--- /dev/null
+### A Pluto.jl notebook ###
+# v0.15.1
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ 504cc192-eb75-11ea-2b6e-af5d4f828086
+begin
+ using PlutoUI, Plots, LinearAlgebra
+ plotly()
+end
+
+# ╔═╡ 5485d760-eb75-11ea-2e25-7b13d58ce554
+let
+ a = 0
+ n = 20
+ f(x, y) = let
+ v = complex(x, y)
+ c = v
+ for i ∈ 1:n
+ v = v^2 + c + a * im
+ if norm(v) > 2
+ return 1-i/n # Normalized.
+ end
+ end
+ 0
+ end
+ x = LinRange(-2, 1, 1000)
+ y = LinRange(-1.5, 1.5, 1000)
+ plot(x, y, f, st = :surface, label = false, camera = (45, 80), c = :grays)
+end
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
+PLUTO_PROJECT_TOML_CONTENTS = """
+[deps]
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
+
+[compat]
+Plots = "~1.18.2"
+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 = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+
+[[Base64]]
+uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+
+[[Bzip2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "c3598e525718abcc440f69cc6d5f60dda0a1b61e"
+uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
+version = "1.0.6+5"
+
+[[Cairo_jll]]
+deps = ["Artifacts", "Bzip2_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 = "e2f47f6d8337369411569fd45ae5753ca10394c6"
+uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
+version = "1.16.0+6"
+
+[[ColorSchemes]]
+deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random", "StaticArrays"]
+git-tree-sha1 = "ed268efe58512df8c7e224d2e170afd76dd6a417"
+uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
+version = "3.13.0"
+
+[[ColorTypes]]
+deps = ["FixedPointNumbers", "Random"]
+git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
+uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
+version = "0.11.0"
+
+[[Colors]]
+deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
+git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
+uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
+version = "0.12.8"
+
+[[Compat]]
+deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
+git-tree-sha1 = "dc7dedc2c2aa9faf59a55c622760a25cbefbe941"
+uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
+version = "3.31.0"
+
+[[CompilerSupportLibraries_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+
+[[Contour]]
+deps = ["StaticArrays"]
+git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
+uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
+version = "0.5.7"
+
+[[DataAPI]]
+git-tree-sha1 = "ee400abb2298bd13bfc3df1c412ed228061a2385"
+uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
+version = "1.7.0"
+
+[[DataStructures]]
+deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
+git-tree-sha1 = "4437b64df1e0adccc3e5d1adbc3ac741095e4677"
+uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+version = "0.18.9"
+
+[[DataValueInterfaces]]
+git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
+uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
+version = "1.0.0"
+
+[[Dates]]
+deps = ["Printf"]
+uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
+
+[[DelimitedFiles]]
+deps = ["Mmap"]
+uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
+
+[[Distributed]]
+deps = ["Random", "Serialization", "Sockets"]
+uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
+
+[[Downloads]]
+deps = ["ArgTools", "LibCURL", "NetworkOptions"]
+uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
+
+[[EarCut_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "92d8f9f208637e8d2d28c664051a00569c01493d"
+uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
+version = "2.1.5+1"
+
+[[Expat_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
+uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
+version = "2.2.10+0"
+
+[[FFMPEG]]
+deps = ["FFMPEG_jll"]
+git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
+uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
+version = "0.4.1"
+
+[[FFMPEG_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "LibVPX_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
+git-tree-sha1 = "3cc57ad0a213808473eafef4845a74766242e05f"
+uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
+version = "4.3.1+4"
+
+[[FixedPointNumbers]]
+deps = ["Statistics"]
+git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
+uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
+version = "0.8.4"
+
+[[Fontconfig_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "35895cf184ceaab11fd778b4590144034a167a2f"
+uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
+version = "2.13.1+14"
+
+[[Formatting]]
+deps = ["Printf"]
+git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
+uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
+version = "0.4.2"
+
+[[FreeType2_jll]]
+deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "cbd58c9deb1d304f5a245a0b7eb841a2560cfec6"
+uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
+version = "2.10.1+5"
+
+[[FriBidi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
+uuid = "559328eb-81f9-559d-9380-de523a88c83c"
+version = "1.0.10+0"
+
+[[GLFW_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
+git-tree-sha1 = "dba1e8614e98949abfa60480b13653813d8f0157"
+uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
+version = "3.3.5+0"
+
+[[GR]]
+deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
+git-tree-sha1 = "b83e3125048a9c3158cbb7ca423790c7b1b57bea"
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+
