The Mandelbrot Set
Simple rendering of the Mandelbrot set. Based on Daniel Shiffman's Mandelbrot Example for Processing.
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function setup() {
createCanvas(710, 400);
pixelDensity(1);
noLoop();
}
function draw() {
background(0);
// 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
const w = 4;
const h = (w * height) / width;
// Start at negative half the width and height
const xmin = -w/2;
const 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
const maxiterations = 100;
// x goes from xmin to xmax
const xmax = xmin + w;
// y goes from ymin to ymax
const ymax = ymin + h;
// Calculate amount we increment x,y for each pixel
const dx = (xmax - xmin) / (width);
const dy = (ymax - ymin) / (height);
// Start y
let y = ymin;
for (let j = 0; j < height; j++) {
// Start x
let x = xmin;
for (let i = 0; i < width; i++) {
// Now we test, as we iterate z = z^2 + cm does z tend towards infinity?
let a = x;
let b = y;
let n = 0;
while (n < maxiterations) {
const aa = a * a;
const bb = b * b;
const twoab = 2.0 * a * b;
a = aa - bb + x;
b = twoab + y;
// Infinty in our finite world is simple, let's just consider it 16
if (dist(aa, bb, 0, 0) > 16) {
break; // Bail
}
n++;
}
// 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
const pix = (i+j*width)*4;
const norm = map(n, 0, maxiterations, 0, 1);
let bright = map(sqrt(norm), 0, 1, 0, 255);
if (n == maxiterations) {
bright = 0;
} else {
// Gosh, we could make fancy colors here if we wanted
pixels[pix + 0] = bright;
pixels[pix + 1] = bright;
pixels[pix + 2] = bright;
pixels[pix + 3] = 255;
}
x += dx;
}
y += dy;
}
updatePixels();
}
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