L Systems

Cover Image

Summary

This assignment dealt with a generative code method called L-Systems. Using push() and pop(), and the Java Turtle library, we were able to display generative artwork and interesting designs.



Task 1 - Humble Beginnings

To familiarize ourselves with the most basic of concepts related to L-Systems, task one required implementing penUP(), goToPoint(), and penDown() as methods of creating simple shapes.

Code Box 1

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import Turtle.*;

Turtle t;

void setup(){
    size(400,400);
    background(255);
    t = new Turtle(this);
    
    t.goToPoint(50, 50);  
    t.setHeading(90);  
    drawLetterI();
    
    t.goToPoint(150, 50);  
    t.setHeading(90);  
    drawLetterT();
}

void drawLetterI(){
    int heightI = 100;
    int widthI = 40;
    
    t.penDown();
    t.forward(widthI);
    t.penUp();
    
    t.back(widthI / 2);
    t.right(90);  
    t.penDown();
    t.forward(heightI);
    t.penUp();
    
    t.left(90);  
    t.forward(widthI / 2); 
    t.penDown();
    t.back(widthI); 
    t.penUp();
}

void drawLetterT(){
    int widthT = 60;
    int heightT = 100;
    
    t.penDown();
    t.forward(widthT);
    t.penUp();
    
    t.back(widthT / 2);
    t.right(90);  
    t.penDown();
    t.forward(heightT);
    t.penUp();
}

Output:


Task 1 Image 1

Code Box 2

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import Turtle.*;

Turtle t;

void setup() {
    size(400, 400);
    background(255);
    t = new Turtle(this);

    // Draw a triangle
    t.goToPoint(10, 100);
    t.setHeading(0);
    drawTriangle();

    // Draw a regular pentagon
    t.goToPoint(100, 100);
    t.setHeading(0);
    drawPentagon();

    // Draw a circle
    t.goToPoint(200, 100);
    t.setHeading(0);
    drawCircle(50);
}

void drawTriangle() {
    int side = 60;
    t.penDown();
    for (int i = 0; i < 3; i++) {
      t.forward(side);
      t.right(120);
    }
    t.penUp();
}

void drawPentagon() {
    int side = 50;
    t.penDown();
    for (int i = 0; i < 5; i++) {
      t.forward(side);
      t.right(72);
    }
    t.penUp();
}

void drawCircle(float r) {
    float step = (2 * PI * r) / 360.0;
    t.penDown();
    for (int i = 0; i < 360; i++) {
      t.forward(step);
      t.right(1);
    }
    t.penUp();
}

Output:


Task 1 Image 2

Task 2 - Square L-System

With the help of a provided code skeleton, a simple square based L-System can be iterated through.

Code Box 3

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// Main Processing Sketch for L-System Assignment

import processing.svg.*;
import processing.pdf.*;
import Turtle.*;

boolean shouldExportAsPDF = false;  // Change to true for PDF export
int numIterations = 0;              // Global iteration counter
BaseLSystem lSys;                   // L-System instance
Turtle t;                           // Turtle instance

void setup() {
    size(1000, 1000);
    background(255);
    stroke(0);
    
    t = new Turtle(this);
    lSys = initSquare();  // Create an instance of our concrete L-System
    
    noLoop();
    printInstructions();
}

void draw() {
    background(255);
    resetTurtle();
    lSys.reset();
    for (int i = 0; i < numIterations; i++) {
      lSys.iterate();
    }
    lSys.drawLSystem(t);
    lSys.printIterationNumber();
    lSys.printState();
}

void keyPressed() {
    switch (key) {
      case 'n':
        numIterations = max(0, numIterations - 1);
        redraw();
        break;
      case 'm':
        numIterations++;
        redraw();
        break;
      case 's':
        String fileType = (shouldExportAsPDF) ? ".pdf" : ".svg";
        String fileName = "H:/Downloads/" + getDateString() + fileType;
        beginRecord((shouldExportAsPDF) ? PDF : SVG, fileName);
        setup();
        draw();
        endRecord();
        println("Saved to file: " + fileName);
        break;
    }
}

void resetTurtle() {
    t.penUp();
    t.clearTurtleHistory();
    t.goToPoint(width-50, height-50);
    t.setHeading(0);
    t.penDown();
}

void printInstructions() {
    println("======== L-System Instructions ========");
    println("Press 'm' to increment the L-system iterations.");
    println("Press 'n' to decrement the L-system iterations.");
    println("Press 's' to save to PDF/SVG.");
    println("=======================================");
}

