add mandelbrot

src/mandelbrot/main.go

@@ -0,0 +1,79 @@
+// Copyright © 2016 Alan A. A. Donovan & Brian W. Kernighan.
+// License: https://creativecommons.org/licenses/by-nc-sa/4.0/
+
+// Mandelbrot emits a PNG image of the Mandelbrot fractal.
+package main
+
+import (
+	"image"
+	"image/color"
+	"image/png"
+	"math/cmplx"
+	"os"
+)
+
+func main() {
+	const (
+		xmin, ymin, xmax, ymax = -2, -2, +2, +2
+		width, height          = 1024, 1024
+	)
+
+	img := image.NewRGBA(image.Rect(0, 0, width, height))
+	for py := 0; py < height; py++ {
+		y := float64(py)/height*(ymax-ymin) + ymin
+		for px := 0; px < width; px++ {
+			x := float64(px)/width*(xmax-xmin) + xmin
+			z := complex(x, y)
+			// Image point (px, py) represents complex value z.
+			img.Set(px, py, mandelbrot(z))
+		}
+	}
+	png.Encode(os.Stdout, img) // NOTE: ignoring errors
+}
+
+func mandelbrot(z complex128) color.Color {
+	const iterations = 200
+	const contrast = 15
+
+	var v complex128
+	for n := uint8(0); n < iterations; n++ {
+		v = v*v + z
+		if cmplx.Abs(v) > 2 {
+			return color.Gray{255 - contrast*n}
+		}
+	}
+	return color.Black
+}
+
+
+// Some other interesting functions:
+func acos(z complex128) color.Color {
+	v := cmplx.Acos(z)
+	blue := uint8(real(v)*128) + 127
+	red := uint8(imag(v)*128) + 127
+	return color.YCbCr{192, blue, red}
+}
+
+func sqrt(z complex128) color.Color {
+	v := cmplx.Sqrt(z)
+	blue := uint8(real(v)*128) + 127
+	red := uint8(imag(v)*128) + 127
+	return color.YCbCr{128, blue, red}
+}
+
+// f(x) = x^4 - 1
+//
+// z' = z - f(z)/f'(z)
+//    = z - (z^4 - 1) / (4 * z^3)
+//    = z - (z - 1/z^3) / 4
+func newton(z complex128) color.Color {
+	const iterations = 37
+	const contrast = 7
+	for i := uint8(0); i < iterations; i++ {
+		z -= (z - 1/(z*z*z)) / 4
+		if cmplx.Abs(z*z*z*z-1) < 1e-6 {
+			return color.Gray{255 - contrast*i}
+		}
+	}
+	return color.Black
+}