Julia Fractals via inverse iteration

julia.jl

using Colors
using ColorVectorSpace
using FileIO
using REPL
using ImageTransformations
using ImageView

@inline function inv_julia_map(z, c, n)
    ws = (1.0, exp(2/3*pi*im), exp(-2/3*pi*im))
    ws[n]*(z - c)^(1/3)
end

@inline function map_color(color, colors, n)
    weight = 0.7
    weight*colors[n] + (1-weight)*color
end

@inline function iter((z,color), n, c, colors)
    z2 = inv_julia_map(z, c, n)
    color2 = map_color(color, colors, n)
    (z2, color2)
end

function tone_map(col, exposure, exponent)
    if col == RGB(0,0,0)
        return col
    end
    a = xyY(col)
    Y = a.Y
    Y = exposure*Y^exponent
    Y = Y / (1 + Y)
    c = xyY(a.x, a.y, Y)
    typeof(col)(c)
end

function gen_samples(c, xrange, yrange, hdr_exposure, hdr_exponent)
    Col = RGB{Float32}
    julia_purple  = Col(0.584, 0.345, 0.698)
    julia_green   = Col(0.22, 0.596, 0.149)
    julia_red     = Col(0.796, 0.235, 0.2)

    colors = (julia_purple, julia_green, julia_red)

    colored_set = fill(Col(0,0,0), length(xrange), length(yrange))
    hit_counter = fill(UInt8(0), length(xrange), length(yrange))

    hitmax = 20

    state = (0.0 + 0.0im, RGB(0.0,0.0,0.0))
    # Find a point on the attractor
    for i=1:1000
        n = 1
        state = iter(state, n, c, colors)
    end
    to_explore = [state]
    eps_x = step(xrange)/100
    eps_y = step(xrange)/100
    invdx = inv(step(xrange))
    invdy = inv(step(yrange))
    # Determenistically draw a tree of samples from the attractor but avoid
    # sampling the same points. Somewhat inspired by
    # https://www.marksmath.org/scholarship/Julia.pdf
    while !isempty(to_explore)
        state = pop!(to_explore)
        z,col = state
        ix = round(Int, (real(z) - first(xrange))*invdx)
        iy = round(Int, (imag(z) - first(yrange))*invdy)
        if !(1 <= ix <= length(xrange) && 1 <= iy <= length(yrange))
            # Hack: only keep points which remain inside the plot - otherwise
            # we can't bound the growth of to_explore
            @warn "Dropped point $z outside plot range"
            continue
        end
        if hit_counter[ix, iy] < hitmax
            hit_counter[ix, iy] += 1
            colored_set[ix, iy] += col
            push!(to_explore, iter(state, 1, c, colors))
            push!(to_explore, iter(state, 2, c, colors))
            push!(to_explore, iter(state, 3, c, colors))
            # Generate new points from trajectories which explore new parts of
            # the space.
            #=
            for i=-1:1
                for j=-1:1
                    z2 = z + i*eps_x + j*eps_y*im
                    s = (z2,col)
                    push!(to_explore, iter(s, 1, c, colors))
                    push!(to_explore, iter(s, 2, c, colors))
                    push!(to_explore, iter(s, 3, c, colors))
                end
            end
            =#
        end
    end
    tone_map.(colored_set, hdr_exposure, hdr_exponent)
end


function loop_with_arrow_keys(f)
    term = REPL.TerminalMenus.terminal
    raw_mode_enabled = REPL.TerminalMenus.enableRawMode(term)
    try
        # Approach stolen from TerminalMenus
        raw_mode_enabled && print(term.out_stream, "\x1b[?25l") # hide the cursor
        result = nothing
        increment = (0,0)
        while true
            k = REPL.TerminalMenus.readKey()
            if k == 3 # CTRL_C
                break
            end
            inc = k == Int(REPL.TerminalMenus.ARROW_UP)    ? (0,  1) :
                  k == Int(REPL.TerminalMenus.ARROW_DOWN)  ? (0, -1) :
                  k == Int(REPL.TerminalMenus.ARROW_LEFT)  ? (-1, 0) :
                  k == Int(REPL.TerminalMenus.ARROW_RIGHT) ? (1,  0) :
                  (0,0)
            increment = increment .+ inc
            if bytesavailable(term.in_stream) == 0
                # Avoid input lag
                result = f(increment, Char(k))
                increment = (0,0)
            end
        end
        return result
    finally
        if raw_mode_enabled
            print(term.out_stream, "\x1b[?25h") # unhide cursor
            REPL.TerminalMenus.disableRawMode(term)
        end
    end
end


len = 1000
xrange = range(-1.3, 1.3, length=len)
yrange = range(-1.3, 1.3, length=len)

