diff --git a/docs/Project.toml b/docs/Project.toml
index fb5dd1c9f..cd40d4a03 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -8,6 +8,8 @@ CTModels = "34c4fa32-2049-4079-8329-de33c2a22e2d"
 CTParser = "32681960-a1b1-40db-9bff-a1ca817385d1"
 CTSolvers = "d3e8d392-8e4b-4d9b-8e92-d7d4e3650ef6"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
+Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
@@ -41,6 +43,8 @@ CTModels = "0.19"
 CTParser = "0.9"
 CTSolvers = "0.5"
 CUDA = "6"
+CairoMakie = "0.15"
+Colors = "0.13"
 CommonSolve = "0.2"
 DifferentiationInterface = "0.7"
 Documenter = "1"
diff --git a/docs/make.jl b/docs/make.jl
index 02e003333..2e349a994 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -344,6 +344,7 @@ with_api_reference(src_dir, ext_dir) do api_pages
                 "Control and variable together" => "examples/control-and-variable.md",
                 "Singular control" => "examples/singular-control.md",
                 "State constraint" => "examples/state-constraint.md",
+                "The logo" => "examples/logo.md",
             ],
             "API Reference" => api_pages_final,
             "Migrating to v2.1" => "migration.md",
diff --git a/docs/src/assets/Manifest.toml b/docs/src/assets/Manifest.toml
index 42734b9b4..11f620bf9 100644
--- a/docs/src/assets/Manifest.toml
+++ b/docs/src/assets/Manifest.toml
@@ -2,7 +2,7 @@
 
 julia_version = "1.12.6"
 manifest_format = "2.0"
-project_hash = "4f120b12e3e55dc3ce2b9dd77987629af1307eb4"
+project_hash = "d3d793016ef8ca79fcd1259ad9538e451318d633"
 
 [[deps.ADNLPModels]]
 deps = ["ADTypes", "ForwardDiff", "LinearAlgebra", "NLPModels", "Requires", "ReverseDiff", "SparseArrays", "SparseConnectivityTracer", "SparseMatrixColorings"]
@@ -90,12 +90,23 @@ weakdeps = ["SparseArrays", "StaticArrays"]
     AdaptSparseArraysExt = "SparseArrays"
     AdaptStaticArraysExt = "StaticArrays"
 
+[[deps.AdaptivePredicates]]
+git-tree-sha1 = "7e651ea8d262d2d74ce75fdf47c4d63c07dba7a6"
+uuid = "35492f91-a3bd-45ad-95db-fcad7dcfedb7"
+version = "1.2.0"
+
 [[deps.AliasTables]]
 deps = ["PtrArrays", "Random"]
 git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff"
 uuid = "66dad0bd-aa9a-41b7-9441-69ab47430ed8"
 version = "1.1.3"
 
+[[deps.Animations]]
+deps = ["Colors"]
+git-tree-sha1 = "e092fa223bf66a3c41f9c022bd074d916dc303e7"
+uuid = "27a7e980-b3e6-11e9-2bcd-0b925532e340"
+version = "0.4.2"
+
 [[deps.ArgTools]]
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 version = "1.1.2"
@@ -161,6 +172,24 @@ version = "1.1.3"
     OpenCL = "08131aa3-fb12-5dee-8b74-c09406e224a2"
     oneAPI = "8f75cd03-7ff8-4ecb-9b8f-daf728133b1b"
 
+[[deps.Automa]]
+deps = ["PrecompileTools", "TranscodingStreams"]
+git-tree-sha1 = "94eab0b3ccdcac361188cc661daf69d4433c1818"
+uuid = "67c07d97-cdcb-5c2c-af73-a7f9c32a568b"
+version = "1.2.0"
+
+[[deps.AxisAlgorithms]]
+deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
+git-tree-sha1 = "01b8ccb13d68535d73d2b0c23e39bd23155fb712"
+uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
+version = "1.1.0"
+
+[[deps.AxisArrays]]
+deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"]
+git-tree-sha1 = "4126b08903b777c88edf1754288144a0492c05ad"
+uuid = "39de3d68-74b9-583c-8d2d-e117c070f3a9"
+version = "0.4.8"
+
 [[deps.BFloat16s]]
 deps = ["LinearAlgebra", "Printf", "Random"]
 git-tree-sha1 = "e386db8b4753b42caac75ac81d0a4fe161a68a97"
@@ -171,6 +200,11 @@ version = "0.6.1"
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 version = "1.11.0"
 
+[[deps.BaseDirs]]
+git-tree-sha1 = "8c290a1b223deaeea9aea44b235d24546da8eb98"
+uuid = "18cc8868-cbac-4acf-b575-c8ff214dc66f"
+version = "1.4.0"
+
 [[deps.BinaryHeaps]]
 deps = ["PrecompileTools"]
 git-tree-sha1 = "0adb6d8d0a4bae93a07d79c8d59eaf617f4c59da"
@@ -199,6 +233,22 @@ git-tree-sha1 = "389ad5c84de1ae7cf0e28e381131c98ea87d54fc"
 uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
 version = "0.5.0"
 
+[[deps.CRC32c]]
+uuid = "8bf52ea8-c179-5cab-976a-9e18b702a9bc"
+version = "1.11.0"
+
+[[deps.CRlibm]]
+deps = ["CRlibm_jll"]
+git-tree-sha1 = "66188d9d103b92b6cd705214242e27f5737a1e5e"
+uuid = "96374032-68de-5a5b-8d9e-752f78720389"
+version = "1.0.2"
+
+[[deps.CRlibm_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "e329286945d0cfc04456972ea732551869af1cfc"
+uuid = "4e9b3aee-d8a1-5a3d-ad8b-7d824db253f0"
+version = "1.0.1+0"
+
 [[deps.CTBase]]
 deps = ["ADTypes", "DocStringExtensions"]
 git-tree-sha1 = "dcf16198ad4281aa276dbe4bc4c1b2e719d6682e"
@@ -234,6 +284,7 @@ deps = ["ADTypes", "CTBase", "CTModels", "CTSolvers", "CommonSolve", "DocStringE
 git-tree-sha1 = "ebd5a2f6b860f423091e523325d8e2b1146b25ce"
 uuid = "1c39547c-7794-42f7-af83-d98194f657c2"
 version = "0.18.0-beta"
+weakdeps = ["Makie", "Plots", "SciMLBase", "StaticArrays"]
 
     [deps.CTFlows.extensions]
     CTFlowsMakie = ["Makie"]
@@ -242,12 +293,6 @@ version = "0.18.0-beta"
     CTFlowsSciMLIntegrator = ["SciMLBase"]
     CTFlowsStaticArrays = ["StaticArrays"]
 
-    [deps.CTFlows.weakdeps]
-    Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
-    Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
-    SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
-    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
-
 [[deps.CTLie]]
 deps = ["CTBase", "DocStringExtensions", "MacroTools"]
 git-tree-sha1 = "be205ccc6abefea748b0989a2d634a1e5a025f90"
@@ -259,6 +304,7 @@ deps = ["CTBase", "DocStringExtensions", "LinearAlgebra", "MLStyle", "MacroTools
 git-tree-sha1 = "4c62f9e77edcea647422d74b257d8ed0670a9a1d"
 uuid = "34c4fa32-2049-4079-8329-de33c2a22e2d"
 version = "0.19.2-beta"
+weakdeps = ["JLD2", "JSON3", "Makie", "Plots"]
 
     [deps.CTModels.extensions]
     CTModelsJLD = "JLD2"
@@ -266,12 +312,6 @@ version = "0.19.2-beta"
     CTModelsMakie = "Makie"
     CTModelsPlots = "Plots"
 
-    [deps.CTModels.weakdeps]
-    JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
-    JSON3 = "0f8b85d8-7281-11e9-16c2-39a750bddbf1"
-    Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
-    Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
-
 [[deps.CTParser]]
 deps = ["CTBase", "DocStringExtensions", "MLStyle", "OrderedCollections", "Parameters", "Unicode"]
 git-tree-sha1 = "3f745c73919729ca654d02e1091fce5583facacc"
@@ -377,6 +417,18 @@ git-tree-sha1 = "9048858c70e1f8006dd5f6fe9b19bb81514e76d3"
 uuid = "9e67e8f6-ba02-4b6c-a7db-3b11ae1e7ab7"
 version = "6.3.1"
 