String getDateString() {
    String time = hour() + "_" + minute() + "_" + second();
    String date = year() + "_" + month() + "_" + day();
    return date + "-" + time;
}

BaseLSystem initSquare() {
    String axiom = "F-F-F-F";
    float moveDistance = 10;
    float rotateAngle = 90;
    float scaleFactor = 1.0;
    return new SquareLSystem(axiom, moveDistance, rotateAngle, scaleFactor);
}

// -----------------------
// BaseLSystem and SquareLSystem classes here...

Output:


Task 2 Image


Task 3 - Making Our Own

Once we've established usage of L-Systems, task 3 involved coming up with our own custom generative designs



Design 1: Serpinski Triangle

Code Box 4

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import processing.svg.*;
import processing.pdf.*;
import Turtle.*;

boolean shouldExportAsPDF = false;  
int numIterations = 0;              
BaseLSystem lSys;                   
Turtle t;                           

void setup() {
    size(1000, 1000);
    background(255);
    stroke(0);
    
    t = new Turtle(this);
    lSys = initSierpinski(); 
    
    noLoop();
    printInstructions();
}

void draw() {
    background(255);
    resetTurtle();
    lSys.reset();
    for (int i = 0; i < numIterations; i++) {
      lSys.iterate();
    }
    lSys.drawLSystem(t);
    lSys.printIterationNumber();
    lSys.printState();
}

void keyPressed() {
    switch (key) {
      case 'n':
        numIterations = max(0, numIterations - 1);
        redraw();
        break;
      case 'm':
        numIterations++;
        redraw();
        break;
      case 's':
        String fileType = (shouldExportAsPDF) ? ".pdf" : ".svg";
        String fileName = "H:/Downloads/" + getDateString() + fileType;
        beginRecord((shouldExportAsPDF) ? PDF : SVG, fileName);
        setup();
        draw();
        endRecord();
        println("Saved to file: " + fileName);
        break;
    }
}

void resetTurtle() {
    t.penUp();
    t.clearTurtleHistory();
    t.goToPoint(width/1.6, height-20);
    t.setHeading(0);
    t.penDown();
}

void printInstructions() {
    println("======== Sierpinski L-System Instructions ========");
    println("Press 'm' to increment the L-system iterations.");
    println("Press 'n' to decrement the L-system iterations.");
    println("Press 's' to save to PDF/SVG.");
    println("==================================================");
}

String getDateString() {
    String time = hour() + "_" + minute() + "_" + second();
    String date = year() + "_" + month() + "_" + day();
    return date + "-" + time;
}

BaseLSystem initSierpinski() {
    String axiom = "A";
    float moveDistance = 5;
    float rotateAngle = 60;
    float scaleFactor = 1.0;
    return new SierpinskiLSystem(axiom, moveDistance, rotateAngle, scaleFactor);
}

// -----------------------
// BaseLSystem and SierpinskiLSystem classes here...

Output:


Task 3 Subtask Image 1

Subtask 3.2

Code Box 5

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import processing.svg.*;
import processing.pdf.*;
import Turtle.*;
import java.util.Stack;

boolean shouldExportAsPDF = false;
int numIterations = 0;
BaseLSystem treeLsys;
Turtle t;

void setup() {
    size(1000, 1000);
    background(255);
    stroke(0);
    
    t = new Turtle(this);
    treeLsys = initTreeLSystem();
    
    noLoop();
    printInstructions();
}

void draw() {
    background(255);
    resetTurtle();
    treeLsys.reset();
    for (int i = 0; i < numIterations; i++) {
      treeLsys.iterate();
    }
    treeLsys.drawLSystem(t);
    treeLsys.printIterationNumber();
    treeLsys.printState();
}

