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.

**The Mandelbrot Set** by Daniel Shiffman. (slight modification by l8l) * Simple rendering of the Mandelbrot set.

size(640, 360); noLoop(); background(255); // Establish a range of values on the complex plane // A different range will allow us to "zoom" in or out on the fractal // It all starts with the width, try higher or lower values float w = 4; float h = (w * height) / width; // Start at negative half the width and height float xmin = -w/2; float ymin = -h/2; // Make sure we can write to the pixels[] array. // Only need to do this once since we don't do any other drawing. loadPixels(); // Maximum number of iterations for each point on the complex plane int maxiterations = 100; // x goes from xmin to xmax float xmax = xmin + w; // y goes from ymin to ymax float ymax = ymin + h; // Calculate amount we increment x,y for each pixel float dx = (xmax - xmin) / (width); float dy = (ymax - ymin) / (height); // Start y float y = ymin; for (int j = 0; j < height; j++) { // Start x float x = xmin; for (int i = 0; i < width; i++) { // Now we test, as we iterate z = z^2 + c does z tend towards infinity? float a = x; float b = y; int n = 0; float max = 4.0; // Infinity in our finite world is simple, let's just consider it 4 float absOld = 0.0; float convergeNumber = maxiterations; // this will change if the while loop breaks due to non-convergence while (n < maxiterations) { // We suppose z = a+ib float aa = a * a; float bb = b * b; float abs = sqrt(aa + bb); if (abs > max) { // |z| = sqrt(a^2+b^2) // Now measure how much we exceeded the maximum: float diffToLast = (float) (abs - absOld); float diffToMax = (float) (max - absOld); convergeNumber = n + diffToMax/diffToLast; break; // Bail } float twoab = 2.0 * a * b; a = aa - bb + x; // this operation corresponds to z -> z^2+c where z=a+ib c=(x,y) b = twoab + y; n++; absOld = abs; } // We color each pixel based on how long it takes to get to infinity // If we never got there, let's pick the color black if (n == maxiterations) { pixels[i+j*width] = color(0); } else { // Gosh, we could make fancy colors here if we wanted float norm = map(convergeNumber, 0, maxiterations, 0, 1); pixels[i+j*width] = color(map(sqrt(norm), 0, 1, 0, 255)); } x += dx; } y += dy; } updatePixels();