+[[deps.Cairo]]
+deps = ["Cairo_jll", "Colors", "Glib_jll", "Graphics", "Libdl", "Pango_jll"]
+git-tree-sha1 = "71aa551c5c33f1a4415867fe06b7844faadb0ae9"
+uuid = "159f3aea-2a34-519c-b102-8c37f9878175"
+version = "1.1.1"
+
+[[deps.CairoMakie]]
+deps = ["CRC32c", "Cairo", "Cairo_jll", "Colors", "FileIO", "FreeType", "GeometryBasics", "LinearAlgebra", "Makie", "PrecompileTools"]
+git-tree-sha1 = "47142129b1777e21da58cff265050b10d8560588"
+uuid = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
+version = "0.15.13"
+
 [[deps.Cairo_jll]]
 deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
 git-tree-sha1 = "1fa950ebc3e37eccd51c6a8fe1f92f7d86263522"
@@ -416,6 +468,18 @@ git-tree-sha1 = "970758a3d591a2a5c2a907c53f2e2f8c1b1d3537"
 uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
 version = "0.7.9"
 
+[[deps.CodecZstd]]
+deps = ["TranscodingStreams", "Zstd_jll"]
+git-tree-sha1 = "da54a6cd93c54950c15adf1d336cfd7d71f51a56"
+uuid = "6b39b394-51ab-5f42-8807-6242bab2b4c2"
+version = "0.8.7"
+
+[[deps.ColorBrewer]]
+deps = ["Colors", "JSON"]
+git-tree-sha1 = "07da79661b919001e6863b81fc572497daa58349"
+uuid = "a2cac450-b92f-5266-8821-25eda20663c8"
+version = "0.4.2"
+
 [[deps.ColorSchemes]]
 deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
 git-tree-sha1 = "b0fd3f56fa442f81e0a47815c92245acfaaa4e34"
@@ -489,6 +553,12 @@ weakdeps = ["InverseFunctions"]
     [deps.CompositionsBase.extensions]
     CompositionsBaseInverseFunctionsExt = "InverseFunctions"
 
+[[deps.ComputePipeline]]
+deps = ["Observables", "Preferences"]
+git-tree-sha1 = "7bc84b769c1d384315e7b5c4ac03a6c303e6cf35"
+uuid = "95dc2771-c249-4cd0-9c9f-1f3b4330693c"
+version = "0.1.8"
+
 [[deps.ConcreteStructs]]
 deps = ["PrecompileTools"]
 git-tree-sha1 = "a72c3b5ce6d2a477f55b5c9b8756e91e695c67f6"
@@ -499,22 +569,30 @@ version = "0.2.8"
 git-tree-sha1 = "b4b092499347b18a015186eae3042f72267106cb"
 uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 version = "1.6.0"
+weakdeps = ["IntervalSets", "LinearAlgebra", "StaticArrays"]
 
     [deps.ConstructionBase.extensions]
     ConstructionBaseIntervalSetsExt = "IntervalSets"
     ConstructionBaseLinearAlgebraExt = "LinearAlgebra"
     ConstructionBaseStaticArraysExt = "StaticArrays"
 
-    [deps.ConstructionBase.weakdeps]
-    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
-    LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
-
 [[deps.Contour]]
 git-tree-sha1 = "439e35b0b36e2e5881738abc8857bd92ad6ff9a8"
 uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
 version = "0.6.3"
 
+[[deps.CoreMath]]
+deps = ["CoreMath_jll"]
+git-tree-sha1 = "8c0480f92b1b1796239156a1b9b1bfb1b39499b4"
+uuid = "b7a15901-be09-4a0e-87d2-2e66b0e09b5a"
+version = "0.1.0"
+
+[[deps.CoreMath_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "a692a4c1dc59a4b8bc0b6403876eb3250fde2bc3"
+uuid = "a38c48d9-6df1-5ac9-9223-b6ada3b5572b"
+version = "0.1.0+0"
+
 [[deps.Crayons]]
 git-tree-sha1 = "54b76cbb40d9a0f5368c880725b2f141da77c94f"
 uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
@@ -547,6 +625,12 @@ git-tree-sha1 = "473e9afc9cf30814eb67ffa5f2db7df82c3ad9fd"
 uuid = "ee1fde0b-3d02-5ea6-8484-8dfef6360eab"
 version = "1.16.2+0"
 
+[[deps.DelaunayTriangulation]]
+deps = ["AdaptivePredicates", "EnumX", "ExactPredicates", "Random"]
+git-tree-sha1 = "c55f5a9fd67bdbc8e089b5a3111fe4292986a8e8"
+uuid = "927a84f5-c5f4-47a5-9785-b46e178433df"
+version = "1.6.6"
+
 [[deps.DelimitedFiles]]
 deps = ["Mmap"]
 git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae"
@@ -666,6 +750,24 @@ deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 version = "1.11.0"
 
+[[deps.Distributions]]
+deps = ["AliasTables", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "Roots", "SpecialFunctions", "Statistics", "StatsAPI", "StatsBase", "StatsFuns"]
+git-tree-sha1 = "a958ab3a40c755563f5e1405c0846cb0446bf19d"
+uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
+version = "0.25.131"
+
+    [deps.Distributions.extensions]
+    DistributionsChainRulesCoreExt = "ChainRulesCore"
+    DistributionsDensityInterfaceExt = "DensityInterface"
+    DistributionsSparseConnectivityTracerExt = "SparseConnectivityTracer"
+    DistributionsTestExt = "Test"
+
+    [deps.Distributions.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    DensityInterface = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
+    SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
+    Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
 [[deps.DocInventories]]
 deps = ["CodecZlib", "Downloads", "TOML"]
 git-tree-sha1 = "e97cfa8680a39396924dcdca4b7ff1014ed5c499"
@@ -706,6 +808,12 @@ deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
 version = "1.7.0"
 
+[[deps.EarCut_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "e3290f2d49e661fbd94046d7e3726ffcb2d41053"
+uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
+version = "2.2.4+0"
+
 [[deps.EnumX]]
 git-tree-sha1 = "c49898e8438c828577f04b92fc9368c388ac783c"
 uuid = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
@@ -752,6 +860,12 @@ version = "0.12.0"
     SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
     oneAPI = "8f75cd03-7ff8-4ecb-9b8f-daf728133b1b"
 
+[[deps.ExactPredicates]]
+deps = ["IntervalArithmetic", "Random", "StaticArrays"]
+git-tree-sha1 = "83231673ea4d3d6008ac74dc5079e77ab2209d8f"
+uuid = "429591f6-91af-11e9-00e2-59fbe8cec110"
+version = "2.2.9"
+
 [[deps.Expat_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "f4d39eee89f1e58c26bf447f1d4156c0125d6838"
@@ -775,6 +889,12 @@ git-tree-sha1 = "7a58e45171b63ed4782f2d36fdee8713a469e6e0"
 uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
 version = "8.1.2+0"
 
+[[deps.FFTA]]
+deps = ["AbstractFFTs", "DocStringExtensions", "LinearAlgebra", "MuladdMacro", "Primes", "Random", "Reexport"]
+git-tree-sha1 = "65e55303b72f4a567a51b174dd2c47496efeb95a"
+uuid = "b86e33f2-c0db-4aa1-a6e0-ab43e668529e"
+version = "0.3.1"
+
 [[deps.FastBroadcast]]
 deps = ["ArrayInterface", "LinearAlgebra", "PrecompileTools"]
 git-tree-sha1 = "c8f8eefadaa330d982bbf5e395c34e53a13ab668"
@@ -828,6 +948,33 @@ weakdeps = ["HTTP"]
     [deps.FileIO.extensions]
     HTTPExt = "HTTP"
 