+[[GR_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
+git-tree-sha1 = "e14907859a1d3aee73a019e7b3c98e9e7b8b5b3e"
+uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
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+
+[[GeometryBasics]]
+deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
+git-tree-sha1 = "15ff9a14b9e1218958d3530cc288cf31465d9ae2"
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+
+[[Gettext_jll]]
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+git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
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+
+[[Glib_jll]]
+deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "47ce50b742921377301e15005c96e979574e130b"
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+[[Grisu]]
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+[[HTTP]]
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+[[IteratorInterfaceExtensions]]
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+[[JSON]]
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+[[JpegTurbo_jll]]
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+[[LaTeXStrings]]
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+[[Latexify]]
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+
+[[LibCURL_jll]]
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+uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
+
+[[LibGit2]]
+deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
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+[[LibSSH2_jll]]
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+
+[[LibVPX_jll]]
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+[[Libffi_jll]]
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+[[Logging]]
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+[[MacroTools]]
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+
+[[Markdown]]
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+
+[[MbedTLS]]
+deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
+git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
+uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
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+
+[[MbedTLS_jll]]
+deps = ["Artifacts", "Libdl"]
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+
+[[Measures]]
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+uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
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+
+[[Missings]]
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+uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
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+
+[[Mmap]]
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+
+[[MozillaCACerts_jll]]
+uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
+
+[[NaNMath]]
+git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
+uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
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+[[NetworkOptions]]
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+
+[[Ogg_jll]]
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+
+[[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:
+# ╠═504cc192-eb75-11ea-2b6e-af5d4f828086
+# ╠═5485d760-eb75-11ea-2e25-7b13d58ce554
+# ╟─00000000-0000-0000-0000-000000000001
+# ╟─00000000-0000-0000-0000-000000000002
--- /dev/null
+### A Pluto.jl notebook ###
+# v0.15.1
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ ce8225de-f0ee-11ea-392d-8b466e106eba
+md"""
+# Category theory
+From the book \"Category theory for programmers\".
+
+Some solutions are posted here: <http://danshiebler.com/2018-11-10-category-solutions/>
+
+One of the goals is to understand this video: <https://www.youtube.com/watch?v=7zr2qnud4XM>
+"""
+
+# ╔═╡ 161953b0-f0ef-11ea-10e7-efb9093f3abe
+md"## 1.4 Challenge"
+
+# ╔═╡ 1d939550-f0f0-11ea-0242-6bb6f9d47e07
+md"**1. Implement, as best as you can, the identity function in your favorite language (or the second favorite, if your favorite language happens to be Haskell).**"
+
+# ╔═╡ 339c9ae0-f0f0-11ea-1782-9741d0cfd212
+id(f) = f # Note: in Julia identity function already exists and is named 'identity'.
+
+# ╔═╡ 244b06b0-f0f2-11ea-3e9b-bd41d3a7709a
+let
+ f = id(sin)
+ f(π/4)
+end
+
+# ╔═╡ 5df73200-f0f0-11ea-06d3-7f00df9ff21a
+md"**2. Implement the composition function in your favorite language. It takes two functions as arguments and returns a function that is their composition.**"
+
+# ╔═╡ 2b194650-f0f2-11ea-282b-fb9e41119331
+compose(f, g) = x -> f(g(x))
+
+# ╔═╡ 8d5c86d0-f0f0-11ea-1eb7-81b63c1f0391
+let
+ f = compose(sin, cos) # Composition already exists as 'f ∘ g'.
+ f(2)
+end
+
+# ╔═╡ 39d69450-f0f1-11ea-380f-657eaa4c2705
+md"**3. Write a program that tries to test that your composition function respects identity.**"
+
+# ╔═╡ 3ec58ca0-f0f1-11ea-3122-d999cdd46d59
+let
+ f = id(sin)
+ g = sin
+ f(2) == g(2),
+ compose(x -> x + 4, id)(5) == 9,
+ compose(id, x -> x + 4)(5) == 9
+end
+
+# ╔═╡ a9f8c960-f0f1-11ea-306b-59fd1e640908
+md"**4. Is the world-wide web a category in any sense? Are links morphisms?**"
+
+# ╔═╡ b27be4f0-f0f1-11ea-3f44-132d777e00c8
+md"Each uri represents a object and each link a morphism to another uri."
+
+# ╔═╡ 529575a0-f0f2-11ea-2860-439efb6131f8
+md"**5. Is Facebook a category, with people as objects and friendships as morphisms?**"
+
+# ╔═╡ 5c0cdc40-f0f2-11ea-0b14-e3ea9217d362
+md"No because A → B and B → C do not imply A → C."
