filled julia set with split complex numbers

juliaset_splitcomplex.jl

### A Pluto.jl notebook ###
# v0.19.36

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ 27baa396-c91b-4e95-838e-b65457a9767e
begin
	using Plots
	using RecipesBase
	using PlutoUI
	using LaTeXStrings

	default(dpi = 150, fontfamily = "Computer Modern", framestyle = :box, grid = false, label = false)
	TableOfContents()
end

# ╔═╡ 0d223560-c436-11ee-1237-fbfdf4242bbd
md"# Julia sets with Split Complex Numbers"

# ╔═╡ e318abdf-493b-4565-870c-49e08637ed96
md"""## Defining the Split Complex Numbers Type

First we wanna make working with split complex numbers easier. So we'll define a `Split{T}` type and define the addition, subtraction, multiplication, division and exponentiation on it. It is possible to never touch split complex numbers throughout this excercise and just work with the matrix group

$\left(\begin{matrix}a & b \\ b & a \end{matrix}\right)$

however where's the fun in that? First things first, lets define the type and then the basic operations on that type that we expect from complex numbers.
"""

# ╔═╡ 49b3f758-a678-4d08-97d4-972cf381ec6c
begin
	import Base:zero
	struct Split{T <: Real} <: Number
		re::T
		im::T
	end
	Split(A::Real, B::Real) = Split(promote(A,B)...)
	Split(A::Real) = Split(A, zero(A))
	zero(::Split) = Split(0, 0)
end

# ╔═╡ 733039ba-cf35-4039-9107-3fffa242ec34
const j = Split(false, true)

# ╔═╡ dd04a81c-d5ae-4295-a247-74f5e38be4c4
md"""And the four basic operations. These are, given $z = a+bj$ and $w = c + dj$ we have

- $(a+bj) + (c+dj)  = (a+c) + (b + d)j$
- $(a+bj) - (c+dj) = (a - c) + (b - d)j$
- $(a+bj)(c+dj)  = ac + bd + (ad + bc)j$
- $(a+bj)/(c+dj) = (a+bj)(c-dj) / (c^2 - d^2)$

"""

# ╔═╡ 362d3609-b14a-46c0-aa13-6392bc45a920
begin
	import Base:+,-,*,/,^,inv,real,imag,conj,abs2,abs,isfinite,==
	
	+(A::Split, B::Split) = Split(A.re + B.re, A.im + B.im)
	+(A::Split, B::T) where {T <: Real} = Split(A.re + B, A.im)
	+(B::T, A::Split) where {T <: Real} = A + B
	
	-(A::Split, B::Split) = Split(A.re - B.re, A.im - B.im)
	-(A::Split, B::T) where {T <: Real} = Split(A.re - B, A.im)
	-(A::Split) = Split(-A.re, -A.im)
	-(B::T, A::Split) where {T <: Real} = -A + B
	
	*(A::Split, B::T) where {T <: Real} = Split(A.re * B, A.im * B)
	*(B::T, A::Split) where {T <: Real} = Split(A.re * B, A.im * B)
	*(A::Split, B::Split) = Split(A.re*B.re + A.im * B.im, A.re * B.im + A.im * B.re)
	
	conj(A::Split) = Split(A.re, -A.im)
	real(A::Split) = A.re
	imag(A::Split) = A.im
	abs2(A::Split) = A.re^2 - A.im^2
	
	/(A::Split, B::T) where {T <: Real} = Split(A.re / B, A.im / B)
	inv(A::Split) = conj(A) / abs2(A)
	/(B::T, A::Split) where {T <: Real} = inv(A) * B
	/(A::Split, B::Split) = A * conj(B) / abs2(B)

	# Taken from Julia sourcecode
	# https://github.com/JuliaLang/julia/blob/3120989f39bb7ef7863c4aab8ab1227cf71eec66/base/complex.jl#L244C1-L246C52
	==(z::Split, w::Split) = (real(z) == real(w)) & (imag(z) == imag(w))
	==(z::Split, x::Real) = isreal(z) && real(z) == x
	==(x::Real, z::Split) = isreal(z) && real(z) == x

	isfinite(A::Split) = isfinite(A.re) && isfinite(A.im)
end

# ╔═╡ 58f4923f-2a6b-4ee2-94e5-6c2f25d18017
begin
	import Base:show
	show(io::IO, A::Split) = imag(A) < 0 ? print(io, "$(A.re) - $(-A.im)j") : print(io, "$(A.re) + $(A.im)j")
end

