mandelbrot.scala

import java.awt.image.BufferedImage
import javax.imageio.ImageIO
import java.io.File

/** The Mandelbrot image with given width and height in pixels. */
class Mandelbrot(width: Int, height: Int) {
    case class Complex(re: Double, im: Double) {
        def *(op: Complex): Complex = {
            Complex(re * op.re - im * op.im, re * op.im + im * op.re)
        }

        def +(op: Complex): Complex = Complex(re + op.re, im + op.im)

        def bounded = re < 2 && im < 2
    }

    /** Scaled from x and y coordinates. */
    def fromPoint(x: Int, y: Int): Complex = {
        Complex(3.5*(x.toDouble / width)-2.5, 2*(y.toDouble / height)-1)
    }

    def draw(path: String) {
        val image = new BufferedImage(width, height, BufferedImage.TYPE_INT_RGB)
        for (x <- 0 until width) {
            for (y <- 0 until height) {
                val c = fromPoint(x, y)
                println(c.re + " " + c.im)
                val rgb = escapeTime(c, 100)
                image.setRGB(x, y, rgb)
            }
        }
        ImageIO.write(image, "png", new File(path))
    }

    /* z(0) = 0
     * z(n+1) = z(n)^2 + c */
    def z(c: Complex): Stream[Complex] = {
        Complex(0, 0) #:: z(c) map {zn => zn * zn + c}
    }

    /** The number of iterations required to escape.
     * Returns max if c does not escape. */
    def escapeTime(c: Complex, max: Int): Int = {
        z(c) zip (0 to max) takeWhile {e => e._1.bounded && e._2 < max} size
    }
}

object Test {
    def main(args: Array[String]) {
        val m = new Mandelbrot(5000, 3000)
        m.draw("test.png")
    }
}