+
+# ╔═╡ 775f27f0-f11a-11ea-0749-a333efba4f47
+md"## 2.7 Challenges"
+
+# ╔═╡ 295e6200-f115-11ea-0871-bf9192c0ace8
+md"""
+**1. Define a higher-order function (or a function object) memoize in your favorite language. This function takes a pure function f as an argument and returns a function that behaves almost exactly like f, except that it only calls the original function once for every argument, stores the result internally, and subsequently returns this stored result every time it’s called with the same argument. You can tell the memoized function from the original by watching its performance. For instance, try to memoize a function that takes a long time to evaluate. You’ll have to wait for the result the first time you call it, but on subsequent calls, with the same argument, you should get the result immediately.**
+"""
+
+# ╔═╡ 88cec670-f1a2-11ea-19b1-93258f66e3c8
+function memoize(f)
+ dic = Dict()
+ v -> let
+ if haskey(dic, v)
+ dic[v]
+ else
+ dic[v] = f(v)
+ end
+ end
+end
+
+# ╔═╡ 633b7b60-f1a2-11ea-0826-d727cdf29f3f
+let
+ using Random
+ function rand_from_seed(seed)
+ rng = MersenneTwister(seed)
+ rand(rng)
+ end
+
+ v1 = rand_from_seed(2) # Always 0.36679641243992434.
+ memoized_rand = memoize(rand_from_seed)
+ v2 = memoized_rand(2) # Also always 0.36679641243992434.
+ md"v1 = $v1, v2 = $v2 (no, it doesn't work)"
+end
+
+# ╔═╡ 8ef36160-f11a-11ea-12ee-474959e79a5a
+let
+ function slow_function(x)
+ sleep(1)
+ x + 42
+ end
+
+ memoized_slow_function = memoize(slow_function)
+
+ t1 = @elapsed memoized_slow_function(2)
+ t2 = @elapsed memoized_slow_function(2)
+ md"First call: $t1 s, second call: $t2 s"
+end
+
+# ╔═╡ 6ca649c0-f1a0-11ea-17ce-85e469a744dc
+md"**Try to memoize a function from your standard library that you normally use to produce random numbers. Does it work?**"
+
+# ╔═╡ 41bca720-f1a2-11ea-3aa6-91c91ce942bd
+md"Nope, it will always produce the same output"
+
+# ╔═╡ 576b30a2-f1a2-11ea-244b-0b664a975ed1
+md"**Most random number generators can be initialized with a seed. Implement a function that takes a seed, calls the random number generator with that seed, and returns the result. Memoize that function. Does it work?**"
+
+# ╔═╡ 9e4fd750-f1a2-11ea-2e87-bf53e8d90d3d
+md"""
+**Which of these C++ functions are pure? Try to memoize them and observe what happens when you call them multiple times: memoized and not.**
+
+```c++
+(a) The factorial function from the example in the text.
+(b) std::getchar()
+(c) bool f() {
+ std::cout << "Hello!" << std::endl;
+ return true;
+}
+(d) int f(int x) {
+ static int y = 0;
+ 25
+ y += x;
+ return y;
+}
+```
+"""
+
+# ╔═╡ d39ac400-f1a3-11ea-3828-e9921179e016
+md"""
+Only (a) is pure and only this one can be memoized.
+"""
+
+# ╔═╡ 17480d70-f1a4-11ea-1fd5-e3c0cd4de97d
+md"**How many different functions are there from Bool to Bool? Can you implement them all?**"
+
+# ╔═╡ 4028fce0-f1a4-11ea-2e43-af5ca402a53a
+let
+ f1(b) = b # Same.
+ f2(b) = !b # The inverse.
+ f3(b) = true # Always true.
+ f4(b) = false # Always false.
+ md"There are only four possible functions"
+end
+
+# ╔═╡ 8e9436b0-f1a4-11ea-1a27-95681bae1e4b
+md"""
+## Notes on Chapter 3
+
+A *preorder* is a category with at most one morphism from any object *a* to any object *b*.
+
+Cycles are forbidden in *partial orders*.
+
+If any two objects are in relation with each other, one way or another then it's a *total order*.
+
+A set of morphisms from object *a* to object *b* in a category *C* is called a *hom-set*: *C(a, b)*.
+
+A *monoid* is a single object with a set of morphisms."""