# ╔═╡ 1de55eae-00f2-4cb4-a1ba-f642f37380c4
inv(1im)

# ╔═╡ e5c9de9b-a3eb-4e4c-87ba-c327609bb479
md"Lets quickly test these"

# ╔═╡ 4c5e82c5-ae40-4011-9834-89bcd10e3415
let
	z = 1 + 2.0j
	w = -2 - 5j

	println("z + w = $(z + w)")
	println("z - w = $(z - w)")
	println("z * w = $(z * w)")
	println("z / w = $(z / w)")
	println("Re(z) = $(real(z))")
	println("Im(w) = $(imag(w))")
	println("conj(z) = $(conj(w))")
	println("|z|² = $(abs2(z))")
end

# ╔═╡ d86d260c-f158-45cd-a2e8-efc0e8fb5279
md"""And we have our algebra! Now to generate julia sets.

## Filled Julia Set

Given a function $f(z)$ where $z \in \mathbb{D}$ (split complex numbers), the julia set $K$ of $f$ are the set of all split complex numbers that *stay bounded* when iterated under $f$. That is to say, if one were to apply the function $f^k = (f \circ f \circ \ldots k \ \textrm{times} \ldots \circ f)$ to some point $z$, if $\|z\|$ stays bounded as $k \to \infty$, then it is an element of $K$.

For this implementation, we'll keep track of the *norm squared*, rather than the norm, since the norm of a split complex number can be negative."""

# ╔═╡ 617358bb-b384-40d8-9733-6f44018b5864
# I'm not implementing _cpow for my special type
f(z) = z*z*z + 3j

# ╔═╡ 1924d662-08f3-441b-b3dc-569f0dc2d97d
function julia_set(f::Function, xlims, ylims; npts = 100, niter = 100, maglim = 100)
	x = range(xlims..., length = npts)
	y = range(ylims..., length = npts)

	z = map(x -> 1j * x, zeros(npts, npts))
	for I in CartesianIndices(z)
		yi = I[1]
		xi = I[2]

		z[I] = x[xi] + y[yi]*j
	end
	z  = reverse!(z; dims = 1)
	z′ = copy(z)
	itercount = zeros(Int, npts, npts)
	
	for _ in 1:niter
		# Find all that have magnetude within [-lim, lim]
		M = abs2.(z)
		idxs = findall(x -> -maglim < x < maglim, M)
		
		# These numbers survive one more iteration
		itercount[idxs] .+= 1
		
		map!(f, view(z′, idxs), view(z, idxs))
		z = z′
	end
	return z′, itercount
end

# ╔═╡ 4155afc4-03eb-4774-b685-cb473f6bdca5
md"Awesome! Now to do this for $z^2 + c$"

# ╔═╡ 5b21ccb2-0db4-4751-8e70-b91d3b54b663
@bind c_real Slider(-10:0.01:10, show_value = true)

# ╔═╡ fd9dfe25-814c-4164-8aeb-0e2ed33e74d7
@bind c_imag Slider(-10:0.01:10, show_value = true)

# ╔═╡ ee0cc683-0150-46e7-a38d-3ab0bc029f0d
begin
	xmin, xmax = (-3, 3)
	ymin, ymax = (-3, 3)
	c_re = round(c_real, digits = 2)
	c_im = round(c_imag, digits = 2)
	sgn = Dict(true => "-", false => "+")
	s1 = sgn[signbit(c_re)]
	s2 = sgn[signbit(c_im)]
	niter = 30
	npts = 200
	M, M_i = julia_set(z -> z*z + c_real + c_imag*j, (xmin, xmax), (ymin, ymax); npts = npts, niter = niter)
	# M = log.(exp.(abs2.(M)))
	
	heatmap(range(xmin, xmax, npts), range(ymin, ymax, npts), 1 ./ M_i, xlim = (xmin, xmax), ylim = (ymin, ymax), alpha = 0.9, title = L"Plot of $f(z) = (z^2 %$(s1) %$(abs(c_re)) %$(s2) %$(abs(c_im)) j)^{10}$", colorbar_title = "1 / Number of interations it takes to explode", aspect_ratio = :equal )
	θ = range(-π, π, length = 1000)
	plot!(cosh.(θ), sinh.(θ), color = :black, linewidth = 3)
	plot!(-cosh.(θ), sinh.(θ), color = :black, linewidth = 3)
	plot!(sinh.(θ), -cosh.(θ), color = :black, linewidth = 3)
	plot!(sinh.(θ), cosh.(θ), color = :black, linewidth = 3)
	vline!([0], color = :black)
	hline!([0], color = :black)
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"

