An L-system (Lindenmayer system) is a formal grammar: a starting "axiom" string is rewritten again and again by replacing each symbol with a longer string according to a set of production rules, producing an ever more complex sequence of instructions. To turn that string into a shape, a "turtle graphics" interpreter walks through it character by character, treating each symbol as a command — move forward and draw a segment, turn by a fixed angle, or push/pop a branch point on a stack — which naturally produces branching plant-like structures. L-systems were developed in 1968 by biologist Aristid Lindenmayer to model the cellular growth patterns of algae and, later, the branching architecture of trees and plants. Because the same few rules are applied recursively, the resulting shapes are self-similar at multiple scales, much like real botanical growth. Today the same technique powers procedural vegetation in games and VFX tools such as SpeedTree.

Characteristics

• Real plants commonly branch at roughly 20–35° from the parent stem; this simulation's variants use 20–25° by default.
• Iteration count (recursion depth) controls complexity — each extra pass exponentially increases the number of segments.
• The structure is fractal / self-similar: zooming into a sub-branch resembles the whole plant.
• A classic minimal example is algae growth: the rule F→FF simply doubles a filament each step.
• Bracketed symbols [ and ] save and restore turtle state, allowing side-branches to split off and rejoin the main stem.
• Small changes to the angle or rule string can produce dramatically different plant "species" from the same engine.
• Used in procedural generation tools (e.g. SpeedTree) and academic plant-modeling research.