+[[deps.FilePaths]]
+deps = ["FilePathsBase", "MacroTools", "Reexport"]
+git-tree-sha1 = "a1b2fbfe98503f15b665ed45b3d149e5d8895e4c"
+uuid = "8fc22ac5-c921-52a6-82fd-178b2807b824"
+version = "0.9.0"
+
+    [deps.FilePaths.extensions]
+    FilePathsGlobExt = "Glob"
+    FilePathsURIParserExt = "URIParser"
+    FilePathsURIsExt = "URIs"
+
+    [deps.FilePaths.weakdeps]
+    Glob = "c27321d9-0574-5035-807b-f59d2c89b15c"
+    URIParser = "30578b45-9adc-5946-b283-645ec420af67"
+    URIs = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
+
+[[deps.FilePathsBase]]
+deps = ["Compat", "Dates"]
+git-tree-sha1 = "3bab2c5aa25e7840a4b065805c0cdfc01f3068d2"
+uuid = "48062228-2e41-5def-b9a4-89aafe57970f"
+version = "0.9.24"
+weakdeps = ["Mmap", "Test"]
+
+    [deps.FilePathsBase.extensions]
+    FilePathsBaseMmapExt = "Mmap"
+    FilePathsBaseTestExt = "Test"
+
 [[deps.FileWatching]]
 uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
 version = "1.11.0"
@@ -837,6 +984,7 @@ deps = ["LinearAlgebra"]
 git-tree-sha1 = "5bad39456d9f0166184fce2248783dd9862645c1"
 uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
 version = "1.17.0"
+weakdeps = ["PDMats", "SparseArrays", "StaticArrays", "Statistics"]
 
     [deps.FillArrays.extensions]
     FillArraysPDMatsExt = "PDMats"
@@ -844,12 +992,6 @@ version = "1.17.0"
     FillArraysStaticArraysExt = "StaticArrays"
     FillArraysStatisticsExt = "Statistics"
 
-    [deps.FillArrays.weakdeps]
-    PDMats = "90014a1f-27ba-587c-ab20-58faa44d9150"
-    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
-    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
-    Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
-
 [[deps.FindFirstFunctions]]
 deps = ["PrecompileTools"]
 git-tree-sha1 = "bba475ce782fc77777f539cf0b7c029207798db1"
@@ -901,12 +1043,24 @@ weakdeps = ["StaticArrays"]
     [deps.ForwardDiff.extensions]
     ForwardDiffStaticArraysExt = "StaticArrays"
 
+[[deps.FreeType]]
+deps = ["CEnum", "FreeType2_jll"]
+git-tree-sha1 = "907369da0f8e80728ab49c1c7e09327bf0d6d999"
+uuid = "b38be410-82b0-50bf-ab77-7b57e271db43"
+version = "4.1.1"
+
 [[deps.FreeType2_jll]]
 deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
 git-tree-sha1 = "70329abc09b886fd2c5d94ad2d9527639c421e3e"
 uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
 version = "2.14.3+1"
 
+[[deps.FreeTypeAbstraction]]
+deps = ["BaseDirs", "ColorVectorSpace", "Colors", "FreeType", "GeometryBasics", "Mmap"]
+git-tree-sha1 = "4ebb930ef4a43817991ba35db6317a05e59abd11"
+uuid = "663a7486-cb36-511b-a19d-713bb74d65c9"
+version = "0.10.8"
+
 [[deps.FriBidi_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "7a214fdac5ed5f59a22c2d9a885a16da1c74bbc7"
@@ -999,6 +1153,28 @@ git-tree-sha1 = "f8eb8f7ba13ea75083531647fc8faeda8d541f07"
 uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
 version = "0.73.27+0"
 
+[[deps.Gamma]]
+deps = ["LogExpFunctions"]
+git-tree-sha1 = "becc397f7cfb06e343496ae6ffb04818a851da51"
+uuid = "a0844989-3bd2-4988-8bea-c9407ab0941b"
+version = "1.2.0"
+
+[[deps.GeometryBasics]]
+deps = ["EarCut_jll", "LinearAlgebra", "PrecompileTools", "Random", "StaticArrays"]
+git-tree-sha1 = "592cfb5ed8b02804f6a9c04091571c393081f73a"
+uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
+version = "0.5.12"
+
+    [deps.GeometryBasics.extensions]
+    ExtentsExt = "Extents"
+    GeometryBasicsGeoInterfaceExt = "GeoInterface"
+    IntervalSetsExt = "IntervalSets"
+
+    [deps.GeometryBasics.weakdeps]
+    Extents = "411431e0-e8b7-467b-b5e0-f676ba4f2910"
+    GeoInterface = "cf35fbd7-0cd7-5166-be24-54bfbe79505f"
+    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
+
 [[deps.GettextRuntime_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll"]
 git-tree-sha1 = "45288942190db7c5f760f59c04495064eedf9340"
@@ -1011,6 +1187,12 @@ git-tree-sha1 = "38044a04637976140074d0b0621c1edf0eb531fd"
 uuid = "61579ee1-b43e-5ca0-a5da-69d92c66a64b"
 version = "9.55.1+0"
 
+[[deps.Giflib_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "6570366d757b50fabae9f4315ad74d2e40c0560a"
+uuid = "59f7168a-df46-5410-90c8-f2779963d0ec"
+version = "5.2.3+0"
+
 [[deps.Git]]
 deps = ["Git_LFS_jll", "Git_jll", "JLLWrappers", "OpenSSH_jll"]
 git-tree-sha1 = "824a1890086880696fc908fe12a17bcf61738bd8"
@@ -1035,12 +1217,24 @@ git-tree-sha1 = "090526e65de8f69648ac156daae153de8b56df62"
 uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
 version = "2.88.3+0"
 
+[[deps.Graphics]]
+deps = ["Colors", "LinearAlgebra", "NaNMath"]
+git-tree-sha1 = "a641238db938fff9b2f60d08ed9030387daf428c"
+uuid = "a2bd30eb-e257-5431-a919-1863eab51364"
+version = "1.1.3"
+
 [[deps.Graphite2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "69ffb934a5c5b7e086a0b4fee3427db2556fba6e"
 uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
 version = "1.3.16+0"
 
+[[deps.GridLayoutBase]]
+deps = ["GeometryBasics", "InteractiveUtils", "Observables"]
+git-tree-sha1 = "93d5c27c8de51687a2c70ec0716e6e76f298416f"
+uuid = "3955a311-db13-416c-9275-1d80ed98e5e9"
+version = "0.11.2"
+
 [[deps.Grisu]]
 git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
 uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
@@ -1081,12 +1275,69 @@ git-tree-sha1 = "c35847ca5b4997fc8418836354a56c459bcf48d8"
 uuid = "e33a78d0-f292-5ffc-b300-72abe9b543c8"
 version = "2.14.0+0"
 
+[[deps.HypergeometricFunctions]]
+deps = ["Gamma", "LinearAlgebra"]
+git-tree-sha1 = "31bb6c92405c084617facc1d7ed9eb6c402d061e"
+uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
+version = "0.3.30"
+
 [[deps.IOCapture]]
 deps = ["Logging", "Random"]
 git-tree-sha1 = "0ee181ec08df7d7c911901ea38baf16f755114dc"
 uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
 version = "1.0.0"
 
+[[deps.ImageAxes]]
+deps = ["AxisArrays", "ImageBase", "ImageCore", "Reexport", "SimpleTraits"]
+git-tree-sha1 = "e12629406c6c4442539436581041d372d69c55ba"
+uuid = "2803e5a7-5153-5ecf-9a86-9b4c37f5f5ac"
+version = "0.6.12"
+
+[[deps.ImageBase]]
+deps = ["ImageCore", "Reexport"]
+git-tree-sha1 = "eb49b82c172811fd2c86759fa0553a2221feb909"
+uuid = "c817782e-172a-44cc-b673-b171935fbb9e"
+version = "0.1.7"
+
+[[deps.ImageCore]]
+deps = ["ColorVectorSpace", "Colors", "FixedPointNumbers", "MappedArrays", "MosaicViews", "OffsetArrays", "PaddedViews", "PrecompileTools", "Reexport"]
+git-tree-sha1 = "8c193230235bbcee22c8066b0374f63b5683c2d3"
+uuid = "a09fc81d-aa75-5fe9-8630-4744c3626534"
+version = "0.10.5"
+
+[[deps.ImageIO]]
+deps = ["FileIO", "IndirectArrays", "JpegTurbo", "LazyModules", "Netpbm", "OpenEXR", "PNGFiles", "QOI", "Sixel", "TiffImages", "UUIDs", "WebP"]
+git-tree-sha1 = "f0f005f997dfb8c5fe23920d99458a9619873893"
+uuid = "82e4d734-157c-48bb-816b-45c225c6df19"
+version = "0.6.10"
+
+[[deps.ImageMetadata]]
+deps = ["AxisArrays", "ImageAxes", "ImageBase", "ImageCore"]
+git-tree-sha1 = "2a81c3897be6fbcde0802a0ebe6796d0562f63ec"
+uuid = "bc367c6b-8a6b-528e-b4bd-a4b897500b49"
+version = "0.9.10"
+
+[[deps.Imath_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "dcc8d0cd653e55213df9b75ebc6fe4a8d3254c65"
+uuid = "905a6f67-0a94-5f89-b386-d35d92009cd1"
+version = "3.2.2+0"
+
+[[deps.IndirectArrays]]
+git-tree-sha1 = "012e604e1c7458645cb8b436f8fba789a51b257f"
+uuid = "9b13fd28-a010-5f03-acff-a1bbcff69959"
+version = "1.0.0"
+
+[[deps.Inflate]]
+git-tree-sha1 = "d1b1b796e47d94588b3757fe84fbf65a5ec4a80d"
+uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
+version = "0.1.5"
+
+[[deps.IntegerMathUtils]]
+git-tree-sha1 = "c72458f1962faeb003bf23cbdb75164fe6280906"
+uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235"
+version = "0.1.4"
+
 [[deps.IntelOpenMP_jll]]
 deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl"]
 git-tree-sha1 = "ec1debd61c300961f98064cfb21287613ad7f303"
@@ -1098,6 +1349,54 @@ deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 version = "1.11.0"
 