#c = -0.45 + 0.75im
#c = -0.23 + 0.72im
#c = -0.22 + 0.73im
#c = -0.09 + 0.79im
#c = -0.1  + 0.79im
#c = -0.16 + 0.75im
c = -0.067 + 0.766im
#c = -0.033 + 0.769im
@info "Drawing julia set" c
incsize = 0.0001
hdr_exposure = 0.5f0
hdr_exponent = 0.5f0
colored_set = gen_samples(c, xrange, yrange, hdr_exposure, hdr_exponent)
guidict = imshow(colored_set)
loop_with_arrow_keys() do increment, key
    global colored_set, c, hdr_exposure, hdr_exponent
    if key == 's'
        save("julia.png", (colored_set))
        return
    end
    if key == ']'
        hdr_exposure *= 2.0f0
    elseif key == '['
        hdr_exposure /= 2.0f0
    end
    if key == ')'
        hdr_exponent *= 2.0f0
    elseif key == '('
        hdr_exponent /= 2.0f0
    end
    c += incsize*(increment[1] + im*increment[2])
    @info "Drawing julia set" c hdr_exposure hdr_exponent
    colored_set = gen_samples(c, xrange, yrange, hdr_exposure, hdr_exponent)
    imshow!(guidict["gui"]["canvas"], colored_set)
end
ImageView.Gtk.destroy(guidict["gui"]["window"])

julia.png

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git-tree-sha1 = "159e24b4313d9197eef900e97fbd7365986f2844"
uuid = "51556ac3-7006-55f5-8cb3-34580c88182d"
version = "0.2.10"

[[ImageFiltering]]
deps = ["CatIndices", "ColorVectorSpace", "ComputationalResources", "DataStructures", "FFTViews", "FFTW", "ImageCore", "ImageMetadata", "LinearAlgebra", "OffsetArrays", "Requires", "SparseArrays", "StaticArrays", "Statistics", "TiledIteration"]
git-tree-sha1 = "f82a52fa2e684d4ed69028b16188852ff94b3f75"
uuid = "6a3955dd-da59-5b1f-98d4-e7296123deb5"
version = "0.6.19"

[[ImageMetadata]]
deps = ["AxisArrays", "ColorVectorSpace", "ImageAxes", "ImageCore", "IndirectArrays"]
git-tree-sha1 = "ff77c7f234e7d8a618958fcf23b6959f2cbef2c6"
uuid = "bc367c6b-8a6b-528e-b4bd-a4b897500b49"
version = "0.9.4"

[[ImageMorphology]]
deps = ["ColorVectorSpace", "ImageCore", "LinearAlgebra", "TiledIteration"]
git-tree-sha1 = "113df7743f1e18da5f5ea5f98eb59ceb77092734"
uuid = "787d08f9-d448-5407-9aad-5290dd7ab264"
version = "0.2.9"

[[ImageQualityIndexes]]
deps = ["ColorVectorSpace", "ImageCore", "ImageDistances", "ImageFiltering", "OffsetArrays", "Statistics"]
git-tree-sha1 = "80484f9e1beae36860ed8022f195d04c751cfec6"
uuid = "2996bd0c-7a13-11e9-2da2-2f5ce47296a9"
version = "0.2.1"

[[ImageShow]]
deps = ["Base64", "FileIO", "ImageCore", "Requires"]
git-tree-sha1 = "c9df184bc7c2e665f971079174aabb7d18f1845f"
uuid = "4e3cecfd-b093-5904-9786-8bbb286a6a31"
version = "0.2.3"

[[ImageTransformations]]
deps = ["AxisAlgorithms", "ColorVectorSpace", "CoordinateTransformations", "IdentityRanges", "ImageCore", "Interpolations", "OffsetArrays", "Rotations", "StaticArrays"]
git-tree-sha1 = "0426a62ca1a23f3b1ee75cc0e47320d859abd6ae"
uuid = "02fcd773-0e25-5acc-982a-7f6622650795"
version = "0.8.9"

[[ImageView]]
deps = ["AxisArrays", "Cairo", "Graphics", "Gtk", "GtkReactive", "Images", "RoundingIntegers", "StatsBase"]
git-tree-sha1 = "0ff703f031fa7c63b110931b8fa49a287d62391e"
uuid = "86fae568-95e7-573e-a6b2-d8a6b900c9ef"
version = "0.10.13"

[[Images]]
deps = ["AxisArrays", "Base64", "ColorVectorSpace", "FileIO", "Graphics", "ImageAxes", "ImageContrastAdjustment", "ImageCore", "ImageDistances", "ImageFiltering", "ImageMetadata", "ImageMorphology", "ImageQualityIndexes", "ImageShow", "ImageTransformations", "IndirectArrays", "OffsetArrays", "Random", "Reexport", "SparseArrays", "StaticArrays", "Statistics", "StatsBase", "TiledIteration"]
git-tree-sha1 = "535bcaae047f017f4fd7331ee859b75f2b27e505"
uuid = "916415d5-f1e6-5110-898d-aaa5f9f070e0"
version = "0.23.3"