[compat]
LaTeXStrings = "~1.3.1"
Plots = "~1.40.0"
PlutoUI = "~0.7.55"
RecipesBase = "~1.3.4"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

julia_version = "1.10.0"
manifest_format = "2.0"
project_hash = "039d8087704b6ada8bd335c147f56c3d5d9b5a25"

[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "c278dfab760520b8bb7e9511b968bf4ba38b7acc"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.2.3"

[[deps.ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.1"

[[deps.Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"

[[deps.Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[deps.BitFlags]]
git-tree-sha1 = "2dc09997850d68179b69dafb58ae806167a32b1b"
uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
version = "0.1.8"

[[deps.Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9e2a6b69137e6969bab0152632dcb3bc108c8bdd"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+1"

[[deps.Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+1"

[[deps.CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "59939d8a997469ee05c4b4944560a820f9ba0d73"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.4"

[[deps.ColorSchemes]]
deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
git-tree-sha1 = "67c1f244b991cad9b0aa4b7540fb758c2488b129"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.24.0"

[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.4"

[[deps.ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"]
git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.10.0"

    [deps.ColorVectorSpace.extensions]
    SpecialFunctionsExt = "SpecialFunctions"

    [deps.ColorVectorSpace.weakdeps]
    SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"

[[deps.Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.10"

[[deps.Compat]]
deps = ["TOML", "UUIDs"]
git-tree-sha1 = "75bd5b6fc5089df449b5d35fa501c846c9b6549b"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "4.12.0"
weakdeps = ["Dates", "LinearAlgebra"]

    [deps.Compat.extensions]
    CompatLinearAlgebraExt = "LinearAlgebra"

[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "1.0.5+1"

[[deps.ConcurrentUtilities]]
deps = ["Serialization", "Sockets"]
git-tree-sha1 = "8cfa272e8bdedfa88b6aefbbca7c19f1befac519"
uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
version = "2.3.0"

[[deps.Contour]]
git-tree-sha1 = "d05d9e7b7aedff4e5b51a029dced05cfb6125781"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.6.2"

[[deps.DataAPI]]
git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.16.0"

[[deps.DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "ac67408d9ddf207de5cfa9a97e114352430f01ed"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.16"

[[deps.Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[deps.DelimitedFiles]]
deps = ["Mmap"]
git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae"
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
version = "1.9.1"

[[deps.DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.9.3"

[[deps.Downloads]]
deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
version = "1.6.0"

[[deps.EpollShim_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8e9441ee83492030ace98f9789a654a6d0b1f643"
uuid = "2702e6a9-849d-5ed8-8c21-79e8b8f9ee43"
version = "0.0.20230411+0"

[[deps.ExceptionUnwrapping]]
deps = ["Test"]
git-tree-sha1 = "dcb08a0d93ec0b1cdc4af184b26b591e9695423a"
uuid = "460bff9d-24e4-43bc-9d9f-a8973cb893f4"
version = "0.1.10"

[[deps.Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "4558ab818dcceaab612d1bb8c19cee87eda2b83c"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.5.0+0"

[[deps.FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"

[[deps.FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "466d45dc38e15794ec7d5d63ec03d776a9aff36e"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.4+1"

[[deps.FileWatching]]
uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"

[[deps.FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"

[[deps.Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.93+0"

[[deps.Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"

[[deps.FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "d8db6a5a2fe1381c1ea4ef2cab7c69c2de7f9ea0"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.13.1+0"

[[deps.FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"

[[deps.GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "ff38ba61beff76b8f4acad8ab0c97ef73bb670cb"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.9+0"

[[deps.GR]]
deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "UUIDs", "p7zip_jll"]
git-tree-sha1 = "3458564589be207fa6a77dbbf8b97674c9836aab"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.73.2"

[[deps.GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "77f81da2964cc9fa7c0127f941e8bce37f7f1d70"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.73.2+0"

[[deps.Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"

[[deps.Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"]
git-tree-sha1 = "e94c92c7bf4819685eb80186d51c43e71d4afa17"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.76.5+0"

[[deps.Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+0"

[[deps.Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"

[[deps.HTTP]]
deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
git-tree-sha1 = "abbbb9ec3afd783a7cbd82ef01dcd088ea051398"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "1.10.1"

[[deps.HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "2.8.1+1"

[[deps.Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "179267cfa5e712760cd43dcae385d7ea90cc25a4"
uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
version = "0.0.5"

