page caps it. Branch angle is the turn made by + and −. Each preset has a textbook angle, but sweeping it changes the plant from a cypress at 10° to a sprawling bush at 45°. Randomness jitters every angle and segment length by a small amount chosen from the seed, which is the difference between a diagram and something that looks grown. At 0 the tree is perfectly symmetric and Regenerate does nothing; at 5 each seed is a different individual of the same species.

Colour shades from a brown trunk to green or autumn tips by branch depth, and the stroke weight thins toward the tips. Mono draws everything in one colour for a silhouette.

Export. The string is regenerated and redrawn at the chosen size, with segment lengths scaled to the canvas height, so the tree fills a phone export as well as a desktop one.

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