gopl-zh.github.com/vendor/gopl.io/ch3/mandelbrot/main.go

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2015-12-09 07:45:11 +00:00
// Copyright © 2016 Alan A. A. Donovan & Brian W. Kernighan.
// License: https://creativecommons.org/licenses/by-nc-sa/4.0/
// See page 61.
//!+
// 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
}