Butterflies and Roses With Julia

I recently came across this tumblr post by Mathhombre in which he had shared some beautiful plots he generated using Geogebra. Since it has been so long since I’ve tried anything with Julia, I thought of recreating some of those plots using Julia. Hence, this post.

In order to plot, make sure you have the following libraries installed.

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using Plots
using PlutoUI
using ColorSchemes

Butterflies

These plots are originally attributed to Daniel Mentrard. He has a large collections of math geogebra projects. One of them is to plot butterflies using polar curves. It is an easy task to reproduce them in Julia. Refer to the $r(\theta)$ formula in the Julia code to find the corresponding equation for each of these plots.

Buttefly #1

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r(θ) = 5sin(2θ) + 3cos(θ)
rval = r.(0:0.01:2π)
p = plot(r, 0:0.01:2π, 
    proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
    linez=rval, c=:dracula, 
    background_color = :transparent, size=(400,400))

Butterfly 1

Butterfly #2

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r1(θ) = (sin(5θ) + 3cos(θ))
r2(θ) = (sin(5θ) - 3cos(θ))
r1val = r1.(0:0.01:2π)
r2val = r2.(0:0.01:2π)
p = plot(r1, 0:0.01:2π, proj=:polar, legend=false, linewidth=2,
        grid=:none, showaxis=false,
        linez=r1val, c=:dracula,
        background_color = :transparent, size=(400,400));
plot!(p, r2, 0:0.01:2π, proj=:polar, legend=false, linewidth=2,
    grid=:none, showaxis=false,
    linez=r2val, c=:dracula,
    background_color = :transparent, size=(400,400))

Butterfly #3

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r1(θ) = 3cos(θ) + sin(7θ)
r2(θ) = -3cos(θ) + sin(7θ)
r1val = r1.(0:0.01:2π)
r2val = r2.(0:0.01:2π)
p = plot(r1, 0:0.01:2π, proj=:polar, legend=false, linewidth=2,
        grid=:none, showaxis=false,
        linez=r1val, c=:dracula,
background_color = :transparent, size=(400,400));
plot!(p, r2, 0:0.01:2π, proj=:polar, legend=false, linewidth=2,
    grid=:none, showaxis=false,
    linez=r2val, c=:dracula,
background_color = :transparent, size=(400,400))

Butterfly #4

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r(θ) = 2sin(2θ)+2cos(0.5θ)
rval = r.(0:0.01:4π)
p = plot(r, 0:0.01:4π, 
    proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
    linez=rval, c=:dracula,
    background_color = :transparent, size=(400,400))

Butterfly #5

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r(θ) = exp(-sin(θ)) - 2cos(4θ) + (sin((2θ-π)/24)^4)
rval = r.(0:0.01:2π)
plot(r, 0:0.01:2π, 
    proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
    linez=rval, c=:dracula,
    background_color = :transparent, size=(400,400))

Butterfly #6

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r(θ) = 1.6 + 1.1cos(2θ) + (sin(5θ)^3)
rval = r.(0:0.01:2π)
plot(r, 0:0.01:2π, 
    proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
    linez=rval, c=:dracula,
    background_color = :transparent, size=(400,400))

Butterfly #7

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r(θ) = exp(sin(θ)-2cos(4θ))
rval = r.(0:0.01:2π)
plot(r, 0:0.01:2π, 
    proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
    linez=rval, c=:dracula,
background_color = :transparent, size=(400,400))

Butterfly #8

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r(θ) = exp(cos(θ)) - 2cos(4θ) + (sin(θ/12)^7)
rval = r.(0:0.01:2π)
plot(r, 0:0.01:2π, 
    proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
    linez=rval, c=:dracula,
    background_color = :transparent, size=(400,400))

