Julia

Julia.jl

using ColorSchemes, Images, FileIO
# and possibly QuartzImageIO (macOS) and/or ImageMagick (Linux)

function julia(z, c, maxiter::Int64)
    for n = 1:maxiter
        if abs(z) > 2
            return n
        end
        z = z^2 + c
    end
    return maxiter
end

# convert a value between oldmin/oldmax to equivalent value between newmin/newmax
remap(value, oldmin, oldmax, newmin, newmax) = ((value - oldmin) / (oldmax - oldmin)) * (newmax - newmin) + newmin

function draw(c, imsize;
      xmin = -1, ymin = -1, xmax  =  1, ymax = 1,
      filename = "julia-set.png")
    imOutput = zeros(RGB{Float32}, imsize, imsize)
    maxiterations = 200
    for col = range(xmin, stop=xmax, length=imsize)
        for row = range(ymin, stop=ymax, length=imsize)
            pixelcolor = julia(complex(row, col), c, maxiterations) / 256
            xpos = convert(Int, round(remap(col, xmin, xmax, 1, imsize)))
            ypos = convert(Int, round(remap(row, ymin, ymax, 1, imsize)))
            imOutput[xpos, ypos] = get(ColorSchemes.vermeer, pixelcolor)
        end
    end
    save(filename, imOutput)
end

draw(-0.4 + 0.6im, 1200)



#################



using Images, Colors, ImageMagick, Interact

const cmap = convert(Array{FixedPointNumbers.Normed{UInt8,8},2}, colormap("RdBu",100)) 
const maxiter = 100

function julia(z,c)
    for n = 1:maxiter
        abs2(z) > 4 && return n-1
        z = z*z + c
    end
    return maxiter
end

julia(.4+.5im, .6+.7im)

let I = -1:.005:1, R = -1:.005:1
data = Array{FixedPointNumbers.Normed{UInt8,8},2}(undef,length(I),length(R))
    img = ImageMeta(data)
    @manipulate for r_ = -0.1:.01:0.1, i_ = .065:.01:85
        for (j,i) in enumerate(I),(k,r) in enumerate(R)
            data[j,k] = Array{FixedPointNumbers.Normed{UInt8,8},2}[julia(r+i*im, r_+i_*im)]
        end
        img
    end
end