Technique · Geometry
L-system
Plants, ferns, seaweed and fractal curves drawn by rewriting rules, with chance, jitter and a pull toward the light.
L-system is drawn geometry, rebuilt as it changes. Every piece on Synapse Drip is made from a recipe that layers techniques like this one, and you can change any of it in the Studio.
Good to know
- The Algorithmic Beauty of Plants, by Przemyslaw Prusinkiewicz and Aristid Lindenmayer (1990), is full of L-system plants and is free to read online.
- Leaves often grow around a stem at the golden angle, about 137.5 degrees, which spreads them out with the least overlap.
- Turtle graphics, from Seymour Papert's Logo language of the 1960s, draws by moving a cursor forward and turning it: the same few commands as here.
- The biologist Aristid Lindenmayer invented L-systems in 1968 to describe how algae grow, cell by cell.
The mathematics
- If a rule turns one F into k symbols, each rewrite makes the string k times longer, so 6 rewrites multiply its length by k^6; that exponential growth is why the count is capped.
- A rewriting system applies every rule to every symbol at once, which is how L-systems model cells dividing at the same time.
In art
- Karl Blossfeldt's 1928 photographs, Urformen der Kunst, showed plant details as if they were architecture and ornament.
- Botanical illustration has always been a balance between the individual plant and the type it stands for.
More ways to use it
Related techniques
Space colonisation · Diffusion-limited aggregation · Flow ribbons · Ridgelines · Curve families · Streamlines · Paint strokes · Stipple and Delaunay portrait