L-systems

Examples

Grammar

Axiom

Rules (one per line, e.g. F=F+F--F+F)

Angle

Iterations

Start direction

Drawing

Symbols

F G …step forward drawing (symbols from the “Drawing” field)fstep forward without drawing+ −turn left / right by the angle& ^pitch down / up (3D)\ /roll left / right (3D)|turn around 180°[ ]save / restore position (branch)!thinner line (×0.7)'next palette colourL Oleaf / flowerF(0.3)=…stochastic rule with a probability

Nature

Random variation of angles and segment lengths - plants look less artificial. The seed fixes the randomness (same seed = same drawing).

Angles

Lengths

Seed

Look

Colour by

Palette

Colour

Line

Tapering

Background

Leaves and flowers (L, O)

Export

PNG at the chosen size or SVG - vector graphics for print, a plotter or a laser cutter.

PNG size

About L-systems

An L-system (Lindenmayer system) is a grammar that rewrites a string: it starts from the axiom and in every iteration replaces each symbol according to the rules - all at once. Biologist Aristid Lindenmayer invented them in 1968 to describe the growth of algae and plants. A “turtle” reads the final string: F is a step forward drawing, + and - are turns, and brackets [ ] save the position - that is how branches appear. The same simple principles give plants, snowflakes, plane-filling curves and aperiodic tilings. The string grows exponentially, so raise the iteration count carefully (limit 6 million symbols).

Drag - pan (in 3D rotate, Shift - pan) · wheel - zoom · G - grow · + / - - iterations · F - fit · H - panel