[[IndirectArrays]]
git-tree-sha1 = "c2a145a145dc03a7620af1444e0264ef907bd44f"
uuid = "9b13fd28-a010-5f03-acff-a1bbcff69959"
version = "0.5.1"

[[IntelOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d979e54b71da82f3a65b62553da4fc3d18c9004c"
uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
version = "2018.0.3+2"

[[InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

[[Interpolations]]
deps = ["AxisAlgorithms", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
git-tree-sha1 = "eb1dd6d5b2275faaaa18533e0fc5f9171cec25fa"
uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
version = "0.13.1"

[[IntervalSets]]
deps = ["Dates", "EllipsisNotation", "Statistics"]
git-tree-sha1 = "93a6d78525feb0d3ee2a2ae83a7d04db1db5663f"
uuid = "8197267c-284f-5f27-9208-e0e47529a953"
version = "0.5.2"

[[IterTools]]
git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.3.0"

[[JLLWrappers]]
git-tree-sha1 = "a431f5f2ca3f4feef3bd7a5e94b8b8d4f2f647a0"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.2.0"

[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9aff0587d9603ea0de2c6f6300d9f9492bbefbd3"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.0.1+3"

[[LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f128cd6cd05ffd6d3df0523ed99b90ff6f9b349a"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.0+3"

[[LazyArtifacts]]
deps = ["Pkg"]
git-tree-sha1 = "4bb5499a1fc437342ea9ab7e319ede5a457c0968"
uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
version = "1.3.0"

[[LibGit2]]
deps = ["Printf"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

[[Libepoxy_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "aeac8ae441bc55be433ab53b729ffac274997320"
uuid = "42c93a91-0102-5b3f-8f9d-e41de60ac950"
version = "1.5.4+1"

[[Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "a2cd088a88c0d37eef7d209fd3d8712febce0d90"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.1+4"

[[Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
git-tree-sha1 = "b391a18ab1170a2e568f9fb8d83bc7c780cb9999"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.5+4"

[[Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.3.0+3"

[[Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ec7f2e8ad5c9fa99fc773376cdbc86d9a5a23cb7"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.36.0+3"

[[Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "8e924324b2e9275a51407a4e06deb3455b1e359f"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.0+7"

[[Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51ad0c01c94c1ce48d5cad629425035ad030bfd5"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.34.0+3"

[[Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "291dd857901f94d683973cdf679984cdf73b56d0"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.1.0+2"

[[Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f879ae9edbaa2c74c922e8b85bb83cc84ea1450b"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.34.0+7"

[[LinearAlgebra]]
deps = ["Libdl"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
git-tree-sha1 = "c253236b0ed414624b083e6b72bfe891fbd2c7af"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
version = "2021.1.1+1"

[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "6a8a2a625ab0dea913aba95c11370589e0239ff0"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.6"

[[MappedArrays]]
deps = ["FixedPointNumbers"]
git-tree-sha1 = "b92bd220c95a8bbe89af28f11201fd080e0e3fe7"
uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
version = "0.3.0"

[[Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "f8c673ccc215eb50fcadb285f522420e29e69e1c"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "0.4.5"

[[Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[MosaicViews]]
deps = ["MappedArrays", "OffsetArrays", "PaddedViews"]
git-tree-sha1 = "614e8d77264d20c1db83661daadfab38e8e4b77e"
uuid = "e94cdb99-869f-56ef-bcf0-1ae2bcbe0389"
version = "0.2.4"

[[NaNMath]]
git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "0.3.5"

[[OffsetArrays]]
deps = ["Adapt"]
git-tree-sha1 = "986e7c0a0ef1863be969d191957ac32cb17d0d79"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.6.0"

[[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 = "4fa2ba51070ec13fcc7517db714445b4ab986bdf"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.0"

[[PCRE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "1b556ad51dceefdbf30e86ffa8f528b73c7df2bb"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
version = "8.42.0+4"

[[PaddedViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "0fa5e78929aebc3f6b56e1a88cf505bb00a354c4"
uuid = "5432bcbf-9aad-5242-b902-cca2824c8663"
version = "0.5.8"

[[Pango_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9a336dee51d20d1ed890c4a8dca636e86e2b76ca"
uuid = "36c8627f-9965-5494-a995-c6b170f724f3"
version = "1.42.4+10"

[[Parameters]]
deps = ["OrderedCollections", "UnPack"]
git-tree-sha1 = "2276ac65f1e236e0a6ea70baff3f62ad4c625345"
uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
version = "0.12.2"

[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6a20a83c1ae86416f0a5de605eaea08a552844a3"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.0+0"

[[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"