Butterfly #9

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a = -2
b = 2
c = 1
d = 4
K = -2.8
r1(θ) = a*sin(b*θ) + c*sin(d*θ) + K
r2(θ) = a*cos(b*θ) + c*sin(d*θ) + K

r1val = r1.(0:0.01:20π)
r2val = r2.(0:0.01:20π)
p = plot(r1, 0:0.01:20π, proj=:polar, legend=false, linewidth=2,
        grid=:none, showaxis=false, lims=(-1,4),
        linez=r1val, c=:dracula,
        background_color = :transparent, size=(400,400));
plot!(p, r2, 0:0.01:20π, proj=:polar, legend=false, linewidth=2,
    grid=:none, showaxis=false, lims=(-1,4),
    linez=r2val, c=:dracula,aspectratio=:equal,
    background_color = :transparent, size=(400,400))

Roses

While plotting the buttefly wasn’t difficult, plotting the roses are even easier, thanks to Pluto.jl’s support for HTML slider objects being binded to variable. Hence, the equations,

r_1(\theta) = a\sin(b\theta) + csin(d\theta) + K

r_2(\theta) = a\cos(b\theta) + csin(d\theta) + K

with parameters $a,b,c,d,K$ were easier to set. Here are some beautiful flowers rendered with Julia and gr plot backend.

Rose #1

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r(θ) = 4sin(-3.2θ) + 3.9
rval = r.(0:0.01:10π)
plot(r, 0:0.01:10π, proj= :polar, legend=false,linewidth=1, 
    mode="lines", axis=false, grid=:none, 
    aspectratio=:equal, lims=:auto,
    linez=rval,
    c=cgrad(:buda,rev=true),
    background_color = :transparent, size=(400,400))

Rose #2

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r(θ) = 3.3sin(3.3θ) + 0.6
rval = r.(0:0.01:30π)
plot(r, 0:0.01:30π, 
    proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false, 
    linez=range(minimum(rval),stop=maximum(rval),length=length(rval)), c=:PuRd_8,
    background_color = :transparent, size=(400,400))

Rose #3

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a = -2
b = 2.9
c = 3
d = 4
K = 0
r1(θ) = a*sin(b*θ) + c*sin(d*θ) + K
r2(θ) = a*cos(b*θ) + c*sin(d*θ) + K
r1val = r1.(0:0.01:20π)
r2val = r2.(0:0.01:20π)
p = plot(r1, 0:0.01:20π, proj=:polar, legend=false, linewidth=1,
        grid=:none, showaxis=false,
        c=:spring,aspectratio=:equal,
        background_color = :transparent, size=(400,400));
plot!(p, r2, 0:0.01:20π, proj=:polar, legend=false, linewidth=1,
    grid=:none, showaxis=false,
    c=:red,aspectratio=:equal,
    background_color = :transparent, size=(400,400))

Rose #4

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a = -1
b = 0.777
c = 2
d = 3.5
K = 3.
r1(θ) = a*sin(b*θ) + c*sin(d*θ) + K
r2(θ) = a*cos(b*θ) + c*sin(d*θ) + K
theta = 0:0.01:33π
r1val = r1.(theta)
r2val = r2.(theta)
p = plot(r1, theta, proj=:polar, legend=false, linewidth=1,
        grid=:none, showaxis=false,
        c=:spring,aspectratio=:equal,
        background_color = :transparent, size=(400,400));
plot!(p, r2, theta, proj=:polar, legend=false, linewidth=1,
    grid=:none, showaxis=false,
    c=:red,aspectratio=:equal,
    background_color = :transparent, size=(400,400))

Rose #∞

Pluto notebook of Julia supports html sliders to be bound to variable values. This allows us to use the sliders and generate the required plots.

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@bind a Slider(-4:0.1:4, default=-2, show_value=true)

The pluto notebook is uploaded to Github gist can be accessed with Binder using this link. Further, the Pluto notebook can be downloaded from the following Github gist.