+[[deps.Interpolations]]
+deps = ["Adapt", "AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
+git-tree-sha1 = "48922d06068130f87e43edef52382e6a94305ae6"
+uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
+version = "0.16.3"
+weakdeps = ["ForwardDiff", "Unitful"]
+
+    [deps.Interpolations.extensions]
+    InterpolationsForwardDiffExt = "ForwardDiff"
+    InterpolationsUnitfulExt = "Unitful"
+
+[[deps.IntervalArithmetic]]
+deps = ["CRlibm", "CoreMath", "MacroTools", "OpenBLASConsistentFPCSR_jll", "Printf", "Random", "RoundingEmulator"]
+git-tree-sha1 = "ff294afb9a15d31d8d7422da138844641a73135f"
+uuid = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
+version = "1.0.11"
+
+    [deps.IntervalArithmetic.extensions]
+    IntervalArithmeticArblibExt = "Arblib"
+    IntervalArithmeticDiffRulesExt = "DiffRules"
+    IntervalArithmeticForwardDiffExt = "ForwardDiff"
+    IntervalArithmeticIntervalSetsExt = "IntervalSets"
+    IntervalArithmeticIrrationalConstantsExt = "IrrationalConstants"
+    IntervalArithmeticLinearAlgebraExt = "LinearAlgebra"
+    IntervalArithmeticRecipesBaseExt = "RecipesBase"
+    IntervalArithmeticSparseArraysExt = "SparseArrays"
+
+    [deps.IntervalArithmetic.weakdeps]
+    Arblib = "fb37089c-8514-4489-9461-98f9c8763369"
+    DiffRules = "b552c78f-8df3-52c6-915a-8e097449b14b"
+    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
+    IrrationalConstants = "92d709cd-6900-40b7-9082-c6be49f344b6"
+    LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+    RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
+    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
+[[deps.IntervalSets]]
+git-tree-sha1 = "79d6bd28c8d9bccc2229784f1bd637689b256377"
+uuid = "8197267c-284f-5f27-9208-e0e47529a953"
+version = "0.7.14"
+weakdeps = ["Random", "RecipesBase", "Statistics"]
+
+    [deps.IntervalSets.extensions]
+    IntervalSetsRandomExt = "Random"
+    IntervalSetsRecipesBaseExt = "RecipesBase"
+    IntervalSetsStatisticsExt = "Statistics"
+
 [[deps.InverseFunctions]]
 git-tree-sha1 = "a779299d77cd080bf77b97535acecd73e1c5e5cb"
 uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
@@ -1131,6 +1430,17 @@ git-tree-sha1 = "b2d91fe939cae05960e760110b328288867b5758"
 uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
 version = "0.2.6"
 
+[[deps.Isoband]]
+deps = ["isoband_jll"]
+git-tree-sha1 = "f9b6d97355599074dc867318950adaa6f9946137"
+uuid = "f1662d9f-8043-43de-a69a-05efc1cc6ff4"
+version = "0.1.1"
+
+[[deps.IterTools]]
+git-tree-sha1 = "42d5f897009e7ff2cf88db414a389e5ed1bdd023"
+uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
+version = "1.10.0"
+
 [[deps.IteratorInterfaceExtensions]]
 git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
 uuid = "82899510-4779-5014-852e-03e436cf321d"
@@ -1182,6 +1492,12 @@ version = "1.14.3"
     [deps.JSON3.weakdeps]
     ArrowTypes = "31f734f8-188a-4ce0-8406-c8a06bd891cd"
 
+[[deps.JpegTurbo]]
+deps = ["CEnum", "FileIO", "ImageCore", "JpegTurbo_jll", "TOML"]
+git-tree-sha1 = "9496de8fb52c224a2e3f9ff403947674517317d9"
+uuid = "b835a17e-a41a-41e7-81f0-2f016b05efe0"
+version = "0.1.6"
+
 [[deps.JpegTurbo_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "037babc10853eeb8e585418922246cb97b8e5b74"
@@ -1229,6 +1545,12 @@ weakdeps = ["EnzymeCore", "LinearAlgebra", "SparseArrays"]
     LinearAlgebraExt = "LinearAlgebra"
     SparseArraysExt = "SparseArrays"
 
+[[deps.KernelDensity]]
+deps = ["Distributions", "DocStringExtensions", "FFTA", "Interpolations", "StatsBase"]
+git-tree-sha1 = "9eda8292dd3268b3b7ec9df21bbfac24e177ec52"
+uuid = "5ab0869b-81aa-558d-bb23-cbf5423bbe9b"
+version = "0.6.12"
+
 [[deps.Krylov]]
 deps = ["LinearAlgebra", "Printf", "SparseArrays"]
 git-tree-sha1 = "71e740d00d71cdb15145d7fe0d6000ec70534598"
@@ -1328,6 +1650,11 @@ deps = ["Artifacts", "Pkg"]
 uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
 version = "1.11.0"
 
+[[deps.LazyModules]]
+git-tree-sha1 = "a560dd966b386ac9ae60bdd3a3d3a326062d3c3e"
+uuid = "8cdb02fc-e678-4876-92c5-9defec4f444e"
+version = "0.3.1"
+
 [[deps.LibCURL]]
 deps = ["LibCURL_jll", "MozillaCACerts_jll"]
 uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
@@ -1652,6 +1979,23 @@ version = "0.10.2"
     cuSOLVER = "887afef0-6a32-4de5-add4-7827692ba8fc"
     cuSPARSE = "b26da814-b3bc-49ef-b0ee-c816305aa060"
 
+[[deps.Makie]]
+deps = ["Animations", "Base64", "CRC32c", "ColorBrewer", "ColorSchemes", "ColorTypes", "Colors", "ComputePipeline", "Contour", "Dates", "DelaunayTriangulation", "Distributions", "DocStringExtensions", "Downloads", "FFMPEG_jll", "FileIO", "FilePaths", "FixedPointNumbers", "Format", "FreeType", "FreeTypeAbstraction", "GeometryBasics", "GridLayoutBase", "ImageBase", "ImageIO", "InteractiveUtils", "Interpolations", "IntervalSets", "InverseFunctions", "Isoband", "KernelDensity", "LaTeXStrings", "LinearAlgebra", "MacroTools", "Markdown", "MathTeXEngine", "Observables", "OffsetArrays", "PNGFiles", "Packing", "Pkg", "PlotUtils", "PolygonOps", "PrecompileTools", "Printf", "REPL", "Random", "RelocatableFolders", "Scratch", "ShaderAbstractions", "SignedDistanceFields", "SparseArrays", "Statistics", "StatsBase", "StatsFuns", "StructArrays", "TriplotBase", "UnicodeFun", "Unitful"]
+git-tree-sha1 = "f2c8715d05bf10f9d4dc354e69dee30b6be53239"
+uuid = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
+version = "0.24.13"
+
+    [deps.Makie.extensions]
+    MakieDynamicQuantitiesExt = "DynamicQuantities"
+
+    [deps.Makie.weakdeps]
+    DynamicQuantities = "06fc5a27-2a28-4c7c-a15d-362465fb6821"
+
+[[deps.MappedArrays]]
+git-tree-sha1 = "0ee4497a4e80dbd29c058fcee6493f5219556f40"
+uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
+version = "0.4.3"
+
 [[deps.Markdown]]
 deps = ["Base64", "JuliaSyntaxHighlighting", "StyledStrings"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
@@ -1663,6 +2007,12 @@ git-tree-sha1 = "93c718d892e73931841089cdc0e982d6dd9cc87b"
 uuid = "d0879d2d-cac2-40c8-9cee-1863dc0c7391"
 version = "0.1.3"
 
