This example is for Processing 3+. If you have a previous version, use the examples included with your software. If you see any errors or have suggestions, please let us know.
Koch Curve by Daniel Shiffman.
Renders a simple fractal, the Koch snowflake. Each recursive level is drawn in sequence.
KochFractal k; void setup() { size(640, 360); frameRate(1); // Animate slowly k = new KochFractal(); } void draw() { background(0); // Draws the snowflake! k.render(); // Iterate k.nextLevel(); // Let's not do it more than 5 times. . . if (k.getCount() > 5) { k.restart(); } } // Koch Curve // A class to manage the list of line segments in the snowflake pattern class KochFractal { PVector start; // A PVector for the start PVector end; // A PVector for the end ArrayList<KochLine> lines; // A list to keep track of all the lines int count; KochFractal() { start = new PVector(0,height-20); end = new PVector(width,height-20); lines = new ArrayList<KochLine>(); restart(); } void nextLevel() { // For every line that is in the arraylist // create 4 more lines in a new arraylist lines = iterate(lines); count++; } void restart() { count = 0; // Reset count lines.clear(); // Empty the array list lines.add(new KochLine(start,end)); // Add the initial line (from one end PVector to the other) } int getCount() { return count; } // This is easy, just draw all the lines void render() { for(KochLine l : lines) { l.display(); } } // This is where the **MAGIC** happens // Step 1: Create an empty arraylist // Step 2: For every line currently in the arraylist // - calculate 4 line segments based on Koch algorithm // - add all 4 line segments into the new arraylist // Step 3: Return the new arraylist and it becomes the list of line segments for the structure // As we do this over and over again, each line gets broken into 4 lines, which gets broken into 4 lines, and so on. . . ArrayList iterate(ArrayList<KochLine> before) { ArrayList now = new ArrayList<KochLine>(); // Create emtpy list for(KochLine l : before) { // Calculate 5 koch PVectors (done for us by the line object) PVector a = l.start(); PVector b = l.kochleft(); PVector c = l.kochmiddle(); PVector d = l.kochright(); PVector e = l.end(); // Make line segments between all the PVectors and add them now.add(new KochLine(a,b)); now.add(new KochLine(b,c)); now.add(new KochLine(c,d)); now.add(new KochLine(d,e)); } return now; } } // The Nature of Code // Daniel Shiffman // http://natureofcode.com // Koch Curve // A class to describe one line segment in the fractal // Includes methods to calculate midPVectors along the line according to the Koch algorithm class KochLine { // Two PVectors, // a is the "left" PVector and // b is the "right PVector PVector a; PVector b; KochLine(PVector start, PVector end) { a = start.copy(); b = end.copy(); } void display() { stroke(255); line(a.x, a.y, b.x, b.y); } PVector start() { return a.copy(); } PVector end() { return b.copy(); } // This is easy, just 1/3 of the way PVector kochleft() { PVector v = PVector.sub(b, a); v.div(3); v.add(a); return v; } // More complicated, have to use a little trig to figure out where this PVector is! PVector kochmiddle() { PVector v = PVector.sub(b, a); v.div(3); PVector p = a.copy(); p.add(v); v.rotate(-radians(60)); p.add(v); return p; } // Easy, just 2/3 of the way PVector kochright() { PVector v = PVector.sub(a, b); v.div(3); v.add(b); return v; } }