Fern 3

Each line in this fern is replaced by a three-step stem with two pairs of side branches. The first pair has two steps per branch. The second pair has one step per branch.

Start with F and apply:

F → F[+FF][-FF]F[-F][+F]F

F draws forward. Plus and minus turn by 22.5 degrees.

Brackets save a branch's starting position and direction. Closing the bracket restores them without drawing a return line, so the main stem continues from the same junction.¹

There are nine F steps in the replacement. On the next round, every one of those steps receives the whole replacement. A two-step side branch therefore receives two copies in succession, while a one-step branch receives one.

The segment count goes from 1 to 9 to 81. Dividing each new segment's length by three keeps the three-step main stem the same height as the line it replaces. The plant stays the same height as more branches appear.

Further reading

• L-system background — Wikipedia
• Drawing L-systems — The Nature of Code

Sources and notes

1. Przemysław Prusinkiewicz and Aristid Lindenmayer, The Algorithmic Beauty of Plants, chapter 1, Springer-Verlag, 1990. Section 1.6 supplies the branching interpretation. ↩

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