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
+PLUTO_PROJECT_TOML_CONTENTS = """
+[deps]
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+"""
+
+# ╔═╡ 00000000-0000-0000-0000-000000000002
+PLUTO_MANIFEST_TOML_CONTENTS = """
+# This file is machine-generated - editing it directly is not advised
+
+[[Random]]
+deps = ["Serialization"]
+uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+
+[[Serialization]]
+uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
+"""
+
+# ╔═╡ Cell order:
+# ╟─ce8225de-f0ee-11ea-392d-8b466e106eba
+# ╟─161953b0-f0ef-11ea-10e7-efb9093f3abe
+# ╟─1d939550-f0f0-11ea-0242-6bb6f9d47e07
+# ╠═339c9ae0-f0f0-11ea-1782-9741d0cfd212
+# ╠═244b06b0-f0f2-11ea-3e9b-bd41d3a7709a
+# ╟─5df73200-f0f0-11ea-06d3-7f00df9ff21a
+# ╠═2b194650-f0f2-11ea-282b-fb9e41119331
+# ╠═8d5c86d0-f0f0-11ea-1eb7-81b63c1f0391
+# ╟─39d69450-f0f1-11ea-380f-657eaa4c2705
+# ╠═3ec58ca0-f0f1-11ea-3122-d999cdd46d59
+# ╟─a9f8c960-f0f1-11ea-306b-59fd1e640908
+# ╟─b27be4f0-f0f1-11ea-3f44-132d777e00c8
+# ╟─529575a0-f0f2-11ea-2860-439efb6131f8
+# ╟─5c0cdc40-f0f2-11ea-0b14-e3ea9217d362
+# ╟─775f27f0-f11a-11ea-0749-a333efba4f47
+# ╟─295e6200-f115-11ea-0871-bf9192c0ace8
+# ╠═88cec670-f1a2-11ea-19b1-93258f66e3c8
+# ╠═8ef36160-f11a-11ea-12ee-474959e79a5a
+# ╟─6ca649c0-f1a0-11ea-17ce-85e469a744dc
+# ╟─41bca720-f1a2-11ea-3aa6-91c91ce942bd
+# ╟─576b30a2-f1a2-11ea-244b-0b664a975ed1
+# ╠═633b7b60-f1a2-11ea-0826-d727cdf29f3f
+# ╟─9e4fd750-f1a2-11ea-2e87-bf53e8d90d3d
+# ╟─d39ac400-f1a3-11ea-3828-e9921179e016
+# ╟─17480d70-f1a4-11ea-1fd5-e3c0cd4de97d
+# ╠═4028fce0-f1a4-11ea-2e43-af5ca402a53a
+# ╠═8e9436b0-f1a4-11ea-1a27-95681bae1e4b
+# ╟─00000000-0000-0000-0000-000000000001
+# ╟─00000000-0000-0000-0000-000000000002
--- /dev/null
+### A Pluto.jl notebook ###
+# v0.15.1
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ 56760c70-eb66-11ea-2335-c9c8cbcb56f3
+begin
+ using Luxor, PlutoUI, Colors
+end
+
+# ╔═╡ 9f433e5e-3606-11eb-2a5c-d70bb3978644
+html"""<style>main { max-width: 100%; margin-right: 0; }</style>"""
+
+# ╔═╡ ebf8a9e0-fe37-11ea-39ae-8b0f814fed81
+#=
+* https://en.wikipedia.org/wiki/Tessellation
+* https://en.wikipedia.org/wiki/Penrose_tiling
+=#
+
+# ╔═╡ 1d2fa270-3493-11eb-33a8-092f981b3b0d
+begin
+ function drawstars(colors)
+ sethue(colors[1])
+ circle(O, 200, :fill)
+ sethue("white")
+ radii = [180, 200, 150]
+ rotations = [π/28, 0, 0]
+ for (n, r) in enumerate(radii)
+ sethue(colors[n + 1])
+ star(O, r, 28, 0.7, rotations[n], :fill)
+ end
+ sethue("black")
+ star(O, 120, 28, 0.7, 0, :fill)
+ end
+
+ blues = [
+ RGB(0.455,0.753,0.89), # main
+ RGB(0.322,0.557,0.639),
+ RGB(0.243,0.396,0.463),
+ RGB(0.133,0.298,0.357)]
+
+ browns = [
+ RGB(0.549,0.384,0.224), # main
+ RGB(0.459,0.298,0.141),
+ RGB(0.376,0.22,0.075),
+ RGB(0.259,0.129,0.043)]
+end
+
+# ╔═╡ 68fd3a00-356f-11eb-288b-d95699f8f8ab
+@draw begin
+ background("black")
+
+ sector(O, 100, 200, π, 3π/2)
+ clip()
+ drawstars(browns)
+ clipreset()
+
+ sector(O, 100, 200, 3π/2, π)
+ clip()
+ drawstars(blues)
+ clipreset()
+end
+
+# ╔═╡ d6ae6110-3609-11eb-27ed-61a7f8ddd3ae
+let
+ d = Dict{String, String}()
+ d["abc"] = "123"
+ typeof(d)
+end
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
+PLUTO_PROJECT_TOML_CONTENTS = """
+[deps]
+Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
+Luxor = "ae8d54c2-7ccd-5906-9d76-62fc9837b5bc"
+PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
+
+[compat]
+Colors = "~0.12.8"
+Luxor = "~2.13.0"
+PlutoUI = "~0.7.9"
+"""
+
+# ╔═╡ 00000000-0000-0000-0000-000000000002
+PLUTO_MANIFEST_TOML_CONTENTS = """