	### 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

	# ╔═╡ b524c16c-db16-11ee-1ed3-915f24a7ee51
	using Plots

	# ╔═╡ 735b6f78-1040-4186-895d-cdfd2bdf04c3
	using PlutoUI

	# ╔═╡ a932a413-4b96-44a8-9cd9-e8a37ad6f67a
	using ColorSchemes

	# ╔═╡ 6704a128-c9ed-4cbc-a4a0-1c788a7108e7
	md"""
	# Butterflies and Roses with Julia
	"""

	# ╔═╡ ba3041cc-fdd2-4652-9cd7-f0f26fddf4f2
	md"""
	I recently came across [this tumblr post by Mathhombre](https://www.tumblr.com/mathhombre/742682152620130304/butterfly-curves) in which he had shared some beautiful plots he generated using Geogebra. Since it has been so long since I've tried anything with Julia, I thought of recreating some of those plots using Julia. Hence, this post.
	"""

	# ╔═╡ 8de9d895-1064-45a5-9098-94b9ab0c2c2c
	# plotly()
	gr()

	# ╔═╡ 90c84cfb-cead-4abc-a748-8e8167359808
	md"### Butterflies"

	# ╔═╡ 45f4d10a-7612-4609-8174-a969ca7a14cf
	md"These plots are originally attributed to [Daniel Mentrard](https://www.geogebra.org/u/daniel+mentrard). He has a large collections of math geogebra projects. One of them is to plot butterflies using polar curves. It is an easy task to reproduce them in Julia. Refer to the $r(\theta)$ formula in the Julia code to find the corresponding equation for each of these plots."

	# ╔═╡ 133d4acf-4ea9-43a6-997f-9accc59efb28
	md"#### Butterfly #1"

	# ╔═╡ 253e2768-156b-4a0a-b904-e7f4ebaf8f42
	let
	r(θ) = 5sin(2θ) + 3cos(θ)
	rval = r.(0:0.01:2π)
	p = plot(r, 0:0.01:2π,
	proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
	linez=rval, c=:dracula,
	background_color = :transparent, size=(400,400))
	# savefig(p, "butterfly_1.png");
	end

	# ╔═╡ 4a30b065-db2f-4337-a04a-c71d1acc5cc4
	md"#### Butterfly #2"

	# ╔═╡ dd7f680f-95a5-4e52-a9c6-5d08c36f70cb
	let
	r1(θ) = (sin(5θ) + 3cos(θ))
	r2(θ) = (sin(5θ) - 3cos(θ))
	r1val = r1.(0:0.01:2π)
	r2val = r2.(0:0.01:2π)
	p = plot(r1, 0:0.01:2π, proj=:polar, legend=false, linewidth=2,
	grid=:none, showaxis=false,
	linez=r1val, c=:dracula,
	background_color = :transparent, size=(400,400));
	plot!(p, r2, 0:0.01:2π, proj=:polar, legend=false, linewidth=2,
	grid=:none, showaxis=false,
	linez=r2val, c=:dracula,
	background_color = :transparent, size=(400,400))
	# savefig(p, "butterfly_2.png");
	end

	# ╔═╡ cb728488-5688-471a-aae2-27a5ec28c3dc
	md"#### Butterfly #3"

	# ╔═╡ 33efa3eb-ee7f-470c-88c8-60d08d4f494c
	let
	r1(θ) = 3cos(θ) + sin(7θ)
	r2(θ) = -3cos(θ) + sin(7θ)
	r1val = r1.(0:0.01:2π)
	r2val = r2.(0:0.01:2π)
	p = plot(r1, 0:0.01:2π, proj=:polar, legend=false, linewidth=2,
	grid=:none, showaxis=false,
	linez=r1val, c=:dracula,
	background_color = :transparent, size=(400,400));
	plot!(p, r2, 0:0.01:2π, proj=:polar, legend=false, linewidth=2,
	grid=:none, showaxis=false,
	linez=r2val, c=:dracula,
	background_color = :transparent, size=(400,400))
	# savefig(p, "butterfly_3.png");
	end

	# ╔═╡ 0c67ae79-2610-4195-9510-68a25cddec81
	md"#### Butterfly #4"

	# ╔═╡ 76184113-ea5f-488e-bcb9-3e2b0a4a3158
	let
	r(θ) = 2sin(2θ)+2cos(0.5θ)
	rval = r.(0:0.01:4π)
	p = plot(r, 0:0.01:4π,
	proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
	linez=rval, c=:dracula,
	background_color = :transparent, size=(400,400))
	# savefig(p, "butterfly_4.png");
	end