[[Reactive]]
deps = ["DataStructures", "Distributed", "Test"]
git-tree-sha1 = "5862d915387ebb954016f50a88e34f79a9e5fcd2"
uuid = "a223df75-4e93-5b7c-acf9-bdd599c0f4de"
version = "0.8.3"

[[Reexport]]
git-tree-sha1 = "57d8440b0c7d98fc4f889e478e80f268d534c9d5"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.0.0"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "cfbac6c1ed70c002ec6361e7fd334f02820d6419"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.2"

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

[[RoundingIntegers]]
deps = ["Test"]
git-tree-sha1 = "293ba0ab32218b9ffd596040224228def84f8da0"
uuid = "d5f540fe-1c90-5db3-b776-2e2f362d9394"
version = "0.2.0"

[[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 = ["ChainRulesCore", "OpenSpecFun_jll"]
git-tree-sha1 = "5919936c0e92cff40e57d0ddf0ceb667d42e5902"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "1.3.0"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "9da72ed50e94dbff92036da395275ed114e04d49"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.0.1"

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

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics"]
git-tree-sha1 = "400aa43f7de43aeccc5b2e39a76a79d262202b76"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.3"

[[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"

[[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"

[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "dc643a9b774da1c2781413fd7b6dcd2c56bb8056"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.17.0+4"

[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"]
git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.18.0+4"

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

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "be0db24f70aae7e2b89f2f3092e93b8606d659a6"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.10+3"

[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "2b3eac39df218762d2d005702d601cd44c997497"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.33+4"

[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[Xorg_libXcomposite_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll"]
git-tree-sha1 = "7c688ca9c957837539bbe1c53629bb871025e423"
uuid = "3c9796d7-64a0-5134-86ad-79f8eb684845"
version = "0.4.5+4"

[[Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[Xorg_libXdamage_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll"]
git-tree-sha1 = "fe4ffb2024ba3eddc862c6e1d70e2b070cd1c2bf"
uuid = "0aeada51-83db-5f97-b67e-184615cfc6f6"
version = "1.1.5+4"

[[Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[Xorg_libXtst_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll", "Xorg_libXi_jll"]
git-tree-sha1 = "0c0a60851f44add2a64069ddf213e941c30ed93c"
uuid = "b6f176f1-7aea-5357-ad67-1d3e565ea1c6"
version = "1.2.3+4"

[[Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[Zlib_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "320228915c8debb12cb434c59057290f0834dbf6"
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.11+18"

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "2c1332c54931e83f8f94d310fa447fd743e8d600"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.4.8+0"

[[adwaita_icon_theme_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "hicolor_icon_theme_jll"]
git-tree-sha1 = "37c9a36ccb876e02876c8a654f1b2e8c1b443a78"
uuid = "b437f822-2cd6-5e08-a15c-8bac984d38ee"
version = "3.33.92+5"

[[at_spi2_atk_jll]]
deps = ["ATK_jll", "Artifacts", "JLLWrappers", "Libdl", "Pkg", "XML2_jll", "Xorg_libX11_jll", "at_spi2_core_jll"]
git-tree-sha1 = "f16ae690aca4761f33d2cb338ee9899e541f5eae"
uuid = "de012916-1e3f-58c2-8f29-df3ef51d412d"
version = "2.34.1+4"

[[at_spi2_core_jll]]
deps = ["Artifacts", "Dbus_jll", "Glib_jll", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXtst_jll"]
git-tree-sha1 = "d2d540cd145f2b2933614649c029d222fe125188"
uuid = "0fc3237b-ac94-5853-b45c-d43d59a06200"
version = "2.34.0+4"

[[gdk_pixbuf_jll]]
deps = ["Artifacts", "Glib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pkg", "Xorg_libX11_jll", "libpng_jll"]
git-tree-sha1 = "031f60d4362fba8f8778b31047491823f5a73000"
uuid = "da03df04-f53b-5353-a52f-6a8b0620ced0"
version = "2.38.2+9"

[[hicolor_icon_theme_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b458a6f6fc2b1a8ca74ed63852e4eaf43fb9f5ea"
uuid = "059c91fe-1bad-52ad-bddd-f7b78713c282"
version = "0.17.0+3"

[[iso_codes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "5ee24c3ae30e006117ec2da5ea50f2ce457c019a"
uuid = "bf975903-5238-5d20-8243-bc370bc1e7e5"
version = "4.3.0+4"

[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "6abbc424248097d69c0c87ba50fcb0753f93e0ee"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.37+6"

[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"

Project.toml

[deps]
ColorVectorSpace = "c3611d14-8923-5661-9e6a-0046d554d3a4"
Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
ImageTransformations = "02fcd773-0e25-5acc-982a-7f6622650795"
ImageView = "86fae568-95e7-573e-a6b2-d8a6b900c9ef"
REPL = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"