LSystem

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Simple c++ L-System generator

• What are L-Systems?
  • Definition
  • Development
• Documentation
  • Grammars
  • LSystem
  • Program example
• Examples
  • Plant
  • Heighway dragon
  • Pleasant error
  • Plant2
  • Penrose Tiling

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What are L-Systems?

Definition

An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar.

L-systems are now commonly known as parametric L systems, defined as a tuple:

G = (V, ω, P),

where

• V (the alphabet) is a set of symbols containing both elements that can be replaced (variables) and those which cannot be replaced ("constants" or "terminals")
• ω (start, axiom or initiator) is a string of symbols from V defining the initial state of the system
• P is a set of production rules or productions defining the way variables can be replaced with combinations of constants and other variables. A production consists of two strings, the predecessor and the successor. For any symbol A which is a member of the set V which does not appear on the left hand side of a production in P, the identity production A → A is assumed; these symbols are called constants or terminals.

Development

Once the L-system is defined, it begins to evolve according to its rules. The initial state of the L-system is its axiom. With further development, this line describing the state will change. The development of L-systems is cyclic. In each development cycle, a line is viewed from beginning to end, character by character. For each symbol, the rule for which the symbol serves as a precursor is searched. If no such rule is found, the symbol is left unchanged. In other words, for those x characters for which there is no explicit rule, the implicit rule applies: X→X. If the corresponding rule is found, the predecessor character is replaced by the following string from this rule.

Documentation

LSystem Grammars

If you want to use only grammars, then use the following classes

#include "src/StandartGrammar.cpp"
#include "src/StochasticGrammar.cpp"

StandartLSystem lsystem(options);
StochasticLSystem lsys(options);

options may contain:

• axiom A String to set the initial axiom
• rules A Vector of the strings with variables and rules

Setting axiom

You can simply set your axiom when you init your L-System.

StandartLSystem lsystem("F-F-F");

You can also set an axiom after initialization:

lsystem.setAxiom("F");

Setting rules

You can simply set your rules when you init your L-System:

DOL

vector<string> rules = {"A => A-B--B+A++AA+B-"};
StandartLSystem lsystem(rules);

Rule string should look like this

A => A-B--B+A++AA+B-

The first character is the variable name. Then '=>' with spaces. After that, there is a variable replacement rule.

Stochastic

vector<string> rules = {"F => F[+F]F[-F][F] (0.7)", "F => F[+F]F (0.3)"};
StochasticLSystem lsystem(rules);

Rule string should look like this

F => F[+F]F[-F][F] (0.7)

The first character is the variable name. Then '=>' with spaces. After that, there is a variable replacement rule. In brackets you must specify the probability of the rule

Also you could start with an empty L-System object, addRule() to edit the L-System later:

lsystem.addRule("B","+A-BB--B-A++A+B");

Getting results

Now that we have set up our L-System set, we can develop our L-System with iterate():

• Iterate once

lsystem.iterate();

• Iterate n-times

int n = 5;
lsystem.iterate(n);

You can get result with getCondition():

lsystem.addRule("B","+A-B-B-A+");
lsystem.iterate();
lsystem.getCondition();
// 'A+A-B-B-A+A'

LSystem

If you want to use graphical interpretation, use the class

#include "src/LSystem.cpp"

LSystem ls;

Settings

ls.setStep(15.0); // set step
ls.setAngle(36.0); // set angle

If you want the symbol not to be used by the interpreter, make it a constant:

ls.addConstant("C");

Produce and interpret LSystem

ls.build(options);
ls.loop();

where options may contain:

• axiom A String to set the initial axiom
• rules A Vector of the strings with variables and rules
• iterations A Int parameter for the number of iterations

Program example

#include "src/LSystem.cpp"

using namespace std;

vector<string> rules = {
  "6 => 81++91----71[-81----61]++",
  "7 => +81--91[---61--71]+",
  "8 => -61++71[+++81++91]-",
  "9 => --81++++61[+91++++71]--71",
  "1 => "
};

int main( int argc, char *argv[]) {
  	LSystem ls;

    ls.addConstant('6');
    ls.addConstant('7');
    ls.addConstant('8');
    ls.addConstant('9');

    ls.setStep(15.0);
    ls.setAngle(36.0);

    ls.build("[7]++[7]++[7]++[7]++[7]", rules, 5);
    ls.loop();
  return 0;
}

}

Output

Examples

Plant

Iterations - 7
Angle - 25 degrees

Axiom	Rules
X	X => F-[[X]+X]+F[+FX]-X F => FF

Heighway dragon

Iterations - 13
Angle - 90 degrees

Axiom	Rules
FX	X => X+YF+ Y => -FX-Y

Pleasant Error

Iterations - 4
Angle - 72 degrees

Axiom	Rules
F-F-F-F-F	F => F-F++F+F-F-F

Plant2

Run plant2_example.cpp to get this example