Simple example I'm cooking up...

mandelbrot.scala

package spire.example

import spire.implicits._
import spire.math._
import spire.syntax._

import scala.annotation.tailrec

object MandelbrotDemo {
  /**
   * Compute whether the complex number c stays contained within a radius-2
   * circle after 'limit' iterations.
   */
  def mandelbrot(c: Complex[Double], limit: Int): Int = {
    @tailrec def loop(z: Complex[Double], n: Int): Int =
      if (n >= limit) n
      else if (z.abs > 2.0) n - 1
      else loop(z * z + c, n + 1)

    loop(c, 1)
  }

  /**
   * Print an ASCII approximation of the 4x4 box from -2-2i to 2+2i.
   */
  def main(args: Array[String]) {
    val res = 26 // number of iterations to try before including pt in the set
    val rows = if (args.isEmpty) 20 else args(0).toInt // rows to print
    val cols = rows * 2 // cols to print. most fonts are roughly 1:2
    val h = 4.0 / rows // height per pixel character
    val w = 4.0 / cols // width per pixel character

    def pt(x: Int, y: Int) = Complex(x * w - 2.0, y * h - 2.0)
    def display(s: String, n: Int) = print(Xterm.rainbow(n) + s)

    // render the area in ASCII, using o's and spaces.
    cfor(0)(_ <= rows, _ + 1) { y =>
      cfor(0)(_ <= cols, _ + 1) { x =>
        // if n<res, color the pixel accordingly, otherwise then we
        // treat it as being in the set.
        val n = mandelbrot(pt(x, y), res)
        val pixel = if (n == res) " " else "x"
        display(pixel, n)
      }
      println(Xterm.clear())
    }
  }
}

object Xterm {
  // r, g, b should be 0-5
  def color(r: Int, g: Int, b: Int) = "\033[38;5;%dm" format (16 + b + (g * 6) + (r * 36))
  def clear() = "\033[0m"

  // given things like rgb(0xffcc99) produce things like color(6, 5, 4)
  def rgb(n: Int) = color(scale(n & 0xff0000), scale(n & 0xff00), scale(n & 0xff))
  private def scale(n: Int) = round((n * 6.0) / 255).toInt

  // 0-25 are colors, 26+ is clear
  def rainbow(n: Int) =
    if (n < 6) Xterm.color(5, n, 0)
    else if (n < 11) Xterm.color(10 - n, 5, 0)
    else if (n < 16) Xterm.color(0, 5, n - 10)
    else if (n < 21) Xterm.color(0, 20 - n, 5)
    else if (n < 26) Xterm.color(n - 20, 0, 5)
    else Xterm.clear()
}