+# This file is machine-generated - editing it directly is not advised
+
+[[AbstractFFTs]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
+uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
+version = "1.0.1"
+
+[[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 = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+
+[[Base64]]
+uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+
+[[Bzip2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
+uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
+version = "1.0.8+0"
+
+[[Cairo]]
+deps = ["Cairo_jll", "Colors", "Glib_jll", "Graphics", "Libdl", "Pango_jll"]
+git-tree-sha1 = "d0b3f8b4ad16cb0a2988c6788646a5e6a17b6b1b"
+uuid = "159f3aea-2a34-519c-b102-8c37f9878175"
+version = "1.0.5"
+
+[[Cairo_jll]]
+deps = ["Artifacts", "Bzip2_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 = "f2202b55d816427cd385a9a4f3ffb226bee80f99"
+uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
+version = "1.16.1+0"
+
+[[ChainRulesCore]]
+deps = ["Compat", "LinearAlgebra", "SparseArrays"]
+git-tree-sha1 = "dcc25ff085cf548bc8befad5ce048391a7c07d40"
+uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+version = "0.10.11"
+
+[[ColorTypes]]
+deps = ["FixedPointNumbers", "Random"]
+git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
+uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
+version = "0.11.0"
+
+[[ColorVectorSpace]]
+deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"]
+git-tree-sha1 = "42a9b08d3f2f951c9b283ea427d96ed9f1f30343"
+uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
+version = "0.9.5"
+
+[[Colors]]
+deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
+git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
+uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
+version = "0.12.8"
+
+[[Compat]]
+deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
+git-tree-sha1 = "dc7dedc2c2aa9faf59a55c622760a25cbefbe941"
+uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
+version = "3.31.0"
+
+[[CompilerSupportLibraries_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+
+[[Dates]]
+deps = ["Printf"]
+uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
+
+[[DelimitedFiles]]
+deps = ["Mmap"]
+uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
+
+[[Distributed]]
+deps = ["Random", "Serialization", "Sockets"]
+uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
+
+[[DocStringExtensions]]
+deps = ["LibGit2"]
+git-tree-sha1 = "a32185f5428d3986f47c2ab78b1f216d5e6cc96f"
+uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
+version = "0.8.5"
+
+[[Downloads]]
+deps = ["ArgTools", "LibCURL", "NetworkOptions"]
+uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
+
+[[Expat_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
+uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
+version = "2.2.10+0"
+
+[[FFMPEG]]
+deps = ["FFMPEG_jll"]
+git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
+uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
+version = "0.4.1"
+
+[[FFMPEG_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
+git-tree-sha1 = "d8a578692e3077ac998b50c0217dfd67f21d1e5f"
+uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
+version = "4.4.0+0"
+
+[[FileIO]]
+deps = ["Pkg", "Requires", "UUIDs"]
+git-tree-sha1 = "256d8e6188f3f1ebfa1a5d17e072a0efafa8c5bf"
+uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
+version = "1.10.1"
+
+[[FixedPointNumbers]]
+deps = ["Statistics"]
+git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
+uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
+version = "0.8.4"
+