	# ╔═╡ d354b029-cbf0-4b0e-aceb-9dfbc829ee20
	md"#### Butterfly #5"

	# ╔═╡ 88e26d47-7790-4552-b039-ffbdac93cdae
	let
	r(θ) = exp(-sin(θ)) - 2cos(4θ) + (sin((2θ-π)/24)^4)
	rval = r.(0:0.01:2π)
	plot(r, 0:0.01:2π,
	proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
	linez=rval, c=:dracula,
	background_color = :transparent, size=(400,400))
	# savefig("butterfly_5.png")
	end

	# ╔═╡ 7d39f3d2-2960-4708-842f-365e2a0b07b3
	md"#### Buttterfly #6"

	# ╔═╡ 1b843c00-ab15-4d2a-865c-639231f5ec3e
	let
	r(θ) = 1.6 + 1.1cos(2θ) + (sin(5θ)^3)
	rval = r.(0:0.01:2π)
	plot(r, 0:0.01:2π,
	proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
	linez=rval, c=:dracula,
	background_color = :transparent, size=(400,400))
	# savefig("butterfly_6.png")
	end

	# ╔═╡ 56dedd44-4811-41b9-8a5a-5431dceb6b1e
	md"#### Butterfly #7"

	# ╔═╡ 30f92721-754a-4bc3-8df8-409fd756393d
	let
	r(θ) = exp(sin(θ)-2cos(4θ))
	rval = r.(0:0.01:2π)
	plot(r, 0:0.01:2π,
	proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
	linez=rval, c=:dracula,
	background_color = :transparent, size=(400,400))
	# savefig("butterfly_7.png")
	end

	# ╔═╡ d55c3dcc-6354-4246-955c-9b8802513038
	md"#### Butterfly #8"

	# ╔═╡ 6d754c24-3fb3-4574-bc77-fa7c324f738a
	let
	r(θ) = exp(cos(θ)) - 2cos(4θ) + (sin(θ/12)^7)
	rval = r.(0:0.01:2π)
	plot(r, 0:0.01:2π,
	proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
	linez=rval, c=:dracula,
	background_color = :transparent, size=(400,400))
	# savefig("butterfly_8.png")
	end

	# ╔═╡ 803fb40f-036d-4b37-ad22-8a41871cf7eb
	md"#### Butterfly #9"

	# ╔═╡ 340eac27-b7d0-414d-97e6-eeeefec69e15
	md"The following butterfly is attributed to mathhombre from tumblr."

	# ╔═╡ c44b6d2f-bfe4-41e4-a772-33299b760d74
	let
	a = -2
	b = 2
	c = 1
	d = 4
	K = -2.8
	r1(θ) = asin(bθ) + csin(dθ) + K
	r2(θ) = acos(bθ) + csin(dθ) + K

	r1val = r1.(0:0.01:20π)
	r2val = r2.(0:0.01:20π)
	p = plot(r1, 0:0.01:20π, proj=:polar, legend=false, linewidth=2,
	grid=:none, showaxis=false, lims=(-1,4),
	linez=r1val, c=:dracula,
	background_color = :transparent, size=(400,400));
	plot!(p, r2, 0:0.01:20π, proj=:polar, legend=false, linewidth=2,
	grid=:none, showaxis=false, lims=(-1,4),
	linez=r2val, c=:dracula,aspectratio=:equal,
	background_color = :transparent, size=(400,400))
	# savefig("butterfly_9.png")
	end

	# ╔═╡ ce4e7a69-d2f8-4b51-8989-52a9983fd178
	md"## Roses"

	# ╔═╡ 24954f47-43b0-44c6-b4b0-9735f9a8f951
	md"""While plotting the buttefly wasn't difficult, plotting the roses are even easier, thanks to `Pluto.jl`'s support for HTML slider objects being binded to variable. Hence, the equations,
	```math
	r_1(\theta) = a\sin(b\theta) + csin(d\theta) + K
	```
	```math
	r_2(\theta) = a\cos(b\theta) + csin(d\theta) + K
	```
	with parameters $a,b,c,d,K$ were easier to set. Here are some beautiful flowers rendered with Julia and gr plot backend."""