+[[deps.MathTeXEngine]]
+deps = ["AbstractTrees", "Automa", "DataStructures", "FreeTypeAbstraction", "GeometryBasics", "LaTeXStrings", "REPL", "RelocatableFolders", "UnicodeFun"]
+git-tree-sha1 = "aa1078778be5a8e5259ff04fbc3d258b3e78d464"
+uuid = "0a4f8689-d25c-4efe-a92b-7142dfc1aa53"
+version = "0.6.9"
+
 [[deps.MaybeInplace]]
 deps = ["ArrayInterface", "LinearAlgebra", "MacroTools", "PrecompileTools"]
 git-tree-sha1 = "f2cde0ae772162f20287b803e623966d0d94dea9"
@@ -1704,6 +2054,12 @@ version = "1.2.0"
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 version = "1.11.0"
 
+[[deps.MosaicViews]]
+deps = ["MappedArrays", "OffsetArrays", "PaddedViews", "StackViews"]
+git-tree-sha1 = "7b86a5d4d70a9f5cdf2dacb3cbe6d251d1a61dbe"
+uuid = "e94cdb99-869f-56ef-bcf0-1ae2bcbe0389"
+version = "0.3.4"
+
 [[deps.MozillaCACerts_jll]]
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 version = "2025.11.4"
@@ -1772,6 +2128,12 @@ git-tree-sha1 = "dbd2e8cd2c1c27f0b584f6661b4309609c5a685e"
 uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
 version = "1.1.4"
 
+[[deps.Netpbm]]
+deps = ["FileIO", "ImageCore", "ImageMetadata"]
+git-tree-sha1 = "d92b107dbb887293622df7697a2223f9f8176fcd"
+uuid = "f09324ee-3d7c-5217-9330-fc30815ba969"
+version = "1.1.1"
+
 [[deps.NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 version = "1.3.0"
@@ -1873,6 +2235,20 @@ weakdeps = ["ForwardDiff"]
     [deps.NonlinearSolveSpectralMethods.extensions]
     NonlinearSolveSpectralMethodsForwardDiffExt = "ForwardDiff"
 
+[[deps.Observables]]
+git-tree-sha1 = "7438a59546cf62428fc9d1bc94729146d37a7225"
+uuid = "510215fc-4207-5dde-b226-833fc4488ee2"
+version = "0.5.5"
+
+[[deps.OffsetArrays]]
+git-tree-sha1 = "117432e406b5c023f665fa73dc26e79ec3630151"
+uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
+version = "1.17.0"
+weakdeps = ["Adapt"]
+
+    [deps.OffsetArrays.extensions]
+    OffsetArraysAdaptExt = "Adapt"
+
 [[deps.Ogg_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "b6aa4566bb7ae78498a5e68943863fa8b5231b59"
@@ -1885,11 +2261,29 @@ git-tree-sha1 = "30870d0f2dc0b2dba76b10df1c58c7f018413e56"
 uuid = "656ef2d0-ae68-5445-9ca0-591084a874a2"
 version = "0.3.34+0"
 
+[[deps.OpenBLASConsistentFPCSR_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "38a93f17e431141c6470bb67a88952a7c4f0e928"
+uuid = "6cdc7f73-28fd-5e50-80fb-958a8875b1af"
+version = "0.3.34+0"
+
 [[deps.OpenBLAS_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
 uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
 version = "0.3.29+0"
 
+[[deps.OpenEXR]]
+deps = ["Colors", "FileIO", "OpenEXR_jll"]
+git-tree-sha1 = "97db9e07fe2091882c765380ef58ec553074e9c7"
+uuid = "52e1d378-f018-4a11-a4be-720524705ac7"
+version = "0.3.3"
+
+[[deps.OpenEXR_jll]]
+deps = ["Artifacts", "Imath_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
+git-tree-sha1 = "fd09db52a90efaae33a3d91f0bc71a22c429e8f1"
+uuid = "18a262bb-aa17-5467-a713-aee519bc75cb"
+version = "3.4.14+0"
+
 [[deps.OpenLibm_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
@@ -2007,6 +2401,34 @@ deps = ["Artifacts", "Libdl"]
 uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
 version = "10.44.0+1"
 
+[[deps.PDMats]]
+deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
+git-tree-sha1 = "123266c25174ef6c8d4718920abc206452cf8de6"
+uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
+version = "0.11.41"
+weakdeps = ["StatsBase"]
+
+    [deps.PDMats.extensions]
+    StatsBaseExt = "StatsBase"
+
+[[deps.PNGFiles]]
+deps = ["Base64", "CEnum", "ImageCore", "IndirectArrays", "OffsetArrays", "libpng_jll"]
+git-tree-sha1 = "32b657a0d57c310a1a172bfc8c8cf68c5e674323"
+uuid = "f57f5aa1-a3ce-4bc8-8ab9-96f992907883"
+version = "0.4.5"
+
+[[deps.Packing]]
+deps = ["GeometryBasics"]
+git-tree-sha1 = "bc5bf2ea3d5351edf285a06b0016788a121ce92c"
+uuid = "19eb6ba3-879d-56ad-ad62-d5c202156566"
+version = "0.5.1"
+
+[[deps.PaddedViews]]
+deps = ["OffsetArrays"]
+git-tree-sha1 = "0fac6313486baae819364c52b4f483450a9d793f"
+uuid = "5432bcbf-9aad-5242-b902-cca2824c8663"
+version = "0.5.12"
+
 [[deps.Pango_jll]]
 deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "1912a9f1b9ca55005b03ba075f8e19993583e237"
@@ -2040,6 +2462,12 @@ weakdeps = ["REPL"]
     [deps.Pkg.extensions]
     REPLExt = "REPL"
 
+[[deps.PkgVersion]]
+deps = ["Pkg"]
+git-tree-sha1 = "f9501cc0430a26bc3d156ae1b5b0c1b47af4d6da"
+uuid = "eebad327-c553-4316-9ea0-9fa01ccd7688"
+version = "0.3.3"
+
 [[deps.PlotThemes]]
 deps = ["PlotUtils", "Statistics"]
 git-tree-sha1 = "41031ef3a1be6f5bbbf3e8073f210556daeae5ca"
@@ -2072,6 +2500,11 @@ version = "1.41.7"
     ImageInTerminal = "d8c32880-2388-543b-8c61-d9f865259254"
     Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
+[[deps.PolygonOps]]
+git-tree-sha1 = "77b3d3605fc1cd0b42d95eba87dfcd2bf67d5ff6"
+uuid = "647866c9-e3ac-4575-94e7-e3d426903924"
+version = "0.1.2"
+
 [[deps.PreallocationTools]]
 deps = ["Adapt", "ArrayInterface", "PrecompileTools", "SciMLPublic"]
 git-tree-sha1 = "cd00e28071a75c98664663f87c2ae447d25c0503"
@@ -2110,11 +2543,23 @@ version = "3.4.8"
     Typstry = "f0ed7684-a786-439e-b1e3-3b82803b501e"
     XLSX = "fdbf4ff8-1666-58a4-91e7-1b58723a45e0"
 
+[[deps.Primes]]
+deps = ["IntegerMathUtils"]
+git-tree-sha1 = "25cdd1d20cd005b52fc12cb6be3f75faaf59bb9b"
+uuid = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae"
+version = "0.5.7"
+
 [[deps.Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 version = "1.11.0"
 