+[[Fontconfig_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
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+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_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_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_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"
+
+[[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"
+
+[[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"
+
+[[libfdk_aac_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
+uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
+version = "2.0.2+0"
+
+[[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 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2021.5.5+0"
+
+[[x265_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.5.0+0"
+"""
+
+# ╔═╡ Cell order:
+# ╟─9f433e5e-3606-11eb-2a5c-d70bb3978644
+# ╠═56760c70-eb66-11ea-2335-c9c8cbcb56f3
+# ╠═ebf8a9e0-fe37-11ea-39ae-8b0f814fed81
+# ╠═1d2fa270-3493-11eb-33a8-092f981b3b0d
+# ╠═68fd3a00-356f-11eb-288b-d95699f8f8ab
+# ╠═d6ae6110-3609-11eb-27ed-61a7f8ddd3ae
+# ╟─00000000-0000-0000-0000-000000000001
+# ╟─00000000-0000-0000-0000-000000000002
--- /dev/null
+### A Pluto.jl notebook ###
+# v0.11.12
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ bd48bd00-ed0d-11ea-2663-f731a2d178a0
+using PlutoUI, Plots, LinearAlgebra
+
+# ╔═╡ 1e0d6c70-ed0f-11ea-1ebb-673f3c8820c5
+md"## Week 4 - Discrete Fourier series"
+
+# ╔═╡ 2f414340-ed0f-11ea-15bf-39c2f92785d5
+begin
+ synthesis(X, n, N) = 1 / N * sum(X(k) * exp(im * 2π / N * n * k) for k ∈ 0:N-1)
+ analysis(x, k, N) = sum(x(n) * exp(-im * 2π / N * n * k) for n ∈ 0:N-1)
+
+ # Input signal 'f'.
+ f(n) = sin(n * 2π / 100) + 0.2 * sin(10 * n * 2π / 100 + π / 4)
+
+ # Analysis of 'f'.
+ N = 100
+ points_in_freq_domain = [analysis(f, k, N) for k ∈ 0:N-1]
+ F(n) = points_in_freq_domain[n % length(points_in_freq_domain) + 1]
+
+ # Synthesis of 'F'.
+ points_in_time_domain = [synthesis(F, n, N) for n ∈ 0:N-1] .|> real
+end
+
+# ╔═╡ 8fb32ce0-ed12-11ea-0d7c-b3d725a40f62
+scatter(0:N-1, f, label = false, title = "Input: f(n)")
+
+# ╔═╡ 47488270-ed12-11ea-0350-876a454b79c8
+scatter(0:N-1, points_in_freq_domain |> imag, label = false, title = "Frequency domain: F(n): Imaginary")
+
+# ╔═╡ 5e0c5710-ed13-11ea-149e-91be4a55745d
+scatter(0:N-1, points_in_freq_domain |> real, label = false, title = "Frequency domain: F(n): Real")
+
+# ╔═╡ f0d0a020-ed12-11ea-1c5b-8959ad6e2ec1
+scatter(0:N-1, points_in_time_domain |> real, label = false, title = "Back to time domain")
+
+# ╔═╡ Cell order:
+# ╠═bd48bd00-ed0d-11ea-2663-f731a2d178a0
+# ╟─1e0d6c70-ed0f-11ea-1ebb-673f3c8820c5
+# ╠═2f414340-ed0f-11ea-15bf-39c2f92785d5
+# ╠═8fb32ce0-ed12-11ea-0d7c-b3d725a40f62
+# ╠═47488270-ed12-11ea-0350-876a454b79c8
+# ╠═5e0c5710-ed13-11ea-149e-91be4a55745d
+# ╠═f0d0a020-ed12-11ea-1c5b-8959ad6e2ec1
--- /dev/null
+### A Pluto.jl notebook ###
+# v0.15.1
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ 0b68706f-ec74-4184-9a4b-d1d455356310
+using LinearAlgebra, Statistics, Plots, PlutoUI, Images, FileIO, DataFrames, Printf
+
+# ╔═╡ dff4f0db-bbca-4796-adca-708c3eb428da
+html"""<style>
+main {
+ max-width: 90% !important;
+ margin-right: 100px !important;
+}
+</style>
+"""
+
+# ╔═╡ 56760c70-eb66-11ea-2335-c9c8cbcb56f3
+begin
+ default(label = false, minorgrid = true) # Default values for plots.
+ plotly()
+end
+
+# ╔═╡ 9f9e6944-a21c-40b1-a57c-02226f537d64
+let
+ # From http://jeanmariechauvet.com/papers/curttrig.html .
+ sin_poly(x) = 1.5706268 * x - 0.6432292 * x^3 + 0.0727102 * x^5 # Number of multiplications: 7, Number of additions: 2.