	# ╔═╡ 49cc8a36-2df8-4ad8-b96c-2d85f9061e36
	md"#### Rose #1"

	# ╔═╡ 230faca2-f5fe-4d03-8fe3-f88e3fd33921
	let
	r(θ) = 4sin(-3.2θ) + 3.9
	rval = r.(0:0.01:10π)
	plot(r, 0:0.01:10π, proj= :polar, legend=false,linewidth=1,
	mode="lines", axis=false, grid=:none,
	aspectratio=:equal, lims=:auto,
	linez=rval,
	c=cgrad(:buda,rev=true),
	background_color = :transparent, size=(400,400))
	# savefig("rose_1.png")
	end

	# ╔═╡ 5a6af14a-69e3-4806-9a4d-e5c73df1340b
	md"#### Rose #2"

	# ╔═╡ 3a2fd51a-b21c-4b43-99de-310806b1fedc
	let
	r(θ) = 3.3sin(3.3θ) + 0.6
	rval = r.(0:0.01:30π)
	plot(r, 0:0.01:30π,
	proj=:polar, legend=false, linewidth=2, grid=:none, showaxis=false,
	linez=range(minimum(rval),stop=maximum(rval),length=length(rval)), c=:PuRd_8,
	background_color = :transparent, size=(400,400))
	# savefig("rose_2.png")
	end

	# ╔═╡ 18f752ed-6f37-4739-a212-85b3d2e86224
	md"#### Rose #3"

	# ╔═╡ f46931aa-16a9-423d-97d2-116846272722
	let
	a = -2
	b = 2.9
	c = 3
	d = 4
	K = 0
	r1(θ) = asin(bθ) + csin(dθ) + K
	r2(θ) = acos(bθ) + csin(dθ) + K
	r1val = r1.(0:0.01:20π)
	r2val = r2.(0:0.01:20π)
	p = plot(r1, 0:0.01:20π, proj=:polar, legend=false, linewidth=1,
	grid=:none, showaxis=false,
	c=:spring,aspectratio=:equal,
	background_color = :transparent, size=(400,400));
	plot!(p, r2, 0:0.01:20π, proj=:polar, legend=false, linewidth=1,
	grid=:none, showaxis=false,
	c=:red,aspectratio=:equal,
	background_color = :transparent, size=(400,400))
	# savefig("rose_3.png")
	end

	# ╔═╡ 49aa2595-d54b-4dc7-8783-89a399f585ed
	md"#### Rose #4"

	# ╔═╡ adf491bb-a90c-48db-bd62-0f8a13e919b2
	let
	a = -1
	b = 0.777
	c = 2
	d = 3.5
	K = 3.
	r1(θ) = asin(bθ) + csin(dθ) + K
	r2(θ) = acos(bθ) + csin(dθ) + K
	theta = 0:0.01:33π
	r1val = r1.(theta)
	r2val = r2.(theta)
	p = plot(r1, theta, proj=:polar, legend=false, linewidth=1,
	grid=:none, showaxis=false,
	c=:spring,aspectratio=:equal,
	background_color = :transparent, size=(400,400));
	plot!(p, r2, theta, proj=:polar, legend=false, linewidth=1,
	grid=:none, showaxis=false,
	c=:red,aspectratio=:equal,
	background_color = :transparent, size=(400,400))
	# savefig("rose_4.png")
	end

	# ╔═╡ 4451158f-b873-43f1-bfa4-2dc710f3ac6a
	md"""#### Rose #∞

	The following sliders (needs Pluto.jl) can be used to generate different flowers based on the parameters. You can try it out generate multiple unique ones!"""

	# ╔═╡ e073c55f-7f61-4a7a-9c37-f125a289cadc
	@bind a Slider(-4:0.1:4, default=-2, show_value=true)

	# ╔═╡ e7f8ec30-c98f-4d80-8198-66e54ee39c94
	@bind b Slider(-4:0.1:4, default=2, show_value=true)

	# ╔═╡ 02576584-c168-4d50-9f28-7076f43754a5
	@bind c Slider(-4:0.1:4, default=2, show_value=true)

	# ╔═╡ aa752202-aa11-4981-b59f-4b10eca7f14e
	@bind d Slider(-4:0.1:4, default=2, show_value=true)

	# ╔═╡ f50caffc-d98b-483c-9ba0-f412ac2039c1
	@bind K Slider(-4:0.1:4, default=-3.5, show_value=true)

	# ╔═╡ 2c6d2853-9aa6-4854-a05d-8ef318102458
	let
	theta = 0:0.01:10π
	r₁(θ) = asin(bθ) + csin(dθ) + K
	r₂(θ) = acos(bθ) + csin(dθ) + K
	r1val = r₁.(theta)
	r2val = r₂.(theta)
	p = plot(r₁, theta, proj= :polar, legend=false,linewidth=1,
	mode="lines", axis=false, grid=:none,
	aspectratio=:equal, lims=:auto,
	linez=r1val,
	c=cgrad(:buda,rev=true))
	plot!(p, r₂, theta, proj= :polar, legend=false,linewidth=1, mode="lines",
	aspectratio=:equal, axis=false, grid=:none, background_color = :transparent,
	linez=r2val,
	c=:twilight)
	end

	# ╔═╡ f08d5ac3-9a6c-409a-a981-a94a980d061e
	md"Further, the colorschemes I've used are all selected from the catalogue in [Julia plot color schemes](https://docs.juliaplots.org/latest/generated/colorschemes/#scientific) or [Named colors](https://juliagraphics.github.io/Colors.jl/stable/namedcolors/). I also tried using plotly backend but it was having some issue. Hence, I am using GR backend. "

	# ╔═╡ 00000000-0000-0000-0000-000000000001
	PLUTO_PROJECT_TOML_CONTENTS = """
	[deps]
	ColorSchemes = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
	Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
	PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"

	[compat]
	ColorSchemes = "~3.24.0"
	Plots = "~1.39.0"
	PlutoUI = "~0.7.58"
	"""

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

	julia_version = "1.9.3"
	manifest_format = "2.0"
	project_hash = "e7dbf2e495bbe3f262c8cbf2e07b9cb7d960cc48"

	[[deps.AbstractPlutoDingetjes]]
	deps = ["Pkg"]
	git-tree-sha1 = "0f748c81756f2e5e6854298f11ad8b2dfae6911a"
	uuid = "6e696c72-6542-2067-7265-42206c756150"
	version = "1.3.0"

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

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

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

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

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

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

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

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

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

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

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

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

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

	[[deps.Compat]]
	deps = ["TOML", "UUIDs"]
	git-tree-sha1 = "c955881e3c981181362ae4088b35995446298b80"
	uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
	version = "4.14.0"
	weakdeps = ["Dates", "LinearAlgebra"]

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

	[[deps.CompilerSupportLibraries_jll]]
	deps = ["Artifacts", "Libdl"]
	uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
	version = "1.0.5+0"

	[[deps.ConcurrentUtilities]]
	deps = ["Serialization", "Sockets"]
	git-tree-sha1 = "9c4708e3ed2b799e6124b5673a712dda0b596a9b"
	uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
	version = "2.3.1"

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

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

	[[deps.DataStructures]]
	deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
	git-tree-sha1 = "0f4b5d62a88d8f59003e43c25a8a90de9eb76317"
	uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
	version = "0.18.18"

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

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

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

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

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

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

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

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

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

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

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

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

	[[deps.Format]]
	git-tree-sha1 = "f3cf88025f6d03c194d73f5d13fee9004a108329"
	uuid = "1fa38f19-a742-5d3f-a2b9-30dd87b9d5f8"
	version = "1.3.6"

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

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

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

	[[deps.GR]]
	deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "UUIDs", "p7zip_jll"]
	git-tree-sha1 = "27442171f28c952804dede8ff72828a96f2bfc1f"
	uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
	version = "0.72.10"