+[[deps.ProgressMeter]]
+deps = ["Distributed", "Printf"]
+git-tree-sha1 = "fbb92c6c56b34e1a2c4c36058f68f332bec840e7"
+uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
+version = "1.11.0"
+
 [[deps.PtrArrays]]
 git-tree-sha1 = "4fbbafbc6251b883f4d2705356f3641f3652a7fe"
 uuid = "43287f4e-b6f4-7ad1-bb20-aadabca52c3d"
@@ -2130,6 +2575,12 @@ weakdeps = ["ForwardDiff"]
     [deps.PureKLU.extensions]
     PureKLUForwardDiffExt = "ForwardDiff"
 
+[[deps.QOI]]
+deps = ["ColorTypes", "FileIO", "FixedPointNumbers"]
+git-tree-sha1 = "472daaa816895cb7aee81658d4e7aec901fa1106"
+uuid = "4b34888f-f399-49d4-9bb3-47ed5cae4e65"
+version = "1.0.2"
+
 [[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 = "144895f6166994730ee7ff8113b981fc360638f1"
@@ -2160,6 +2611,18 @@ git-tree-sha1 = "672c938b4b4e3e0169a07a5f227029d4905456f2"
 uuid = "e99dba38-086e-5de3-a5b1-6e4c66e897c3"
 version = "6.10.2+1"
 
+[[deps.QuadGK]]
+deps = ["DataStructures", "LinearAlgebra"]
+git-tree-sha1 = "5e8e8b0ab68215d7a2b14b9921a946fee794749e"
+uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
+version = "2.11.3"
+
+    [deps.QuadGK.extensions]
+    QuadGKEnzymeExt = "Enzyme"
+
+    [deps.QuadGK.weakdeps]
+    Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+
 [[deps.REPL]]
 deps = ["InteractiveUtils", "JuliaSyntaxHighlighting", "Markdown", "Sockets", "StyledStrings", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
@@ -2182,6 +2645,21 @@ git-tree-sha1 = "c6ec94d2aaba1ab2ff983052cf6a606ca5985902"
 uuid = "e6cf234a-135c-5ec9-84dd-332b85af5143"
 version = "1.6.0"
 
+[[deps.RangeArrays]]
+git-tree-sha1 = "b9039e93773ddcfc828f12aadf7115b4b4d225f5"
+uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d"
+version = "0.3.2"
+
+[[deps.Ratios]]
+deps = ["Requires"]
+git-tree-sha1 = "1342a47bf3260ee108163042310d26f2be5ec90b"
+uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
+version = "0.4.5"
+weakdeps = ["FixedPointNumbers"]
+
+    [deps.Ratios.extensions]
+    RatiosFixedPointNumbersExt = "FixedPointNumbers"
+
 [[deps.RecipesBase]]
 deps = ["PrecompileTools"]
 git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff"
@@ -2275,6 +2753,45 @@ git-tree-sha1 = "f5f3c09103951beae390666a18e084655996370b"
 uuid = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 version = "1.17.0"
 
+[[deps.Rmath]]
+deps = ["Random", "Rmath_jll"]
+git-tree-sha1 = "5b3d50eb374cea306873b371d3f8d3915a018f0b"
+uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
+version = "0.9.0"
+
+[[deps.Rmath_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "6d40b2fe70437b01397d2a4d5b020008da4e7019"
+uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
+version = "0.5.2+0"
+
+[[deps.Roots]]
+deps = ["Accessors", "CommonSolve", "Printf"]
+git-tree-sha1 = "13a9e0164267bb9ebc55c1c5d72fceea8f09555b"
+uuid = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
+version = "3.0.7"
+
+    [deps.Roots.extensions]
+    RootsChainRulesCoreExt = "ChainRulesCore"
+    RootsForwardDiffExt = "ForwardDiff"
+    RootsIntervalRootFindingExt = "IntervalRootFinding"
+    RootsSymPyExt = "SymPy"
+    RootsSymPyPythonCallExt = "SymPyPythonCall"
+    RootsUnitfulExt = "Unitful"
+
+    [deps.Roots.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+    IntervalRootFinding = "d2bf35a9-74e0-55ec-b149-d360ff49b807"
+    SymPy = "24249f21-da20-56a4-8eb1-6a02cf4ae2e6"
+    SymPyPythonCall = "bc8888f7-b21e-4b7c-a06a-5d9c9496438c"
+    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
+
+[[deps.RoundingEmulator]]
+git-tree-sha1 = "40b9edad2e5287e05bd413a38f61a8ff55b9557b"
+uuid = "5eaf0fd0-dfba-4ccb-bf02-d820a40db705"
+version = "0.2.1"
+
 [[deps.RuntimeGeneratedFunctions]]
 deps = ["ExprTools", "PrecompileTools", "SHA", "Serialization"]
 git-tree-sha1 = "6cb9b83354089fcb33c643773acfd3235f2f1bf5"
@@ -2285,6 +2802,12 @@ version = "0.5.25"
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 version = "0.7.0"
 
+[[deps.SIMD]]
+deps = ["PrecompileTools"]
+git-tree-sha1 = "e24dc23107d426a096d3eae6c165b921e74c18e4"
+uuid = "fdea26ae-647d-5447-a871-4b548cad5224"
+version = "3.7.2"
+
 [[deps.SPRAL_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Hwloc_jll", "JLLWrappers", "Libdl", "METIS_jll", "libblastrampoline_jll"]
 git-tree-sha1 = "139fa63f03a16b3d859d925ee9149dfc15f21ece"
@@ -2405,12 +2928,29 @@ git-tree-sha1 = "c5391c6ace3bc430ca630251d02ea9687169ca68"
 uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 version = "1.1.2"
 
+[[deps.ShaderAbstractions]]
+deps = ["ColorTypes", "FixedPointNumbers", "GeometryBasics", "LinearAlgebra", "Observables", "StaticArrays"]
+git-tree-sha1 = "818554664a2e01fc3784becb2eb3a82326a604b6"
+uuid = "65257c39-d410-5151-9873-9b3e5be5013e"
+version = "0.5.0"
+
+[[deps.SharedArrays]]
+deps = ["Distributed", "Mmap", "Random", "Serialization"]
+uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
+version = "1.11.0"
+
 [[deps.Showoff]]
 deps = ["Dates", "Grisu"]
 git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
 uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
 version = "1.0.3"
 
+[[deps.SignedDistanceFields]]
+deps = ["Statistics"]
+git-tree-sha1 = "3949ad92e1c9d2ff0cd4a1317d5ecbba682f4b92"
+uuid = "73760f76-fbc4-59ce-8f25-708e95d2df96"
+version = "0.4.1"
+
 [[deps.SimpleNonlinearSolve]]
 deps = ["ADTypes", "ArrayInterface", "BracketingNonlinearSolve", "CommonSolve", "ConcreteStructs", "DifferentiationInterface", "FastClosures", "FiniteDiff", "ForwardDiff", "LineSearch", "LinearAlgebra", "MaybeInplace", "NonlinearSolveBase", "PrecompileTools", "Reexport", "SciMLBase", "SciMLLogging", "Setfield", "StaticArraysCore"]
 git-tree-sha1 = "72a05aa23361506d9574ff09f86d7d55b6f5af4c"
@@ -2427,6 +2967,18 @@ version = "2.14.1"
     ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
     Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 
+[[deps.SimpleTraits]]
+deps = ["InteractiveUtils", "MacroTools"]
+git-tree-sha1 = "7ddb0b49c109481b046972c0e4ab02b2127d6a75"
+uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
+version = "0.9.6"
+
+[[deps.Sixel]]
+deps = ["Dates", "FileIO", "ImageCore", "IndirectArrays", "OffsetArrays", "REPL", "libsixel_jll"]
+git-tree-sha1 = "0494aed9501e7fb65daba895fb7fd57cc38bc743"
+uuid = "45858cf5-a6b0-47a3-bbea-62219f50df47"
+version = "0.1.5"
+
 [[deps.Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 version = "1.11.0"
@@ -2520,6 +3072,12 @@ git-tree-sha1 = "4f96c596b8c8258cc7d3b19797854d368f243ddc"
 uuid = "860ef19b-820b-49d6-a774-d7a799459cd3"
 version = "1.0.4"
 
