85 lines
1.7 KiB
Go
85 lines
1.7 KiB
Go
// 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
|
|
}
|