Lindenmayer system (L-system) fractals were conceived by Aristid Lidenmayer in 1968. They were originally used for the study of biological models related to plant development. Lidenmayer tried to describe the growth process of living organisms, especially that of branching patterns of plants. These systems are created by following a certain axiom and certain production rules. Examples include the Koch curve and the Koch snowflake.

The Koch curve starts with a line. This is the axiom. Then it follows the production rules:

1. Divide the line into three equal segments.

2. Replace the middle segment by an equilateral triangle whose sides are the same length as the middle segment.

3. Remove the base of the triangle.

The process is now repeated for the four resulting lines.

The Koch snowflake follows the same production rules, but the axiom is an equilateral triangle instead of a line.

Another example is the Lidenmayer tree.

It starts with the axiom which a vertical line. The production rule is simple and consists in adding to more nodes with an angle of 120° from the previous line.