+[[deps.StackViews]]
+deps = ["OffsetArrays"]
+git-tree-sha1 = "be1cf4eb0ac528d96f5115b4ed80c26a8d8ae621"
+uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15"
+version = "0.1.2"
+
 [[deps.StaticArrays]]
 deps = ["LinearAlgebra", "PrecompileTools", "Random", "StaticArraysCore"]
 git-tree-sha1 = "fac51faf3bb96e8bc0bf6f9f39ca4955652776bb"
@@ -2558,12 +3116,37 @@ git-tree-sha1 = "adb9da019510162e67a4493fc235c23203d8b09e"
 uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 version = "0.34.13"
 
+[[deps.StatsFuns]]
+deps = ["HypergeometricFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "91a5737baed20ee31f3faea0e51f57461f6a689e"
+uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
+version = "2.2.1"
+weakdeps = ["ChainRulesCore", "InverseFunctions"]
+
+    [deps.StatsFuns.extensions]
+    StatsFunsChainRulesCoreExt = "ChainRulesCore"
+    StatsFunsInverseFunctionsExt = "InverseFunctions"
+
 [[deps.StringManipulation]]
 deps = ["PrecompileTools"]
 git-tree-sha1 = "773065c6e0e903924a9d838259be74338422aef2"
 uuid = "892a3eda-7b42-436c-8928-eab12a02cf0e"
 version = "0.5.0"
 
+[[deps.StructArrays]]
+deps = ["ConstructionBase", "DataAPI", "Tables"]
+git-tree-sha1 = "ad8002667372439f2e3611cfd14097e03fa4bccd"
+uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
+version = "0.7.3"
+weakdeps = ["Adapt", "GPUArraysCore", "KernelAbstractions", "LinearAlgebra", "SparseArrays", "StaticArrays"]
+
+    [deps.StructArrays.extensions]
+    StructArraysAdaptExt = "Adapt"
+    StructArraysGPUArraysCoreExt = ["GPUArraysCore", "KernelAbstractions"]
+    StructArraysLinearAlgebraExt = "LinearAlgebra"
+    StructArraysSparseArraysExt = "SparseArrays"
+    StructArraysStaticArraysExt = "StaticArrays"
+
 [[deps.StructTypes]]
 deps = ["Dates", "UUIDs"]
 git-tree-sha1 = "159331b30e94d7b11379037feeb9b690950cace8"
@@ -2642,6 +3225,12 @@ deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 version = "1.11.0"
 
+[[deps.TiffImages]]
+deps = ["CodecZstd", "ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "Mmap", "OffsetArrays", "PkgVersion", "PrecompileTools", "ProgressMeter", "SIMD", "UUIDs"]
+git-tree-sha1 = "9ca5f1f2d42f80df4b8c9f6ab5a64f438bbd9976"
+uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
+version = "0.11.9"
+
 [[deps.TimerOutputs]]
 deps = ["ExprTools", "Printf"]
 git-tree-sha1 = "3748bd928e68c7c346b52125cf41fff0de6937d0"
@@ -2671,6 +3260,11 @@ git-tree-sha1 = "0c45878dcfdcfa8480052b6ab162cdd138781742"
 uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
 version = "0.11.3"
 
+[[deps.TriplotBase]]
+git-tree-sha1 = "4d4ed7f294cda19382ff7de4c137d24d16adc89b"
+uuid = "981d1d27-644d-49a2-9326-4793e63143c3"
+version = "0.1.0"
+
 [[deps.TruncatedStacktraces]]
 deps = ["InteractiveUtils", "MacroTools", "Preferences"]
 git-tree-sha1 = "ea3e54c2bdde39062abf5a9758a23735558705e1"
@@ -2702,6 +3296,21 @@ git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
 uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
 version = "0.4.1"
 
+[[deps.Unitful]]
+deps = ["Dates", "LinearAlgebra", "Random"]
+git-tree-sha1 = "57e1b2c9de4bd6f40ecb9de4ac1797b81970d008"
+uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
+version = "1.28.0"
+weakdeps = ["ConstructionBase", "ForwardDiff", "InverseFunctions", "LaTeXStrings", "Latexify", "NaNMath", "Printf"]
+
+    [deps.Unitful.extensions]
+    ConstructionBaseUnitfulExt = "ConstructionBase"
+    ForwardDiffExt = "ForwardDiff"
+    InverseFunctionsUnitfulExt = "InverseFunctions"
+    LatexifyExt = ["Latexify", "LaTeXStrings"]
+    NaNMathExt = "NaNMath"
+    PrintfExt = "Printf"
+
 [[deps.UnoSolver]]
 deps = ["LinearAlgebra", "OpenBLAS32_jll", "SolverCore", "Uno_jll"]
 git-tree-sha1 = "6787f703903f0b2457b80c49ffe1b05c3d965b56"
@@ -2748,6 +3357,18 @@ git-tree-sha1 = "96478df35bbc2f3e1e791bc7a3d0eeee559e60e9"
 uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
 version = "1.24.0+0"
 
+[[deps.WebP]]
+deps = ["CEnum", "ColorTypes", "FileIO", "FixedPointNumbers", "ImageCore", "libwebp_jll"]
+git-tree-sha1 = "aa1ca3c47f119fbdae8770c29820e5e6119b83f2"
+uuid = "e3aaa7dc-3e4b-44e0-be63-ffb868ccd7c1"
+version = "0.1.3"
+
+[[deps.WoodburyMatrices]]
+deps = ["LinearAlgebra", "SparseArrays"]
+git-tree-sha1 = "248a7031b3da79a127f14e5dc5f417e26f9f6db7"
+uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
+version = "1.1.0"
+
 [[deps.XML2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
 git-tree-sha1 = "80d3930c6347cfce7ccf96bd3bafdf079d9c0390"
@@ -2973,6 +3594,12 @@ git-tree-sha1 = "b6a34e0e0960190ac2a4363a1bd003504772d631"
 uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
 version = "0.61.1+0"
 
+[[deps.isoband_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "51b5eeb3f98367157a7a12a1fb0aa5328946c03c"
+uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4"
+version = "0.2.3+0"
+
 [[deps.libaom_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "ef17c47d22224aaecc76e597ab21a072e025cf7b"
@@ -3026,6 +3653,12 @@ git-tree-sha1 = "e51150d5ab85cee6fc36726850f0e627ad2e4aba"
 uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
 version = "1.6.58+0"
 
+[[deps.libsixel_jll]]
+deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "libpng_jll"]
+git-tree-sha1 = "c1733e347283df07689d71d61e14be986e49e47a"
+uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
+version = "1.10.5+0"
+
 [[deps.libva_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll", "Xorg_libXext_jll", "Xorg_libXfixes_jll", "libdrm_jll"]
 git-tree-sha1 = "7dbf96baae3310fe2fa0df0ccbb3c6288d5816c9"
@@ -3038,6 +3671,12 @@ git-tree-sha1 = "11e1772e7f3cc987e9d3de991dd4f6b2602663a5"
 uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
 version = "1.3.8+0"
 
