Seven presets: fractal tree, fern, Koch snowflake, Dragon curve, Sierpiński triangle, bush, Hilbert curve. Space cycles presets; arrow keys adjust depth and angle.
In 1968, Aristid Lindenmayer was a Hungarian biologist at the University of Utrecht trying to describe how algae cells divide. He needed a notation that captured something Chomsky's grammars couldn't: the fact that all cells in a filament divide at once, in parallel, not one after another in sequence. So he invented his own formal grammar, applied every rule simultaneously to every symbol, and called the result a parallel rewriting system. He was not thinking about art.
The core idea is almost aggressively simple. You start with an axiom — a seed string like F — and a table of rewrite rules. At each step, every symbol in the string expands according to its rule. Apply four iterations of F → FF+[+F-F-F]-[-F+F+F] and the string grows to roughly 14,000 characters. Feed that string to a turtle that treats F as "draw forward," +/- as turns, and [/] as push/pop stack, and you get a branching tree indistinguishable from hand-drawn botanical illustration.
The entire expansion engine is eight lines:
function produce(axiom, rules, iterations) {
let s = axiom;
for (let i = 0; i < iterations; i++) {
let n = '';
for (const ch of s) {
n += rules[ch] || ch;
}
s = n;
}
return s;
}
That's the whole engine. No recursion, no tree structure, no clever data structure. Each character either matches a rule and expands, or passes through unchanged. The exponential growth is implicit: a string of length k with all characters matching rules becomes a string of average-rule-length × k after one step. At depth 5 for the fern preset, the output string has roughly 32,000 characters. The turtle walks every one of them in a single pass.
What Lindenmayer couldn't have expected in 1968 is that his grammar for algae would produce, with different rules and angles, the Koch snowflake (angle 60°), the Hilbert space-filling curve (angle 90°), the Dragon curve, and the Sierpiński triangle. The same formalism that models cell division also exhausts a plane. Prusinkiewicz made this visual in 1986 by connecting L-systems to LOGO turtle graphics — a decision that turned a theoretical biology tool into one of the most productive notations in procedural generation.
The depth control in the explorer reveals something worth seeing slowly: at depth 1 or 2, you're looking at a skeleton. By depth 4 or 5, the full self-similar structure is locked in. Depth 6 starts to stress the browser. The string length scales exponentially, but the picture barely changes after a certain point — each additional depth level fills gaps too small to distinguish at screen resolution. The form converges before the computation does.
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