Domain colouring

using Colors, Images

x_max = 1.2
x_min = -x_max
y_max = x_max
y_min = -y_max
width = 1920
height = width

function f(z)
    return z^5 + im*z^6*conj(z) - z^3/(conj(z)^2) + im*z^7*conj(z)^6
end

function coloured(z)
    θ = angle(z)
    # Convert from [-pi,pi] to [0,2pi]
    if θ < 0
        θ += 2pi
    end

    h = 180/pi*θ % 360
    s = 1
    # Circles
    v1 = abs(z)%1*0.2 + 0.8
    # Radial lines
    v2 = (θ/2pi)%0.125 + 0.875
    # Uncomment for more contrast
    v1 = abs(z)%1
    v2 = (θ/2pi)%0.125 *8
    v = (v1+v2)/2

    return HSV(h,s,v)
end


image = Array{Union{Nothing,HSV}}(nothing, height, width)

for j in 1:height
    for i in 1:width
        x = (x_max-x_min)*(j-width/2)/width
        y = (y_max-y_min)*(i-height/2)/height

        # Iterate function
        pt = x + y*im
        for k in 1:1 # only iterating once for now
            pt = f(pt)
        end
        colour = coloured(pt)

        # Incase we divide by zero
        if isnan(colour.h)
            colour = HSV(0, colour.s, colour.v)
        end

        if isnan(colour.v)
            colour = HSV(colour.h, colour.s, 0)
        end

        image[i, j] = colour
    end
end

save("out.png", image)