This post explains how to generate a Mandelbrot set in parallel using Golang goroutines
.
Source code here: https://github.com/GiselaMD/parallel-mandelbrot-go
Mandelbrot Set
For those that are interest in what's a Mandelbrot set, check https://en.wikipedia.org/wiki/Mandelbrot_set
The set formula is based on the position of x
and y
coordinates:
x = x*x - y*y + a
y = 2*x*y + b
We also check if x*x + y*y > 4
to set the color.
But instead of going into math details, I would like to explain how we can use gourotines
to render that Mandelbrot set on the screen.
Getting into the code
This program is based on 4 main values that are going to impact the performance and resolution of the Mandelbrot set.
maxIter = 1000
samples = 200
numBlocks = 64
numThreads = 16
maxIter
defines how many times the mandelbrot formula will be calculated, resulting onx
andy
values.samples
is the number of interactions that generates RGB color values.numBlocks
is in how many pieces do you want to divide the image.numThreads
is the number ofgourotines
that will be created.
To render the result on the screen I've used the Pixel library (github.com/faiface/pixel). On the main function we have something like this:
func main() {
pixelgl.Run(run)
}
Calling pixelgl.Run puts PixelGL in control of the main function and there's no way for us to run any code in the main function anymore. That's why we need to pass another function inside pixelgl.Run, which is the run
function.
func run() {
log.Println("Initial processing...")
pixelCount = 0
img = image.NewRGBA(image.Rect(0, 0, imgWidth, imgHeight))
cfg := pixelgl.WindowConfig{
Title: "Parallel Mandelbrot in Go",
Bounds: pixel.R(0, 0, imgWidth, imgHeight),
VSync: true,
}
win, err := pixelgl.NewWindow(cfg)
if err != nil {
panic(err)
}
log.Println("Rendering...")
start := time.Now()
workBuffer := make(chan WorkItem, numBlocks)
threadBuffer := make(chan bool, numThreads)
drawBuffer := make(chan Pix, pixelTotal)
workBufferInit(workBuffer)
go workersInit(drawBuffer, workBuffer, threadBuffer)
go drawThread(drawBuffer, win)
for !win.Closed() {
pic := pixel.PictureDataFromImage(img)
sprite := pixel.NewSprite(pic, pic.Bounds())
sprite.Draw(win, pixel.IM.Moved(win.Bounds().Center()))
win.Update()
if showProgress {
fmt.Printf("\r%d/%d (%d%%)", pixelCount, pixelTotal, int(100*(float64(pixelCount)/float64(pixelTotal))))
}
if pixelCount == pixelTotal {
end := time.Now()
fmt.Println("\nFinished with time = ", end.Sub(start))
pixelCount++
if closeOnEnd {
break
}
}
}
}
The run
function is responsible for initialising and updating the window as well as creating the channels that will be used for our gourotines
.
The workBuffer
is the channel responsible for adding the information of each block (based on numBlocks
). Inside the workBufferInit
, the initial and final x
and y
values are sent to the channel so that each gourotines
that gets that piece of the image to work on can calculate the color without needing to know the global data, only what's the range of x
and y
of that block.
func workBufferInit(workBuffer chan WorkItem) {
var sqrt = int(math.Sqrt(numBlocks))
for i := sqrt - 1; i >= 0; i-- {
for j := 0; j < sqrt; j++ {
workBuffer <- WorkItem{
initialX: i * (imgWidth / sqrt),
finalX: (i + 1) * (imgWidth / sqrt),
initialY: j * (imgHeight / sqrt),
finalY: (j + 1) * (imgHeight / sqrt),
}
}
}
}
The threadBuffer
is responsible for creating goroutines
based on the numThreads
and controlling when a goroutine
is done with its work so we can run another in its place. That logic inside workersInit
goroutine
.
func workersInit(drawBuffer chan Pix, workBuffer chan WorkItem, threadBuffer chan bool) {
for i := 1; i <= numThreads; i++ {
threadBuffer <- true
}
for range threadBuffer {
workItem := <-workBuffer
go workerThread(workItem, drawBuffer, threadBuffer)
}
}
For each workItem
that we receive from the workBuffer
(each block) we create a goroutine
called workerThread
to handle all the Mandelbrot set logic.
