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Generating Fractals with L-Systems: Grammar Rules and Axioms

Explore the fascinating world of L-systems for generating fractals and other complex shapes. L-systems utilize simple rules and an axiom to create intricate patterns. The fundamental alphabet includes characters such as F (forward), f (forward without drawing), and symbols for angles and turns. Two examples are showcased: the Cantor middle-thirds set and the Koch curve, each illustrating how iteration and grammar rules can yield stunning visual results. Dive into the details of how to model plants and fractals using L-systems techniques.

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Generating Fractals with L-Systems: Grammar Rules and Axioms

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  1. L systems(Aristid Lindenmayer) Grammars for generating fractals (and other shapes) Need “axiom” and “grammar rules” Alphabet for rules: {F,f,+,} + Turn counterclockwise by a specified angle q  Turn clockwise by a specified angle q F Move forward one step (length L) while drawing a line f Move forward one step (length L) without drawing a line

  2. Example 1: Cantor middle thirds set axiom: S = F rules: F FfF ffff Initial L = 1 At each step, set L to L/3 F F f F F f F fff F f F  

  3. Example 2: Koch curve S = F axiom: S = F rules: F  FF++FF +  +  q = 60 degrees Initial L = 1 At each step, set L to L/3 + + F F F  F  F  + + F F F   F

  4. http://www.allenpike.com/modeling-plants-with-l-systems/

  5. Netlogo L-systems exercise

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