+
+ sin_ref(x) = sin(pi/2 * x)
+
+ function sin_bhaskara(x)
+ x₂ = abs(pi/2 * x)
+ # Number of multiplications: 4, Number of division: 1 Number of additions: 3.
+ y = 16 * x₂ * (π - x₂) / (5 * π^2 - 4 * x₂ * (π - x₂))
+ y * sign(x)
+ end
+
+ delta_poly(x) = abs(sin_poly(x) - sin_ref(x))
+ delta_bhaskara(x) = abs(sin_bhaskara(x) - sin_ref(x)) * 200
+
+ #plot(LinRange(-2, 2, 1000), delta)
+ #plot!(LinRange(-2, 2, 1000), sin_poly)
+ plot(LinRange(-2, 2, 1000), sin_ref)
+ plot!(LinRange(-2, 2, 1000), sin_bhaskara)
+ plot!(LinRange(-2, 2, 1000), delta_bhaskara)
+end
+
+# ╔═╡ 33678d31-93b2-4f6c-a2a4-a88cfdfea323
+md"---"
+
+# ╔═╡ 476f7d9e-3b3c-455d-90ce-8b70f8984eda
+function throughput(array_size, speed)
+ sample_per_sec_for_unit_speed = 200 # For 1 m/s.
+ one_sample_size = 112
+ header_size = 6
+ array_sizes_size = 14 * 4
+ speed * sample_per_sec_for_unit_speed / array_size * (array_size * one_sample_size + array_sizes_size + header_size)
+end
+
+# ╔═╡ 54d970a1-2bb7-4ec2-9dc2-6249497447d7
+function format_bytes(bytes)
+ if bytes / 1024^2 > 1
+ @sprintf("%.2f MB", bytes / 1024^2)
+ else
+ @sprintf("%.0f kB", bytes / 1024)
+ end
+end
+
+# ╔═╡ 268abf9c-d869-4e7e-b02e-079d1be2d9cf
+let
+ df = DataFrame(speed = Float64[], array_size = Float64[], throughput = Float64[], formatted_throughput = String[])
+
+ for array_size ∈ [1 10 100]
+ for speed ∈ [10 50 100 150]
+ tp = throughput(array_size, speed)
+ push!(
+ df,
+ [
+ speed
+ array_size
+ tp
+ format_bytes(tp) * "/s"
+ ]
+ )
+ end
+ end
+ df
+end
+
+# ╔═╡ 31c1ddf4-c7a5-45b3-93b2-acf5ebef8d5e
+14 * 4
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
+PLUTO_PROJECT_TOML_CONTENTS = """
+[deps]
+DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
+Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
+Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
+[compat]
+DataFrames = "~1.2.0"
+FileIO = "~1.10.1"
+Images = "~0.24.1"
+Plots = "~1.18.2"
+PlutoUI = "~0.7.9"
+"""
+
+# ╔═╡ 00000000-0000-0000-0000-000000000002
+PLUTO_MANIFEST_TOML_CONTENTS = """
+# This file is machine-generated - editing it directly is not advised
+
+[[AbstractFFTs]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
+uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
+version = "1.0.1"
+
+[[Adapt]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
+uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+version = "3.3.1"
+
+[[ArgTools]]
+uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
+
+[[ArrayInterface]]
+deps = ["IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
+git-tree-sha1 = "045ff5e1bc8c6fb1ecb28694abba0a0d55b5f4f5"
+uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+version = "3.1.17"
+
+[[Artifacts]]
+uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+
+[[AxisAlgorithms]]
+deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
+git-tree-sha1 = "a4d07a1c313392a77042855df46c5f534076fab9"
+uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
+version = "1.0.0"
+
+[[AxisArrays]]
+deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"]
+git-tree-sha1 = "f31f50712cbdf40ee8287f0443b57503e34122ef"
+uuid = "39de3d68-74b9-583c-8d2d-e117c070f3a9"
+version = "0.4.3"
+
+[[Base64]]
+uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+
+[[Bzip2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "c3598e525718abcc440f69cc6d5f60dda0a1b61e"
+uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
+version = "1.0.6+5"
+
+[[CEnum]]
+git-tree-sha1 = "215a9aa4a1f23fbd05b92769fdd62559488d70e9"
+uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
+version = "0.4.1"
+
+[[Cairo_jll]]
+deps = ["Artifacts", "Bzip2_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 = "e2f47f6d8337369411569fd45ae5753ca10394c6"
+uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
+version = "1.16.0+6"
+
+[[CatIndices]]
+deps = ["CustomUnitRanges", "OffsetArrays"]
+git-tree-sha1 = "a0f80a09780eed9b1d106a1bf62041c2efc995bc"
+uuid = "aafaddc9-749c-510e-ac4f-586e18779b91"