void keyPressed() {
    switch (key) {
      case 'n':
        numIterations = max(0, numIterations - 1);
        redraw();
        break;
      case 'm':
        numIterations++;
        redraw();
        break;
      case 's':
        String fileType = (shouldExportAsPDF) ? ".pdf" : ".svg";
        String fileName = "H:/Downloads/" + getDateString() + fileType;
        beginRecord((shouldExportAsPDF) ? PDF : SVG, fileName);
        setup();
        draw();
        endRecord();
        println("Saved to file: " + fileName);
        break;
    }
}

void resetTurtle() {
    t.penUp();
    t.clearTurtleHistory();
    t.goToPoint(width/2, height-50);
    t.setHeading(0);
    t.penDown();
}

void printInstructions() {
    println("======== Instructions ========");
    println("Press 'm' to increment tree iterations.");
    println("Press 'n' to decrement tree iterations.");
    println("Press 's' to save to PDF/SVG.");
    println("================================");
}

String getDateString() {
    String time = hour() + "_" + minute() + "_" + second();
    String date = year() + "_" + month() + "_" + day();
    return date + "-" + time;
}

BaseLSystem initTreeLSystem() {
    String axiom = "F";
    float moveDistance = 3;
    float rotateAngle = 90;
    float scaleFactor = 1.0;
    return new TreeLSystem(axiom, moveDistance, rotateAngle, scaleFactor);
}

// -----------------------
// BaseLSystem and TreeLSystem classes here...

Output:


Task 3 Subtask Image 2

Subtask 3.3

Code Box 6

Show Code 

import processing.svg.*;
import processing.pdf.*;
import Turtle.*;

boolean shouldExportAsPDF = false;
int numIterations = 0;
BaseLSystem hexLsys;
Turtle t;

void setup() {
    size(1000, 1000);
    background(255);
    stroke(0);
    
    t = new Turtle(this);
    hexLsys = initHexagonLSystem();
    
    noLoop();
    printInstructions();
}

void draw() {
    background(255);
    resetTurtle();
    hexLsys.reset();
    for (int i = 0; i < numIterations; i++) {
      hexLsys.iterate();
    }
    hexLsys.drawLSystem(t);
    hexLsys.printIterationNumber();
    hexLsys.printState();
}

void keyPressed() {
    switch(key) {
      case 'n':
        numIterations = max(0, numIterations - 1);
        redraw();
        break;
      case 'm':
        numIterations++;
        redraw();
        break;
      case 's':
        String fileType = (shouldExportAsPDF) ? ".pdf" : ".svg";
        String fileName = "H:/Downloads/hexLsystem-" + getDateString() + fileType;
        beginRecord((shouldExportAsPDF) ? PDF : SVG, fileName);
        setup();
        draw();
        endRecord();
        println("Saved to file: " + fileName);
        break;
    }
}

void resetTurtle() {
    t.penUp();
    t.clearTurtleHistory();
    t.goToPoint(width/2, height/2);
    t.setHeading(0);
    t.penDown();
}

void printInstructions() {
    println("======== Hexagon L-System Instructions ========");
    println("Press 'm' to increment iterations.");
    println("Press 'n' to decrement iterations.");
    println("Press 's' to save to PDF/SVG (H:/Downloads).");
    println("============================================");
}

String getDateString() {
    String time = hour() + "_" + minute() + "_" + second();
    String date = year() + "_" + month() + "_" + day();
    return date + "-" + time;
}

BaseLSystem initHexagonLSystem() {
    String axiom = "F+F-F-F-F-F";
    float moveDistance = 10;
    float rotateAngle = 60;
    float scaleFactor = 1.0;
    return new HexagonLSystem(axiom, moveDistance, rotateAngle, scaleFactor);
}

// -----------------------
// BaseLSystem and HexagonLSystem classes here...

Output:


Task 3 Subtask Image 3

Task 4 - Laser Engraving

Last Step was to bring some of the designs to life. Using the ITLL Laser Cutters and the included code for exporting svgs, I was able to accomplish this easily.



Task 4 Image 1

Task 4 Image 2

Task 4 Image 3

Task 4 Image 4

Task 4 Image 5

Conclusion

This was a very fun and interesting assignment, and I learned a lot about L-systems and generative designing.