[[deps.HypertextLiteral]]
deps = ["Tricks"]
git-tree-sha1 = "7134810b1afce04bbc1045ca1985fbe81ce17653"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.5"

[[deps.IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "8b72179abc660bfab5e28472e019392b97d0985c"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.4"

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

[[deps.IrrationalConstants]]
git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.2.2"

[[deps.JLFzf]]
deps = ["Pipe", "REPL", "Random", "fzf_jll"]
git-tree-sha1 = "a53ebe394b71470c7f97c2e7e170d51df21b17af"
uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c"
version = "0.1.7"

[[deps.JLLWrappers]]
deps = ["Artifacts", "Preferences"]
git-tree-sha1 = "7e5d6779a1e09a36db2a7b6cff50942a0a7d0fca"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.5.0"

[[deps.JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.4"

[[deps.JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "60b1194df0a3298f460063de985eae7b01bc011a"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "3.0.1+0"

[[deps.LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+0"

[[deps.LERC_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434"
uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
version = "3.0.0+1"

[[deps.LLVMOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "d986ce2d884d49126836ea94ed5bfb0f12679713"
uuid = "1d63c593-3942-5779-bab2-d838dc0a180e"
version = "15.0.7+0"

[[deps.LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.1+0"

[[deps.LaTeXStrings]]
git-tree-sha1 = "50901ebc375ed41dbf8058da26f9de442febbbec"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.1"

[[deps.Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Printf", "Requires"]
git-tree-sha1 = "f428ae552340899a935973270b8d98e5a31c49fe"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.16.1"

    [deps.Latexify.extensions]
    DataFramesExt = "DataFrames"
    SymEngineExt = "SymEngine"

    [deps.Latexify.weakdeps]
    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
    SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8"

[[deps.LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
version = "0.6.4"

[[deps.LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
version = "8.4.0+0"

[[deps.LibGit2]]
deps = ["Base64", "LibGit2_jll", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[deps.LibGit2_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll"]
uuid = "e37daf67-58a4-590a-8e99-b0245dd2ffc5"
version = "1.6.4+0"

[[deps.LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
version = "1.11.0+1"

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

[[deps.Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+1"

[[deps.Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.7+0"

[[deps.Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "6f73d1dd803986947b2c750138528a999a6c7733"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.6.0+0"

[[deps.Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"

[[deps.Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "f9557a255370125b405568f9767d6d195822a175"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.17.0+0"

[[deps.Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"

[[deps.Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "2da088d113af58221c52828a80378e16be7d037a"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.5.1+1"

[[deps.Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.36.0+0"

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

[[deps.LogExpFunctions]]
deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "7d6dd4e9212aebaeed356de34ccf262a3cd415aa"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.26"

    [deps.LogExpFunctions.extensions]
    LogExpFunctionsChainRulesCoreExt = "ChainRulesCore"
    LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables"
    LogExpFunctionsInverseFunctionsExt = "InverseFunctions"

    [deps.LogExpFunctions.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"

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

[[deps.LoggingExtras]]
deps = ["Dates", "Logging"]
git-tree-sha1 = "c1dd6d7978c12545b4179fb6153b9250c96b0075"
uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
version = "1.0.3"

[[deps.MIMEs]]
git-tree-sha1 = "65f28ad4b594aebe22157d6fac869786a255b7eb"
uuid = "6c6e2e6c-3030-632d-7369-2d6c69616d65"
version = "0.1.4"

[[deps.MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "2fa9ee3e63fd3a4f7a9a4f4744a52f4856de82df"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.13"

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

[[deps.MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "NetworkOptions", "Random", "Sockets"]
git-tree-sha1 = "c067a280ddc25f196b5e7df3877c6b226d390aaf"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.1.9"

[[deps.MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.2+1"

[[deps.Measures]]
git-tree-sha1 = "c13304c81eec1ed3af7fc20e75fb6b26092a1102"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.2"

[[deps.Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "f66bdc5de519e8f8ae43bdc598782d35a25b1272"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.1.0"

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

[[deps.MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
version = "2023.1.10"

[[deps.NaNMath]]
deps = ["OpenLibm_jll"]
git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "1.0.2"

[[deps.NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
version = "1.2.0"

[[deps.Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+1"

[[deps.OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.23+2"

[[deps.OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
version = "0.8.1+2"

[[deps.OpenSSL]]
deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"]
git-tree-sha1 = "51901a49222b09e3743c65b8847687ae5fc78eb2"
uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c"
version = "1.4.1"