+version = "0.2.2"
+
+[[ChainRulesCore]]
+deps = ["Compat", "LinearAlgebra", "SparseArrays"]
+git-tree-sha1 = "dcc25ff085cf548bc8befad5ce048391a7c07d40"
+uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+version = "0.10.11"
+
+[[ColorSchemes]]
+deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random", "StaticArrays"]
+git-tree-sha1 = "ed268efe58512df8c7e224d2e170afd76dd6a417"
+uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
+version = "3.13.0"
+
+[[ColorTypes]]
+deps = ["FixedPointNumbers", "Random"]
+git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
+uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
+version = "0.11.0"
+
+[[ColorVectorSpace]]
+deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"]
+git-tree-sha1 = "42a9b08d3f2f951c9b283ea427d96ed9f1f30343"
+uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
+version = "0.9.5"
+
+[[Colors]]
+deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
+git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
+uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
+version = "0.12.8"
+
+[[Compat]]
+deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
+git-tree-sha1 = "dc7dedc2c2aa9faf59a55c622760a25cbefbe941"
+uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
+version = "3.31.0"
+
+[[CompilerSupportLibraries_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+
+[[ComputationalResources]]
+git-tree-sha1 = "52cb3ec90e8a8bea0e62e275ba577ad0f74821f7"
+uuid = "ed09eef8-17a6-5b46-8889-db040fac31e3"
+version = "0.3.2"
+
+[[Contour]]
+deps = ["StaticArrays"]
+git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
+uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
+version = "0.5.7"
+
+[[CoordinateTransformations]]
+deps = ["LinearAlgebra", "StaticArrays"]
+git-tree-sha1 = "6d1c23e740a586955645500bbec662476204a52c"
+uuid = "150eb455-5306-5404-9cee-2592286d6298"
+version = "0.6.1"
+
+[[Crayons]]
+git-tree-sha1 = "3f71217b538d7aaee0b69ab47d9b7724ca8afa0d"
+uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
+version = "4.0.4"
+
+[[CustomUnitRanges]]
+git-tree-sha1 = "537c988076d001469093945f3bd0b300b8d3a7f3"
+uuid = "dc8bdbbb-1ca9-579f-8c36-e416f6a65cce"
+version = "1.0.1"
+
+[[DataAPI]]
+git-tree-sha1 = "ee400abb2298bd13bfc3df1c412ed228061a2385"
+uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
+version = "1.7.0"
+
+[[DataFrames]]
+deps = ["Compat", "DataAPI", "Future", "InvertedIndices", "IteratorInterfaceExtensions", "LinearAlgebra", "Markdown", "Missings", "PooledArrays", "PrettyTables", "Printf", "REPL", "Reexport", "SortingAlgorithms", "Statistics", "TableTraits", "Tables", "Unicode"]
+git-tree-sha1 = "1dadfca11c0e08e03ab15b63aaeda55266754bad"
+uuid = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+version = "1.2.0"
+
+[[DataStructures]]
+deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
+git-tree-sha1 = "4437b64df1e0adccc3e5d1adbc3ac741095e4677"
+uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+version = "0.18.9"
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+git-tree-sha1 = "52c5f816857bfb3291c7d25420b1f4aca0a74d18"
+uuid = "06e1c1a7-607b-532d-9fad-de7d9aa2abac"
+version = "0.3.0"
+
+[[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"
+
+[[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 = "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"
+
+[[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 = "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:
+# ╠═dff4f0db-bbca-4796-adca-708c3eb428da
+# ╠═0b68706f-ec74-4184-9a4b-d1d455356310
+# ╠═56760c70-eb66-11ea-2335-c9c8cbcb56f3
+# ╠═9f9e6944-a21c-40b1-a57c-02226f537d64
+# ╟─33678d31-93b2-4f6c-a2a4-a88cfdfea323
+# ╠═476f7d9e-3b3c-455d-90ce-8b70f8984eda
+# ╠═54d970a1-2bb7-4ec2-9dc2-6249497447d7
+# ╠═268abf9c-d869-4e7e-b02e-079d1be2d9cf
+# ╠═31c1ddf4-c7a5-45b3-93b2-acf5ebef8d5e
+# ╟─00000000-0000-0000-0000-000000000001
+# ╟─00000000-0000-0000-0000-000000000002
projects / julia_notebooks.git / commitdiff