+[[deps.libwebp_jll]]
+deps = ["Artifacts", "Giflib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libglvnd_jll", "Libtiff_jll", "libpng_jll"]
+git-tree-sha1 = "4e4282c4d846e11dce56d74fa8040130b7a95cb3"
+uuid = "c5f90fcd-3b7e-5836-afba-fc50a0988cb2"
+version = "1.6.0+0"
+
 [[deps.mtdev_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "b4d631fd51f2e9cdd93724ae25b2efc198b059b1"
diff --git a/docs/src/assets/Project.toml b/docs/src/assets/Project.toml
index fb5dd1c9f..cd40d4a03 100644
--- a/docs/src/assets/Project.toml
+++ b/docs/src/assets/Project.toml
@@ -8,6 +8,8 @@ CTModels = "34c4fa32-2049-4079-8329-de33c2a22e2d"
 CTParser = "32681960-a1b1-40db-9bff-a1ca817385d1"
 CTSolvers = "d3e8d392-8e4b-4d9b-8e92-d7d4e3650ef6"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
+Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
@@ -41,6 +43,8 @@ CTModels = "0.19"
 CTParser = "0.9"
 CTSolvers = "0.5"
 CUDA = "6"
+CairoMakie = "0.15"
+Colors = "0.13"
 CommonSolve = "0.2"
 DifferentiationInterface = "0.7"
 Documenter = "1"
diff --git a/docs/src/assets/logo.png b/docs/src/assets/logo.png
new file mode 100644
index 000000000..706dde78b
Binary files /dev/null and b/docs/src/assets/logo.png differ
diff --git a/docs/src/examples/logo.md b/docs/src/examples/logo.md
new file mode 100644
index 000000000..2a94819b3
--- /dev/null
+++ b/docs/src/examples/logo.md
@@ -0,0 +1,182 @@
+# [The logo](@id examples-logo)
+
+```@meta
+Draft = false
+```
+
+The OptimalControl.jl logo is not a drawing. It is the solution of an optimal control
+problem — an **energy-minimal low-thrust orbit transfer** — solved once and repeated by
+symmetry.
+
+![The OptimalControl.jl logo](../assets/logo.png)
+
+A spacecraft spirals from a low circular orbit out to a higher one under continuous weak
+thrust. Two-body dynamics do not care which way is up, so the same optimal transfer, rotated
+by ``\pm 120°``, gives three trajectories at once — and their three departure points sit
+exactly where the three dots of the Julia logo go, winding onto the outer orbit around the
+central body.
+
+This page rebuilds that figure from scratch.
+
+## The transfer problem
+
+Normalised two-body dynamics (gravitational parameter ``\mu = 1``). The state is the
+spacecraft's position and velocity in the orbital plane,
+
+```math
+x = (x_1, x_2, x_3, x_4) = (\text{position}, \text{velocity}),
+```
+
+and the control ``u = (u_1, u_2)`` is the thrust acceleration. The spacecraft starts on a
+circular orbit of radius ``r_0`` and must reach a circular orbit of radius ``r_f``: at the
+final time it has to be at the right radius, at the right (circular) speed, and with **zero
+radial velocity** — the final angular position is free. Along the way it minimises the thrust
+energy ``\int \|u\|^2``.
+
+```@example logo
+using OptimalControl
+using NLPModelsIpopt
+
+r0 = 1.1      # departure orbit radius
+rf = 2.2      # target orbit radius
+tf = 2π       # transfer duration — sets how far the trajectory winds
+
+ocp = @def begin
+    t ∈ [0, tf], time
+    x ∈ R⁴,      state
+    u ∈ R²,      control
+
+    x(0) == [r0, 0, 0, 1 / sqrt(r0)]          # circular orbit of radius r0
+
+    x₁(tf)^2 + x₂(tf)^2 == rf^2               # insertion radius
+    x₃(tf)^2 + x₄(tf)^2 == 1 / rf             # circular speed at radius rf
+    x₁(tf) * x₃(tf) + x₂(tf) * x₄(tf) == 0    # zero radial velocity
+
+    ẋ(t) == [ x₃(t),
+              x₄(t),
+             -x₁(t) / (x₁(t)^2 + x₂(t)^2)^(3 / 2) + u₁(t),
+             -x₂(t) / (x₁(t)^2 + x₂(t)^2)^(3 / 2) + u₂(t) ]
+
+    ∫(u₁(t)^2 + u₂(t)^2) → min
+end
+```
+
+## Solving it
+
+Low-thrust transfers are hard to solve from a cold start, so we warm-start with a crude
+analytical spiral: let the radius grow linearly from ``r_0`` to ``r_f`` and advance the angle
+at the local Keplerian rate ``\dot\theta = r^{-3/2}``. (More on initial guesses in
+[Initial guess](@ref solve-initial-guess).)
+
+```@example logo
+k = (rf - r0) / tf
+
+function spiral_guess(t)
+    r  = r0 + k * t
+    θ  = (2 / k) * (1 / sqrt(r0) - 1 / sqrt(r))
+    dθ = r^(-3 / 2)
+    return [r * cos(θ), r * sin(θ),
+            k * cos(θ) - r * dθ * sin(θ), k * sin(θ) + r * dθ * cos(θ)]
+end
+
+sol = solve(ocp; grid_size = 400, display = false,
+            init = (state = spiral_guess, control = t -> [0, 0]))
+
+xf = state(sol)(tf)
+(insertion_radius = sqrt(xf[1]^2 + xf[2]^2),
+ insertion_speed  = sqrt(xf[3]^2 + xf[4]^2),
+ radial_velocity  = xf[1] * xf[3] + xf[2] * xf[4],
+ thrust_energy    = objective(sol))
+```
+
+The insertion radius and speed reach their targets and the radial velocity is zero: the
+spacecraft arrives tangent to the outer orbit.
+
+## Looking at the solution
+
+The site's documentation renders solution plots with [Plots.jl](https://docs.juliaplots.org);
+here we use the [Makie](https://docs.makie.org) backend instead — load a Makie package and the
+`Makie.plot` method for a solution becomes available.
+
+```@example logo
+using CairoMakie
+
+Makie.plot(sol)
+```
+
+The thrust (``u_1, u_2``) stays small throughout — this is a *low-thrust* transfer, nudging
+the orbit rather than forcing it. The right-hand column is the costate, the adjoint of
+Pontryagin's Maximum Principle, which the solver returns alongside the state and control.
+
+## The trajectory in the plane
+
+The logo lives in the ``(x_1, x_2)`` plane. One transfer is a single spiral from the inner
+orbit to the outer one.
+
+```@example logo
+xt  = state(sol)
+arc = [Point2f(xt(t)[1], xt(t)[2]) for t in range(0, tf; length = 500)]
+
+circle(r) = [Point2f(r * cos(a), r * sin(a)) for a in range(0, 2π; length = 300)]
+
+fig = Figure(size = (460, 460))
+ax  = Axis(fig[1, 1]; aspect = DataAspect())
+lines!(ax, circle(r0); color = (:gray, 0.5))
+lines!(ax, circle(rf); color = (:gray, 0.5))
+lines!(ax, arc;        color = :purple, linewidth = 3)
+scatter!(ax, arc[1];   color = :purple, markersize = 14)
+fig
+```
+
+## Three-fold symmetry
+
+Two-body dynamics are **rotation-equivariant**: if ``t \mapsto x(t)`` is an optimal transfer,
+so is the whole trajectory rotated by any fixed angle — same cost, same constraints. Rotating
+the solved spiral by ``0`` and ``\pm 2\pi/3`` gives three transfers for the price of one.
+
+Colour them with the Julia logo palette, drop a dot at each departure point, add the target
+orbit in Julia blue and the central body, and the logo is done.
+
+```@example logo
+using Colors
+
+rot(ψ) = [cos(ψ) -sin(ψ); sin(ψ) cos(ψ)]
+jl = Colors.JULIA_LOGO_COLORS                     # (red, green, blue, purple)
+
+# departure points placed as the Julia-logo dots — green on top
+arms = [(7π / 6, jl.red), (π / 2, jl.green), (11π / 6, jl.purple)]
+
+fig = Figure(size = (600, 600), backgroundcolor = :transparent)
+ax  = Axis(fig[1, 1]; aspect = DataAspect(), backgroundcolor = :transparent)
+hidedecorations!(ax)
+hidespines!(ax)
+limits!(ax, -1.32rf, 1.32rf, -1.32rf, 1.32rf)
+
+poly!(ax, circle(rf); color = :white)            # white disk behind everything
+
+for (ψ, c) in arms
+    P = [Point2f(rot(ψ) * p) for p in arc]
+    lines!(ax, P; color = c, linewidth = 13)
+    scatter!(ax, P[1]; color = :white, markersize = 80)   # halo
+    scatter!(ax, P[1]; color = c,      markersize = 60)   # coloured dot
+end
+
+lines!(ax, circle(rf); color = jl.blue, linewidth = 13)   # target orbit
+scatter!(ax, Point2f(0, 0); color = :white,  markersize = 50)
+scatter!(ax, Point2f(0, 0); color = jl.blue, markersize = 100)
+
+fig
+```
+
+That is the figure the site uses as its logo (`docs/src/assets/logo.png`) and, downscaled, as
+its favicon.
+
+The published asset is produced by a slightly more elaborate script — crisper strokes, a few
+tuning knobs — kept in the repository at `.extras/logos/logo-gagnant/`. The optimal control
+problem it solves is exactly the one above.
+
+## See also
+
+- [Initial guess](@ref solve-initial-guess) — the warm-start used here, and the others.
+- [Plot](@ref results-plot) — the Plots backend, and what a solution plot shows.
+- [Example gallery](@ref examples-gallery) — the other worked problems.