[[deps.OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "60e3045590bd104a16fefb12836c00c0ef8c7f8c"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "3.0.13+0"

[[deps.Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.2+0"

[[deps.OrderedCollections]]
git-tree-sha1 = "dfdf5519f235516220579f949664f1bf44e741c5"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.6.3"

[[deps.PCRE2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
version = "10.42.0+1"

[[deps.Parsers]]
deps = ["Dates", "PrecompileTools", "UUIDs"]
git-tree-sha1 = "8489905bcdbcfac64d1daa51ca07c0d8f0283821"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.8.1"

[[deps.Pipe]]
git-tree-sha1 = "6842804e7867b115ca9de748a0cf6b364523c16d"
uuid = "b98c9c47-44ae-5843-9183-064241ee97a0"
version = "1.3.0"

[[deps.Pixman_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl"]
git-tree-sha1 = "64779bc4c9784fee475689a1752ef4d5747c5e87"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.42.2+0"

[[deps.Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.10.0"

[[deps.PlotThemes]]
deps = ["PlotUtils", "Statistics"]
git-tree-sha1 = "1f03a2d339f42dca4a4da149c7e15e9b896ad899"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "3.1.0"

[[deps.PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "862942baf5663da528f66d24996eb6da85218e76"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.4.0"

[[deps.Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"]
git-tree-sha1 = "38a748946dca52a622e79eea6ed35c6737499109"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.40.0"

    [deps.Plots.extensions]
    FileIOExt = "FileIO"
    GeometryBasicsExt = "GeometryBasics"
    IJuliaExt = "IJulia"
    ImageInTerminalExt = "ImageInTerminal"
    UnitfulExt = "Unitful"

    [deps.Plots.weakdeps]
    FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
    GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
    IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
    ImageInTerminal = "d8c32880-2388-543b-8c61-d9f865259254"
    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"

[[deps.PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"]
git-tree-sha1 = "68723afdb616445c6caaef6255067a8339f91325"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.55"

[[deps.PrecompileTools]]
deps = ["Preferences"]
git-tree-sha1 = "03b4c25b43cb84cee5c90aa9b5ea0a78fd848d2f"
uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
version = "1.2.0"

[[deps.Preferences]]
deps = ["TOML"]
git-tree-sha1 = "00805cd429dcb4870060ff49ef443486c262e38e"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.4.1"

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

[[deps.Qt6Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Vulkan_Loader_jll", "Xorg_libSM_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_cursor_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "libinput_jll", "xkbcommon_jll"]
git-tree-sha1 = "37b7bb7aabf9a085e0044307e1717436117f2b3b"
uuid = "c0090381-4147-56d7-9ebc-da0b1113ec56"
version = "6.5.3+1"

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

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

[[deps.RecipesBase]]
deps = ["PrecompileTools"]
git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.3.4"

[[deps.RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "PrecompileTools", "RecipesBase"]
git-tree-sha1 = "45cf9fd0ca5839d06ef333c8201714e888486342"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.6.12"

[[deps.Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[deps.RelocatableFolders]]
deps = ["SHA", "Scratch"]
git-tree-sha1 = "ffdaf70d81cf6ff22c2b6e733c900c3321cab864"
uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
version = "1.0.1"

[[deps.Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.3.0"

[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"

[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "3bac05bc7e74a75fd9cba4295cde4045d9fe2386"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.2.1"

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

[[deps.Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[deps.SimpleBufferStream]]
git-tree-sha1 = "874e8867b33a00e784c8a7e4b60afe9e037b74e1"
uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
version = "1.1.0"

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

[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "66e0a8e672a0bdfca2c3f5937efb8538b9ddc085"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.2.1"

[[deps.SparseArrays]]
deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
version = "1.10.0"

[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
version = "1.10.0"

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1ff449ad350c9c4cbc756624d6f8a8c3ef56d3ed"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.7.0"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "1d77abd07f617c4868c33d4f5b9e1dbb2643c9cf"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.34.2"

[[deps.SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "7.2.1+1"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.3"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

[[deps.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

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

[[deps.TranscodingStreams]]
git-tree-sha1 = "54194d92959d8ebaa8e26227dbe3cdefcdcd594f"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.10.3"
weakdeps = ["Random", "Test"]

    [deps.TranscodingStreams.extensions]
    TestExt = ["Test", "Random"]

[[deps.Tricks]]
git-tree-sha1 = "eae1bb484cd63b36999ee58be2de6c178105112f"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.8"

[[deps.URIs]]
git-tree-sha1 = "67db6cc7b3821e19ebe75791a9dd19c9b1188f2b"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.5.1"

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

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

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.Unitful]]
deps = ["Dates", "LinearAlgebra", "Random"]
git-tree-sha1 = "3c793be6df9dd77a0cf49d80984ef9ff996948fa"
uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
version = "1.19.0"

    [deps.Unitful.extensions]
    ConstructionBaseUnitfulExt = "ConstructionBase"
    InverseFunctionsUnitfulExt = "InverseFunctions"

    [deps.Unitful.weakdeps]
    ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"

[[deps.UnitfulLatexify]]
deps = ["LaTeXStrings", "Latexify", "Unitful"]
git-tree-sha1 = "e2d817cc500e960fdbafcf988ac8436ba3208bfd"
uuid = "45397f5d-5981-4c77-b2b3-fc36d6e9b728"
version = "1.6.3"

[[deps.Unzip]]
git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.2.0"

[[deps.Vulkan_Loader_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Wayland_jll", "Xorg_libX11_jll", "Xorg_libXrandr_jll", "xkbcommon_jll"]
git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59"
uuid = "a44049a8-05dd-5a78-86c9-5fde0876e88c"
version = "1.3.243+0"

[[deps.Wayland_jll]]
deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "7558e29847e99bc3f04d6569e82d0f5c54460703"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.21.0+1"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "93f43ab61b16ddfb2fd3bb13b3ce241cafb0e6c9"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.31.0+0"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
git-tree-sha1 = "801cbe47eae69adc50f36c3caec4758d2650741b"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.12.2+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[deps.XZ_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "522b8414d40c4cbbab8dee346ac3a09f9768f25d"
uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
version = "5.4.5+0"

[[deps.Xorg_libICE_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "e5becd4411063bdcac16be8b66fc2f9f6f1e8fe5"
uuid = "f67eecfb-183a-506d-b269-f58e52b52d7c"
version = "1.0.10+1"

[[deps.Xorg_libSM_jll]]
deps = ["Libdl", "Pkg", "Xorg_libICE_jll"]
git-tree-sha1 = "4a9d9e4c180e1e8119b5ffc224a7b59d3a7f7e18"
uuid = "c834827a-8449-5923-a945-d239c165b7dd"
version = "1.2.3+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.8.6+0"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.11+0"

[[deps.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"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.4+0"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.1+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.15.0+0"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.2+0"

[[deps.Xorg_xcb_util_cursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"]
git-tree-sha1 = "04341cb870f29dcd5e39055f895c39d016e18ccd"
uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43"
version = "0.1.4+0"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.6+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.39.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.5.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.5+0"

[[deps.eudev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
version = "3.2.9+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a68c9655fbe6dfcab3d972808f1aafec151ce3f8"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.43.0+0"

[[deps.gperf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
version = "3.1.1+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+1"

[[deps.libevdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
version = "1.11.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libinput_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
version = "1.18.0+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "93284c28274d9e75218a416c65ec49d0e0fcdf3d"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.40+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.6+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.52.0+1"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+1"
"""

# ╔═╡ Cell order:
# ╟─0d223560-c436-11ee-1237-fbfdf4242bbd
# ╠═27baa396-c91b-4e95-838e-b65457a9767e
# ╟─e318abdf-493b-4565-870c-49e08637ed96
# ╠═49b3f758-a678-4d08-97d4-972cf381ec6c
# ╠═733039ba-cf35-4039-9107-3fffa242ec34
# ╠═58f4923f-2a6b-4ee2-94e5-6c2f25d18017
# ╟─dd04a81c-d5ae-4295-a247-74f5e38be4c4
# ╠═362d3609-b14a-46c0-aa13-6392bc45a920
# ╠═1de55eae-00f2-4cb4-a1ba-f642f37380c4
# ╟─e5c9de9b-a3eb-4e4c-87ba-c327609bb479
# ╠═4c5e82c5-ae40-4011-9834-89bcd10e3415
# ╟─d86d260c-f158-45cd-a2e8-efc0e8fb5279
# ╠═617358bb-b384-40d8-9733-6f44018b5864
# ╠═1924d662-08f3-441b-b3dc-569f0dc2d97d
# ╟─4155afc4-03eb-4774-b685-cb473f6bdca5
# ╠═5b21ccb2-0db4-4751-8e70-b91d3b54b663
# ╠═fd9dfe25-814c-4164-8aeb-0e2ed33e74d7
# ╠═ee0cc683-0150-46e7-a38d-3ab0bc029f0d
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002