Mathematical roses in a Pluto.jl notebook

roses.jl

### A Pluto.jl notebook ###
# v0.19.40

using Markdown
using InteractiveUtils

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

# ╔═╡ aeed7ffa-8408-11ec-20de-edf09cfb404b
using Luxor, Waveforms, Colors, PlutoUI

# ╔═╡ d7cdc039-f8fe-4983-971f-51a1325c0c25
md"# Mathematical *rose* drawings

Playing around with some mathematical shapes called *rhodonea curves* - a la [Wikipedia: Rose (Mathematics)](https://en.wikipedia.org/wiki/Rose_(mathematics)) page

The equations and a bit of nitty gritty about how to draw is [here](https://en.wikipedia.org/wiki/Rose_(mathematics)#Specification)

Denis Schluppeck, 2022-02, @schluppeck
"

# ╔═╡ 70bc790d-953a-4a9c-bbfb-7b700161f114
begin
	@bind ticks Clock(1,false,true);
end

# ╔═╡ 3aadf649-2a61-4701-b1d7-9f90fef8be45
md"""pick a background colour: $(@bind bgcolor ColorPicker(default=colorant"antiquewhite") ) """

# ╔═╡ 529d71ca-928a-4b65-9a21-9a90866b84d6
"""
rose(θ, k, r) 

	returns a `x,y` tuple for a particular value of `θ` and `r`, given the parameter
	k ... k is normally represented as the fraction ``\\frac{n}{d}``.

	To plot a complete rose, θ needs to cover ``[0..2dπ]``

	Example:

		t = range(0, 2*2π, length = 100);
		coords = rose.(t, 2, 25)

"""
rose(θ, k, r) = Point(r * cosd(θ) * cosd(k*θ), r * sind(θ) * cosd(k*θ))

# ╔═╡ 2577e418-a854-4f56-aaee-1932d9c5d323
"""
edgy_rose(θ, k, r) 

	a sawtooth version of a traditional rose... 

	returns a `x,y` tuple for a particular value of `θ` and `r`, given the parameter
	k ... k is normally represented as the fraction ``\\frac{n}{d}``.

	To plot a complete rose, θ needs to cover ``[0..2dπ]``

	Example:

		t = range(0, 2*2π, length = 100);
		coords = edgy_rose.(t, 2, 25)

"""
edgy_rose(θ, k, r) = Point(r * cosd(θ) * sawtoothwave(deg2rad(k*θ)), r * sind(θ) * sawtoothwave(deg2rad(k*θ)))

# ╔═╡ e7088cbb-f85d-407d-a200-302018293781
"""
pointy_rose(θ, k, r) 

	a trianglewave() version of a traditional rose... 

	returns a `x,y` tuple for a particular value of `θ` and `r`, given the parameter
	k. k is normally represented as the fraction ``\\frac{n}{d}``.

	To plot a complete rose, θ needs to cover ``[0..2dπ]``

	Example:

		t = range(0, 2*2π, length = 100);
		coords = pointy_rose.(t, 2, 25)

"""
pointy_rose(θ, k, r) = Point(r * cosd(θ) * trianglewave(deg2rad(k*θ)), r * sind(θ) * trianglewave(deg2rad(k*θ)))

# ╔═╡ 82a5c50a-7d9c-4076-9891-53c70f37818b
begin
	drawingFunctions = [rose, pointy_rose, edgy_rose];
	nRoses = length(drawingFunctions);
	md"There are $(nRoses) different drawing functions..."
	
end

# ╔═╡ 483c4f5b-3c80-4f44-8ec7-8520590fc0e4
md"""Select a drawing function by hand: $(@bind whichRose Select(drawingFunctions))
and watch the drawing update... or click the Start button below to cycle through the different drawing functions 😀
"""

