## Posts Tagged ‘**Fractals**’

## L-systems continued

I have extended my previous L-systems implementation by adding more symbols, which allow me to create 3-D figures. This time I used OpenGL for rendering and QT for the GUI. Below is a screenshot of my program and the 3-D “tree” that it generated. Also below, is my code for the L-system class, the heart of the program. The class is responsible for rewriting strings based on the rules and symbols given.

LSystem::LSystem(string start, Rule rule) : rules(rule) { startAxiom = start; lang = ""; } void LSystem::run(int iterations) { string curr = startAxiom; for (int i = 0; i < iterations; i++) { for (int j = 0; j < curr.size(); j++) { string buff = rules.getRule(curr[j]); if (!buff.empty()) { curr.replace(j, 1, buff); j += buff.size() - 1; } } } lang = curr; } string LSystem::getGenString() { return lang; }

## 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: