### A Pluto.jl notebook ### # v0.15.1 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 el = $(esc(element)) global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing el end end # ╔═╡ 4cc48d02-4a5b-4915-97d8-0026da9ae700 begin using PlutoUI using Plots using Formatting end # ╔═╡ c0bf87f9-5a42-4e66-99d1-f3077b802523 md" # Infinite Chain Riddler This week's [Riddler](https://fivethirtyeight.com/features/will-riddler-nation-win-gold-in-archery/) asks us to consider an infinitely long chain whose link lengths decrease as a fixed proportion $f \in (0, 1)$ of each preceding link (i.e if $\ell_n$ is the length of the $n^{th}$ link, then $\ell_{n+1} = f \cdot \ell_n).$ This chain also has the property that whenever you adjust the angle $\theta$ between any pair of successive links, then every other pair of sequential links will bend to form the same angle (i.e. $\angle(\text{link}_n, \text{link}_{n+1}) = \theta$ for all $n$). Since $f < 1$, the chain has a finite length, and the links tend toward a limiting point, which we will refer to as the chain's end point or tail. Assuming that the chain starts out in a straight line (i.e. $\theta = 0)$, what curve does the chain's end point sweep out as we vary $\theta$? " # ╔═╡ 6a0cfb0b-6cc2-486e-8694-67307c53a765 md" ## Playing With a Chain's Parameters First let's see play around with a chain for fixed values of $f$ and $\theta$. The key thing here is to keep track of where the tail end of the curve goes as we vary $\theta$. " # ╔═╡ bbba98ef-7a17-4975-9653-f8919afa911c md"Choose value for successive chain length fraction $f$." # ╔═╡ 3967ffdb-0b8e-4cf0-9451-1bd4346285fc @bind f_chain_plot PlutoUI.Slider((0.01):0.01:(1-0.01), default = 0.75, show_value=true) # ╔═╡ 9ee2366b-8b87-4af2-9296-e90e27b397f6 md"Choose angle between successive links, $\theta \in [-π,π]$ (selection is in Radians)." # ╔═╡ c61e4740-a6e1-4f54-8f82-64b81382b12a begin @bind θ_chain_plot PlutoUI.Slider(0:(0.0001 * π):(2*π), default = π/4, show_value=true) end # ╔═╡ 103a99aa-c342-42e2-9787-08d5bd1aee52 md"Choose number of links to plot, $n_\text{chain}$ (note, only really useful when $f\approx 1$)." # ╔═╡ e7eed1c8-904e-473b-a636-8622b55ac087 @bind n_links_chain_plot PlutoUI.Slider(1:1000, default = 50, show_value=true) # ╔═╡ 76e889d9-8ad6-4d96-9813-42da8217b22f md" ## End Point Path The following figure animates the curve traced out by the chain's end point, overlayed on top of the the full path traced out by the chain's tail. The chain's tail is computed in two ways, first I just sum up a finite (but large enough) number of chain links to get a decent approximation -- as in the example above. This is the \"Approx\" curve, in green. Next I compare to the analytical solution (derived elsewhere), which gives the \"Exact\" curve in purple. The approximation depends on the number of chain links, $n_\text{chain}$. When $f$ is large (i.e. $f \approx 1$), then more chain links are required to get a decent approximation. " # ╔═╡ 6521e297-ef0b-4daf-ac51-83996058ff6f md"Choose value for successive chain length fraction $f$" # ╔═╡ 143fe525-ca03-41ed-ab81-63ef67393f43 @bind f_end_point_plot PlutoUI.Slider(0.01:0.01:0.99, default = 0.75, show_value=true) # ╔═╡ 9d75d083-f04d-479e-af5a-c488198252ff md"Choose number of links to plot, $n_\text{chain}$" # ╔═╡ d547a57b-187b-4355-89bb-e8d5389b740f @bind n_links_end_point_plot PlutoUI.Slider(1:1000, default = 50, show_value=true) # ╔═╡ 31a5828b-4179-4130-b202-ca323e3df609 md"This results in the following path." # ╔═╡ d4bd6b41-5d67-4b95-9a37-1ea416cd07f5 md" # Functions to do the work " # ╔═╡ 83c20e93-869c-4c54-be36-321ff67aa6b2 md"## Generating chains" # ╔═╡ e5f11638-f202-11eb-12ce-cf474f01afb2 function chain_link_endpoints(θ, f = 0.75, n_links = 5) ϕ = cumsum(θ .* ones(n_links)) # each link θ relative to last μ = cumprod(f .* ones(n_links)) # each link f * length of last Δp = hcat([μ .* cos.(ϕ) μ .* sin.(ϕ)]) # displacements for all but first link Δp = vcat([1 0], Δp) # add the first link's displacement p = cumsum(vcat([0 0], Δp), dims = 1) # location for each point on chain return p end # ╔═╡ 932a6971-3bbd-4e2d-97fd-4aeda4a25250 "Plot a chain" function plot_chains(θ, f = 0.75, n_links = 5, mark_end_point = false) p = chain_link_endpoints(θ, f, n_links) g = plot(p[:, 1], p[:, 2], #legend=false, label="", title="Chain Orientation\nθ=" * format(θ, precision=2), aspect_ratio=:equal, xlims = (0, 1.1 * (1/(1 - f))), ylims = (-0.5 * (1/(1-f)), 0.5 * (1/(1-f))) ) if mark_end_point==true scatter!([p[end,1]], [p[end, 2]], label="") end return g end # ╔═╡ 0e66477a-6d34-4830-8639-b0bda38ad88a plot_chains(θ_chain_plot, f_chain_plot, n_links_chain_plot, true) # ╔═╡ 8848f5ea-2757-4c27-9cba-61d76fc68953 md"## Approximating Chain End Point" # ╔═╡ 74447e39-3d78-4138-9ebf-48326de1c735 "Approximate a chain's end point for a single value of θ" function end_point(θ, f, n_links) # Use last point as approximate end point return chain_link_endpoints(θ, f, n_links)[end, :] end # ╔═╡ 7b036492-05c6-4a80-b0ba-34750982d176 "Compute path traced out by a chain's end point" function end_point_trace(f, n_links, n_theta) θ = 0:((2*π)/n_theta):(2 * π) q = reduce(hcat, end_point.(θ, f, n_links)) q = transpose(q) return q end # ╔═╡ 73be50eb-f4de-4d1c-b555-bdd99a203925 "Plot path traced out by a chain's end point" function plot_end_point(f, n_links, n_theta, plot_on_new_figure=true) # Approximate solution q = end_point_trace(f, n_links, n_theta) # Analytic Solution θ = 0:((2*π)/n_theta):(2*π) x2 = (1 .- f * cos.(θ)) ./ (f^2 .- 2 * f * cos.(θ) .+ 1) y2 = (f * sin.(θ)) ./ (f^2 .- 2 * f * cos.(θ) .+ 1) if plot_on_new_figure == true plot( title="Curve Traced by\nChain's End Point", xlims = (0, 1.1 * (1/(1 - f))), ylims = (-0.5 * (1/(1-f)), 0.5 * (1/(1-f))), aspect_ratio=:equal ) end # Plot the approximate solution plot!(q[:, 1], q[:, 2], label="Approx", aspect_ratio=:equal) # Plot the exact solution plot!(x2, y2, label="Exact") end # ╔═╡ 909da079-8d40-4328-b864-13ab13f2f19a begin n_gif_frames = 100 @gif for i in 0:n_gif_frames θ_animation = i * (2*π / n_gif_frames) plot_chains(θ_animation, f_end_point_plot, n_links_end_point_plot, true) plot_end_point(f_end_point_plot, n_links_end_point_plot, 10_000, false) end end # ╔═╡ 00000000-0000-0000-0000-000000000001 PLUTO_PROJECT_TOML_CONTENTS = """ [deps] Formatting = "59287772-0a20-5a39-b81b-1366585eb4c0" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" [compat] Formatting = "~0.4.2" Plots = "~1.19.4" PlutoUI = "~0.7.9" """ # ╔═╡ 00000000-0000-0000-0000-000000000002 PLUTO_MANIFEST_TOML_CONTENTS = """ # This file is machine-generated - editing it directly is not advised [[Adapt]] deps = ["LinearAlgebra"] git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7" uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" version = "3.3.1" [[ArgTools]] uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" [[Artifacts]] uuid = 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"Printf", "SHA"] uuid = "76f85450-5226-5b5a-8eaa-529ad045b433" [[LibSSH2_jll]] deps = ["Artifacts", "Libdl", "MbedTLS_jll"] uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8" [[LibVPX_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "12ee7e23fa4d18361e7c2cde8f8337d4c3101bc7" uuid = "dd192d2f-8180-539f-9fb4-cc70b1dcf69a" version = "1.10.0+0" [[Libdl]] uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb" [[Libffi_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "761a393aeccd6aa92ec3515e428c26bf99575b3b" uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490" version = "3.2.2+0" [[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" [[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 = "c333716e46366857753e273ce6a69ee0945a6db9" uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8" version = "1.42.0+0" [[Libiconv_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778" uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531" version = "1.16.1+1" [[Libmount_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73" uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9" version = "2.35.0+0" [[Libtiff_jll]] deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"] git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9" uuid = "89763e89-9b03-5906-acba-b20f662cd828" version = "4.3.0+0" [[Libuuid_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066" uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700" version = "2.36.0+0" [[LinearAlgebra]] deps = ["Libdl"] uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" [[Logging]] uuid = "56ddb016-857b-54e1-b83d-db4d58db5568" [[MacroTools]] deps = ["Markdown", "Random"] git-tree-sha1 = "6a8a2a625ab0dea913aba95c11370589e0239ff0" uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09" version = "0.5.6" [[Markdown]] deps = ["Base64"] uuid = "d6f4376e-aef5-505a-96c1-9c027394607a" [[MbedTLS]] deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"] git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe" uuid = "739be429-bea8-5141-9913-cc70e7f3736d" version = "1.0.3" [[MbedTLS_jll]] deps = ["Artifacts", "Libdl"] uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1" [[Measures]] git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f" uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e" version = "0.3.1" [[Missings]] deps = ["DataAPI"] git-tree-sha1 = "4ea90bd5d3985ae1f9a908bd4500ae88921c5ce7" uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28" version = "1.0.0" [[Mmap]] uuid = "a63ad114-7e13-5084-954f-fe012c677804" [[MozillaCACerts_jll]] uuid = "14a3606d-f60d-562e-9121-12d972cd8159" [[NaNMath]] git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb" uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3" version = "0.3.5" [[NetworkOptions]] uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" [[Ogg_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f" uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051" version = "1.3.5+0" [[OpenSSL_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a" uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95" version = "1.1.10+0" [[Opus_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720" uuid = "91d4177d-7536-5919-b921-800302f37372" version = "1.3.2+0" [[OrderedCollections]] git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c" uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d" version = "1.4.1" [[PCRE_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488" uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc" version = "8.44.0+0" [[Parsers]] deps = ["Dates"] git-tree-sha1 = "94bf17e83a0e4b20c8d77f6af8ffe8cc3b386c0a" uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0" version = "1.1.1" [[Pixman_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29" uuid = "30392449-352a-5448-841d-b1acce4e97dc" version = "0.40.1+0" [[Pkg]] deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"] uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" [[PlotThemes]] deps = ["PlotUtils", "Requires", "Statistics"] git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d" uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a" version = "2.0.1" [[PlotUtils]] deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"] git-tree-sha1 = "501c20a63a34ac1d015d5304da0e645f42d91c9f" uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043" version = "1.0.11" [[Plots]] deps = ["Base64", "Contour", "Dates", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs"] git-tree-sha1 = "1e72752052a3893d0f7103fbac728b60b934f5a5" uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" version = "1.19.4" [[PlutoUI]] deps = ["Base64", "Dates", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "Suppressor"] git-tree-sha1 = "44e225d5837e2a2345e69a1d1e01ac2443ff9fcb" uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8" version = "0.7.9" [[Preferences]] deps = ["TOML"] git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a" uuid = "21216c6a-2e73-6563-6e65-726566657250" version = "1.2.2" [[Printf]] deps = ["Unicode"] uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" [[Qt5Base_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"] git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8" uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1" version = "5.15.3+0" [[REPL]] deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"] uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb" [[Random]] deps = ["Serialization"] uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" [[RecipesBase]] git-tree-sha1 = "b3fb709f3c97bfc6e948be68beeecb55a0b340ae" uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01" version = "1.1.1" [[RecipesPipeline]] deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"] git-tree-sha1 = "2a7a2469ed5d94a98dea0e85c46fa653d76be0cd" uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c" version = "0.3.4" [[Reexport]] git-tree-sha1 = "5f6c21241f0f655da3952fd60aa18477cf96c220" uuid = "189a3867-3050-52da-a836-e630ba90ab69" version = "1.1.0" [[Requires]] deps = ["UUIDs"] git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621" uuid = "ae029012-a4dd-5104-9daa-d747884805df" version = "1.1.3" [[SHA]] uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce" [[Scratch]] deps = ["Dates"] git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda" uuid = "6c6a2e73-6563-6170-7368-637461726353" version = "1.1.0" [[Serialization]] uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b" [[SharedArrays]] deps = ["Distributed", "Mmap", "Random", "Serialization"] uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383" [[Showoff]] deps = ["Dates", "Grisu"] git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de" uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f" version = "1.0.3" [[Sockets]] uuid = "6462fe0b-24de-5631-8697-dd941f90decc" [[SortingAlgorithms]] deps = ["DataStructures"] git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508" uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c" version = "1.0.1" [[SparseArrays]] deps = ["LinearAlgebra", "Random"] uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" [[StaticArrays]] deps = ["LinearAlgebra", "Random", "Statistics"] git-tree-sha1 = "885838778bb6f0136f8317757d7803e0d81201e4" uuid = "90137ffa-7385-5640-81b9-e52037218182" version = "1.2.9" [[Statistics]] deps = ["LinearAlgebra", "SparseArrays"] uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" [[StatsAPI]] git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510" uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0" version = "1.0.0" [[StatsBase]] deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"] git-tree-sha1 = "fed1ec1e65749c4d96fc20dd13bea72b55457e62" uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" version = "0.33.9" [[StructArrays]] deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"] git-tree-sha1 = "000e168f5cc9aded17b6999a560b7c11dda69095" uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a" version = "0.6.0" [[Suppressor]] git-tree-sha1 = "a819d77f31f83e5792a76081eee1ea6342ab8787" uuid = "fd094767-a336-5f1f-9728-57cf17d0bbfb" version = "0.2.0" [[TOML]] deps = ["Dates"] uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76" [[TableTraits]] deps = ["IteratorInterfaceExtensions"] git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39" uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c" version = "1.0.1" [[Tables]] deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"] git-tree-sha1 = "8ed4a3ea724dac32670b062be3ef1c1de6773ae8" uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c" version = "1.4.4" [[Tar]] deps = ["ArgTools", "SHA"] uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e" [[Test]] deps = ["InteractiveUtils", "Logging", "Random", "Serialization"] uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [[URIs]] git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355" uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4" version = "1.3.0" [[UUIDs]] deps = ["Random", "SHA"] uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" [[Unicode]] uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" [[Wayland_jll]] deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"] git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23" uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89" version = "1.19.0+0" [[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" [[XML2_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"] git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a" uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a" version = "2.9.12+0" [[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" [[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_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_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_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_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" [[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" [[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" [[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" [[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" [[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 = ["Libdl"] uuid = "83775a58-1f1d-513f-b197-d71354ab007a" [[Zstd_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6" uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" version = "1.5.0+0" [[libass_jll]] deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] git-tree-sha1 = "acc685bcf777b2202a904cdcb49ad34c2fa1880c" uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" version = "0.14.0+4" [[libfdk_aac_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "7a5780a0d9c6864184b3a2eeeb833a0c871f00ab" uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" version = "0.1.6+4" [[libpng_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c" uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" version = "1.6.38+0" [[libvorbis_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb" uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" version = "1.3.7+0" [[nghttp2_jll]] deps = ["Artifacts", "Libdl"] uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" [[p7zip_jll]] deps = ["Artifacts", "Libdl"] uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" [[x264_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f" uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" version = "2020.7.14+2" [[x265_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab" uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" version = "3.0.0+3" [[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" """ # ╔═╡ Cell order: # ╟─c0bf87f9-5a42-4e66-99d1-f3077b802523 # ╟─6a0cfb0b-6cc2-486e-8694-67307c53a765 # ╟─bbba98ef-7a17-4975-9653-f8919afa911c # ╟─3967ffdb-0b8e-4cf0-9451-1bd4346285fc # ╟─9ee2366b-8b87-4af2-9296-e90e27b397f6 # ╟─c61e4740-a6e1-4f54-8f82-64b81382b12a # ╟─103a99aa-c342-42e2-9787-08d5bd1aee52 # ╟─e7eed1c8-904e-473b-a636-8622b55ac087 # ╠═0e66477a-6d34-4830-8639-b0bda38ad88a # ╟─76e889d9-8ad6-4d96-9813-42da8217b22f # ╟─6521e297-ef0b-4daf-ac51-83996058ff6f # ╟─143fe525-ca03-41ed-ab81-63ef67393f43 # ╟─9d75d083-f04d-479e-af5a-c488198252ff # ╟─d547a57b-187b-4355-89bb-e8d5389b740f # ╠═909da079-8d40-4328-b864-13ab13f2f19a # ╟─31a5828b-4179-4130-b202-ca323e3df609 # ╟─d4bd6b41-5d67-4b95-9a37-1ea416cd07f5 # ╟─83c20e93-869c-4c54-be36-321ff67aa6b2 # ╠═e5f11638-f202-11eb-12ce-cf474f01afb2 # ╠═932a6971-3bbd-4e2d-97fd-4aeda4a25250 # ╟─8848f5ea-2757-4c27-9cba-61d76fc68953 # ╠═74447e39-3d78-4138-9ebf-48326de1c735 # ╠═7b036492-05c6-4a80-b0ba-34750982d176 # ╠═73be50eb-f4de-4d1c-b555-bdd99a203925 # ╠═4cc48d02-4a5b-4915-97d8-0026da9ae700 # ╟─00000000-0000-0000-0000-000000000001 # ╟─00000000-0000-0000-0000-000000000002