func workerThread(workItem WorkItem, drawBuffer chan Pix, threadBuffer chan bool) {
for x := workItem.initialX; x < workItem.finalX; x++ {
for y := workItem.initialY; y < workItem.finalY; y++ {
var colorR, colorG, colorB int
for k := 0; k < samples; k++ {
a := height*ratio*((float64(x)+RandFloat64())/float64(imgWidth)) + posX
b := height*((float64(y)+RandFloat64())/float64(imgHeight)) + posY
c := pixelColor(mandelbrotIteraction(a, b, maxIter))
colorR += int(c.R)
colorG += int(c.G)
colorB += int(c.B)
}
var cr, cg, cb uint8
cr = uint8(float64(colorR) / float64(samples))
cg = uint8(float64(colorG) / float64(samples))
cb = uint8(float64(colorB) / float64(samples))
drawBuffer <- Pix{
x, y, cr, cg, cb,
}
}
}
threadBuffer <- true
}
func mandelbrotIteraction(a, b float64, maxIter int) (float64, int) {
var x, y, xx, yy, xy float64
for i := 0; i < maxIter; i++ {
xx, yy, xy = x*x, y*y, x*y
if xx+yy > 4 {
return xx + yy, i
}
// xn+1 = x^2 - y^2 + a
x = xx - yy + a
// yn+1 = 2xy + b
y = 2*xy + b
}
return xx + yy, maxIter
}
func pixelColor(r float64, iter int) color.RGBA {
insideSet := color.RGBA{R: 0, G: 0, B: 0, A: 255}
// check if it's inside the set
if r > 4 {
// return hslToRGB(float64(0.70)-float64(iter)/3500*r, 1, 0.5)
return hslToRGB(float64(iter)/100*r, 1, 0.5)
}
return insideSet
}
The drawBuffer
is the channel that receives the values from the goroutines
that are calculating the Mandelbrot set and once it receives data, the drawThread
goroutine
sets the pixel RGB value into the image and then the run
function updates the window.
func drawThread(drawBuffer chan Pix, win *pixelgl.Window) {
for i := range drawBuffer {
img.SetRGBA(i.x, i.y, color.RGBA{R: i.cr, G: i.cg, B: i.cb, A: 255})
pixelCount++
}
}
We also have some utils functions for generating random data and converting hsl and hue to RGB:
var randState = uint64(time.Now().UnixNano())
func RandUint64() uint64 {
randState = ((randState ^ (randState << 13)) ^ (randState >> 7)) ^ (randState << 17)
return randState
}
func RandFloat64() float64 {
return float64(RandUint64() / 2) / (1 << 63)
}
func hueToRGB(p, q, t float64) float64 {
if t < 0 { t += 1 }
if t > 1 { t -= 1 }
switch {
case t < 1.0 / 6.0:
return p + (q - p) * 6 * t
case t < 1.0 / 2.0:
return q
case t < 2.0 / 3.0:
return p + (q - p) * (2.0 / 3.0 - t) * 6
default:
return p
}
}
func hslToRGB(h, s, l float64) color.RGBA {
var r, g, b float64
if s == 0 {
r, g, b = l, l, l
} else {
var q, p float64
if l < 0.5 {
q = l * (1 + s)
} else {
q = l + s - l * s
}
p = 2 * l - q
r = hueToRGB(p, q, h + 1.0 / 3.0)
g = hueToRGB(p, q, h)
b = hueToRGB(p, q, h - 1.0 / 3.0)
}
return color.RGBA{ R: uint8(r * 255), G: uint8(g * 255), B: uint8(b * 255), A: 255 }
}
That's it for today!
Hope you enjoy it 😊
🇧🇷 This post is also available in Portuguese published by Daniel who collaborated in this project. Check his post: https://danielferreiradev.medium.com/fractal-de-mandelbrot-paralelo-usando-golang-4ba497d9bbc5
Source code here: https://github.com/GiselaMD/parallel-mandelbrot-go
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