# ╔═╡ f997f56e-2553-4153-b7fc-92b1d09f3482
begin
	ticks
	#	drawingFunction = animating ? drawingFunctions[ticks%nRoses + 1 ] : whichRose
	drawingFunction = drawingFunctions[ticks%nRoses + 1 ];

end

# ╔═╡ 7dce4ac8-acd4-46b4-8ffb-a5b451df8bdb
begin
	ticks
	# set up drawing
	W, H = 800, 800
	nCols, nRows = 7, 7 
	Drawing(W, H, string(drawingFunction, ".png"))

	# set origin and make tiles
	origin()
		
	ttiles = Tiler(W, H, nRows, nCols, margin=10)

	# decide on a radius of shapes, to fit within a single tile
	R = 0.8*minimum([ttiles.tilewidth, ttiles.tileheight])/2

	background(bgcolor)
	
	setline(1.5)

	# step through each tile and draw a rose
	for (pos, n) in ttiles
		origin()
		translate(pos)
		n = ttiles.currentcol
		d = ttiles.currentrow
		k = n/d

		randomhue()
		setopacity(0.4)   	
		drawpath(
			Path(drawingFunction.(range(0, 360*2*d; length=360), k, R)), 
			:fill)
		
		setopacity(1)   	
		sethue("black")
		drawpath(
			Path(drawingFunction.(range(0, 360*2*d; length=360), k, R)), 
			:stroke)
	end

finish()
preview()
		
end

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[[OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.21+4"

[[OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "648107615c15d4e09f7eca16307bc821c1f718d8"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.13+0"

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

[[PCRE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
version = "8.44.0+0"

[[Pango_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9bc1871464b12ed19297fbc56c4fb4ba84988b0d"
uuid = "36c8627f-9965-5494-a995-c6b170f724f3"
version = "1.47.0+0"

[[Parsers]]
deps = ["Dates"]
git-tree-sha1 = "0b5cfbb704034b5b4c1869e36634438a047df065"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.2.1"

[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"

[[Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.9.0"

[[PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "UUIDs"]
git-tree-sha1 = "ae6145ca68947569058866e443df69587acc1806"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.32"

[[Preferences]]
deps = ["TOML"]
git-tree-sha1 = "2cf929d64681236a2e074ffafb8d568733d2e6af"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.2.3"

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

[[Profile]]
deps = ["Printf"]
uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"

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

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

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

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

[[Rsvg]]
deps = ["Cairo", "Glib_jll", "Librsvg_jll"]
git-tree-sha1 = "3d3dc66eb46568fb3a5259034bfc752a0eb0c686"
uuid = "c4c386cf-5103-5370-be45-f3a111cca3b8"
version = "1.0.0"

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

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

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

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

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
version = "1.9.0"

[[SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "Pkg", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "5.10.1+6"

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

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

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

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

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

[[Waveforms]]
git-tree-sha1 = "532113cb46e2da7019672f7879b97ada3edd3dc6"
uuid = "cb13b1c6-351e-5134-b3ad-d6a530956a82"
version = "0.1.1"

[[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_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"
version = "1.2.13+0"

[[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 = "c23323cd30d60941f8c68419a70905d9bdd92808"
uuid = "da03df04-f53b-5353-a52f-6a8b0620ced0"
version = "2.42.6+1"

[[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"

[[libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+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 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[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:
# ╟─d7cdc039-f8fe-4983-971f-51a1325c0c25
# ╟─aeed7ffa-8408-11ec-20de-edf09cfb404b
# ╟─82a5c50a-7d9c-4076-9891-53c70f37818b
# ╟─483c4f5b-3c80-4f44-8ec7-8520590fc0e4
# ╟─70bc790d-953a-4a9c-bbfb-7b700161f114
# ╟─f997f56e-2553-4153-b7fc-92b1d09f3482
# ╟─7dce4ac8-acd4-46b4-8ffb-a5b451df8bdb
# ╟─3aadf649-2a61-4701-b1d7-9f90fef8be45
# ╟─529d71ca-928a-4b65-9a21-9a90866b84d6
# ╟─2577e418-a854-4f56-aaee-1932d9c5d323
# ╟─e7088cbb-f85d-407d-a200-302018293781
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002