## Exploring L-systems

Some time ago I came across an interesting idea about using a variant of a formal grammar, an L-system, to draw fractals and plants. For those familiar with formal grammars an L-system grammar is defined as such:

where

is a set of variables

is a set of constants

is the start axiom

is a set of production rules

How does an L-system grammar differ from a formal grammar you ask? The difference lies in the way the production rules are applied. A formal grammar generates a language by applying its production rules one at a time. Whereas an L-system grammar generates an L-system by applying as many rules as it can per iteration. Wikipedia has much more on L-systems and formal grammars if you are interested.

What’s amazing about L-systems is that they’re simple concepts but they’re used to model complex natural phenomena such as the growth of plants. We can visually see what L-systems are capable of if we combine them with computer graphics. To accomplish this we give certain symbols of an L-system extra meaning. For example, if an L-System grammar contains a variable and constants , we can say that the also means to draw forward, and the also mean to draw left and right by some angle.

The screenshots below are my implementation of L-systems (developed with Java using Swing for GUI).

This one is called a dragon curve

An older screenshot of my program generating a plant:

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