	[[deps.GR_jll]]
	deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"]
	git-tree-sha1 = "025d171a2847f616becc0f84c8dc62fe18f0f6dd"
	uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
	version = "0.72.10+0"

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

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

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

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

	[[deps.HTTP]]
	deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
	git-tree-sha1 = "db864f2d91f68a5912937af80327d288ea1f3aee"
	uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
	version = "1.10.3"

	[[deps.HarfBuzz_jll]]
	deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
	git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
	uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
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	[[deps.Hyperscript]]
	deps = ["Test"]
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	uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
	version = "0.0.5"

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

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

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

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

	[[deps.JLFzf]]
	deps = ["Pipe", "REPL", "Random", "fzf_jll"]
	git-tree-sha1 = "a53ebe394b71470c7f97c2e7e170d51df21b17af"
	uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c"
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	[[deps.JLLWrappers]]
	deps = ["Artifacts", "Preferences"]
	git-tree-sha1 = "7e5d6779a1e09a36db2a7b6cff50942a0a7d0fca"
	uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
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	[[deps.JSON]]
	deps = ["Dates", "Mmap", "Parsers", "Unicode"]
	git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a"
	uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
	version = "0.21.4"

	[[deps.JpegTurbo_jll]]
	deps = ["Artifacts", "JLLWrappers", "Libdl"]
	git-tree-sha1 = "3336abae9a713d2210bb57ab484b1e065edd7d23"
	uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
	version = "3.0.2+0"

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

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

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

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

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

	[[deps.Latexify]]
	deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"]
	git-tree-sha1 = "cad560042a7cc108f5a4c24ea1431a9221f22c1b"
	uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
	version = "0.16.2"

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

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

	[[deps.LibCURL]]
	deps = ["LibCURL_jll", "MozillaCACerts_jll"]
	uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
	version = "0.6.3"

	[[deps.LibCURL_jll]]
	deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
	uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
	version = "7.84.0+0"

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

	[[deps.LibSSH2_jll]]
	deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
	uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
	version = "1.10.2+0"

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

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

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

	[[deps.XML2_jll]]
	deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
	git-tree-sha1 = "07e470dabc5a6a4254ffebc29a1b3fc01464e105"
	uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
	version = "2.12.5+0"

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

	[[deps.XZ_jll]]
	deps = ["Artifacts", "JLLWrappers", "Libdl"]
	git-tree-sha1 = "37195dcb94a5970397ad425b95a9a26d0befce3a"
	uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
	version = "5.6.0+0"

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

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

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

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

	[[deps.Xorg_libXcursor_jll]]
	deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
	git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
	uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
	version = "1.2.0+4"

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

	[[deps.Xorg_libXext_jll]]
	deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
	git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
	uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
	version = "1.3.4+4"

	[[deps.Xorg_libXfixes_jll]]
	deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
	git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
	uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
	version = "5.0.3+4"

	[[deps.Xorg_libXi_jll]]
	deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
	git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
	uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
	version = "1.7.10+4"

	[[deps.Xorg_libXinerama_jll]]
	deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
	git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
	uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
	version = "1.1.4+4"

	[[deps.Xorg_libXrandr_jll]]
	deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
	git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
	uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
	version = "1.5.2+4"

	[[deps.Xorg_libXrender_jll]]
	deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
	git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
	uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
	version = "0.9.10+4"

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

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

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

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

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

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

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

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

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

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

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

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

	[[deps.Zlib_jll]]
	deps = ["Libdl"]
	uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
	version = "1.2.13+0"

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

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

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

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

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

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

	[[deps.libblastrampoline_jll]]
	deps = ["Artifacts", "Libdl"]
	uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
	version = "5.8.0+0"

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

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

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

	[[deps.libpng_jll]]
	deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
	git-tree-sha1 = "1ea2ebe8ffa31f9c324e8c1d6e86b4165b84a024"
	uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
	version = "1.6.43+0"

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

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

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

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

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

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

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

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