Mandelbrot Set in Julia

mandelbrot.jl

using Images, Colors, ColorSchemes
using CuArrays, GPUArrays

# get the number of steps
function get_steps(c::Complex, max_steps)
    z = Complex(0.0, 0.0) # 0 + 0im
    for i=1:max_steps
        z = z*z+c
        if abs2(z) >= 4
            return i
        end
    end
    return max_steps+1
end

function get_color(colorscheme, step, max_steps)
    if step == max_steps+1
        return [0.0, 0.0, 0.0]
    end
    color = get(colorscheme, step, (1, max_steps))
    return [color.r, color.g, color.b]
end

function get_cmap(colorscheme, max_steps)
    colors = zeros(Float64, (3, max_steps+1))
    for i=1:max_steps 
        colors[:,i] = get_color(colorscheme, i, max_steps)
    end
    colors[:,max_steps+1] = [0.0, 0.0, 0.0]
    return colors
end

function mandelbrot_plot()
    width = 1000
    height = 600

    max_steps = 3500
    steps = zeros(Int, (height, width))
   
    # range for real values
    cr_min = -0.7491597623
    cr_max = -0.7491597623+0.0000000004

    # range for imaginary values
    ci_min = 0.1005089256
    
    range = cr_max - cr_min
    dot_size = range/width
    ci_max = ci_min + height*dot_size

    # println("cr: $cr_min - $cr_max")
    # println("ci: $ci_min - $ci_max")

    image = zeros(Float64, (3, height, width))
    complexes = zeros(ComplexF64, (height, width))
    steps = zeros(Int, (height, width))
    cu_steps = CuArray(zeros(Int, (height, width)))

    colorscheme = ColorSchemes.inferno
    colorscheme_sized = get_cmap(colorscheme, max_steps)
    x, y = 1,1
    for ci=ci_min:dot_size:ci_max-dot_size
        x = 1
        for cr=cr_min:dot_size:cr_max-dot_size
            complexes[y,x] = Complex(cr, ci)
            x += 1
        end
        y += 1
    end
    cu_complexes = CuArray(complexes)
    cu_steps .= get_steps.(cu_complexes, max_steps)
    GPUArrays.synchronize(cu_steps)
    steps = Array(cu_steps)
    
    image = colorscheme_sized[:, steps]
    
    save("images/test.bmp", colorview(RGB, image))
end

@time mandelbrot_plot();

Manifest.toml

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[[OffsetArrays]]
git-tree-sha1 = "a416e2f267e2c8729f25bcaf1ce19d2893faf393"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.3.1"

[[OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9db77584158d0ab52307f8c04f8e7c08ca76b5b3"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.3+4"

[[OrderedCollections]]
git-tree-sha1 = "cf59cfed2e2c12e8a2ff0a4f1e9b2cd8650da6db"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.3.2"

[[PaddedViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "91d229e113e8975a399e40d7c0b1ddf4da6d3c59"
uuid = "5432bcbf-9aad-5242-b902-cca2824c8663"
version = "0.5.7"

[[Parameters]]
deps = ["OrderedCollections", "UnPack"]
git-tree-sha1 = "38b2e970043613c187bd56a995fe2e551821eb4a"
uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
version = "0.12.1"

[[Pkg]]
deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[Random]]
deps = ["Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[RangeArrays]]
git-tree-sha1 = "b9039e93773ddcfc828f12aadf7115b4b4d225f5"
uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d"
version = "0.3.2"

[[Ratios]]
git-tree-sha1 = "37d210f612d70f3f7d57d488cb3b6eff56ad4e41"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.0"

[[Reexport]]
deps = ["Pkg"]
git-tree-sha1 = "7b1d07f411bc8ddb7977ec7f377b97b158514fe0"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "0.2.0"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "e05c53ebc86933601d36212a93b39144a2733493"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.1"

[[Rotations]]
deps = ["LinearAlgebra", "StaticArrays", "Statistics"]
git-tree-sha1 = "2ed8d8a16d703f900168822d83699b8c3c1a5cd8"
uuid = "6038ab10-8711-5258-84ad-4b1120ba62dc"
version = "1.0.2"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "daf7aec3fe3acb2131388f93a4c409b8c7f62226"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
version = "0.9.3"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures", "Random", "Test"]
git-tree-sha1 = "03f5898c9959f8115e30bc7226ada7d0df554ddd"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "0.3.1"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[SpecialFunctions]]
deps = ["OpenSpecFun_jll"]
git-tree-sha1 = "7286f31f27e3335cba31c618ac344a35eceac060"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "1.1.0"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "da4cf579416c81994afd6322365d00916c79b8ae"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "0.12.5"

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics"]
git-tree-sha1 = "7bab7d4eb46b225b35179632852b595a3162cb61"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.2"

[[Test]]
deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[TiledIteration]]
deps = ["OffsetArrays"]
git-tree-sha1 = "05f74c5b3c00d5336bc109416df2df907e3bd91d"
uuid = "06e1c1a7-607b-532d-9fad-de7d9aa2abac"
version = "0.2.5"

[[TimerOutputs]]
deps = ["Printf"]
git-tree-sha1 = "3318281dd4121ecf9713ce1383b9ace7d7476fdd"
uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
version = "0.5.7"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "59e2ad8fd1591ea019a5259bd012d7aee15f995c"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.3"

Project.toml

[deps]
ColorSchemes = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
CuArrays = "3a865a2d-5b23-5a0f-bc46-62713ec82fae"
GPUArrays = "0c68f7d7-f131-5f86-a1c3-88cf8149b2d7"
Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0"

[compat]
julia = "1.5"