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// 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
}