🌿 L-System Fractal Generator

An L-system (Lindenmayer system) is a formal grammar invented by the biologist Aristid Lindenmayer in 1968 to model the growth of plants and algae. You start from a short axiom string and repeatedly replace each symbol using a set of rewrite rules, so the string grows more detailed with every pass. The final string is then read as a sequence of turtle-graphics commands — move, turn, branch — that trace out the fractal on screen.

Each symbol is a drawing instruction for an imaginary turtle. F and G move forward while drawing a line; + turns left by the set angle and - turns right; [ pushes the current position and heading onto a stack (starting a branch) and ] pops them back (returning to where the branch began). Those two bracket commands are what let a single rule sprout stems and leaves, producing lifelike, tree-like forms from just a few characters.

To build your own fractal, set an axiom and one rule per line. The classic Koch curve uses axiom F, rule F=F+F--F+F, and an angle of 60° — each pass replaces every F with four smaller ones. Because each rewrite can multiply the string length, growth is exponential, so the generator caps iterations at 7 and applies a length guard that stops runaway patterns before they freeze your browser.