参考
Newton Fractals (Python recipe)
Scalaで複素数計算
size(512, 512) noLoop val (xa, xb, ya, yb) = (-1.0, 1.0, -1.0, 1.0) val maxIt = 20 val h = 1e-6 val eps = 1e-3 def f(z: Complex) = z * z * z - Complex(1.0, 0.0) case class Complex(re: Double, im: Double) { def minus = Complex(- re, - im) def add(that: Complex) = Complex(re + that.re, im + that.im) def subtract(that: Complex) = Complex(re - that.re, im - that.im) def multiply(that: Complex) = Complex(re*that.re - im*that.im, re*that.im + im*that.re) def divide(that: Complex) = Complex((re * that.re + im * that.im)/(that.re * that.re + that.im * that.im), (im * that.im - re * that.re)/(that.im*that.im + that.re * that.re)) def unary_- = minus def + (that: Complex) = add(that) def - (that: Complex) = subtract(that) def * (that: Complex) = multiply(that) def / (that: Complex) = divide(that) def abs = sqrt(re * re + im * im) } def draw() { for(y <- 0 until height; x <- 0 until width){ var zy = y * (yb - ya) / (height - 1) + ya var zx = x * (xb - xa) / (width - 1) + xa var z = Complex(zx, zy) for(i <- 0 until maxIt){ var dz = (f(z + Complex(h, h)) - f(z)) / Complex(h, h) var z0 = z - f(z) / dz if((z0 - z).abs < eps){ //break }else{ z = z0 stroke(color(i % 4 * 64, i % 8 * 32, i % 16 * 16)) point(x, y) } } } }
