using Plots
gr()
using LaTeXStrings
using LaTeXStrings: latexstring

Circle

θ = 0:0.01:2π
x = @. cos(θ)
y = @. sin(θ)

p = plot(
    xlabel = L"x",
    ylabel = L"y",
    xlim = [-1, 1],
    ylim = [-1, 2],
    aspect_ratio = :equal,
)

plot!(p, x, y, label = L"x^2+y^2 = 1")

Astroid

θ = 0:0.01:2π
a = 2
x = @. a * cos(θ)^3
y = @. a * sin(θ)^3

eq = latexstring("x^{2/3}+y^{2/3} = $a^{2/3}")

p = plot(
    title = eq,
    xlabel = L"x",
    ylabel = L"y",
    xlim = [-2, 2],
    ylim = [-2, 2],
    aspect_ratio = :equal,
)

plot!(p, x, y, label = :false)

Lissajous

θ = 0:0.01:2π
x = @. sin(θ)
y = @. sin(2θ)

eq = latexstring("y^2=4x^2(1-x^2)")

p = plot(
    title = eq,
    xlabel = L"x",
    ylabel = L"y",
    xlim = [-1, 1],
    ylim = [-1, 1],
    aspect_ratio = :equal,
)

plot!(p, x, y, label=false)

Archimedean Spiral

θ = 0:0.01:2π
a = 2
r = @. a*θ
x = @. r * cos(θ)
y = @. r * sin(θ)

eq = L"r=a\theta"

p = plot(
    title = eq,
    xlabel = L"x",
    ylabel = L"y",
    aspect_ratio = :equal,
)

plot!(p, x, y, label = :false)

Cardioid

θ = 0:0.01:2π
a = 2
r = @. a*(1+cos(θ))
x = @. r * cos(θ)
y = @. r * sin(θ)

eq = L"r=a(1+\cos(\theta))"

p = plot(
    title = eq,
    xlabel = L"x",
    ylabel = L"y",
    aspect_ratio = :equal,
)

plot!(p, x, y, label = :false)

Rose Curve

n = 2

θ = 0:0.01:2π
a = 2
n = 2
r = @. a*sin(n*θ)
x = @. r * cos(θ)
y = @. r * sin(θ)

eq = latexstring("r=a\\sin($n\\theta)")

p = plot(
    title = eq,
    xlabel = L"x",
    ylabel = L"y",
    aspect_ratio = :equal,
)

plot!(p, x, y, label = :false)

n = 3

θ = 0:0.01:2π
a = 2
n = 3
r = @. a*sin(n*θ)
x = @. r * cos(θ)
y = @. r * sin(θ)

eq = latexstring("r=a\\sin($n\\theta)")

p = plot(
    title = eq,
    xlabel = L"x",
    ylabel = L"y",
    aspect_ratio = :equal,
)

plot!(p, x, y, label=false)

n = 4

θ = 0:0.01:2π
a = 2
n = 4
r = @. a*sin(n*θ)
x = @. r * cos(θ)
y = @. r * sin(θ)

eq = latexstring("r=a\\sin($n\\theta)")

p = plot(
    title = eq,
    xlabel = L"x",
    ylabel = L"y",
    aspect_ratio = :equal,
)

plot!(p, x, y, label = :false)

Rose (gif)

θ = 0:0.01:2π
a = 2
anim = @animate for n in 2:10
    r = @. a*sin(n*θ)
    x = @. r * cos(θ)
    y = @. r * sin(θ)

    eq = latexstring("r=a\\sin($n\\theta)")

    p = plot(
        title = eq,
        xlabel = L"x",
        ylabel = L"y",
        xlim=[-3,3],
        ylim=[-3,3],
        aspect_ratio = :equal,
    )

    plot!(p, x, y, label = :false)
end

gif(anim, joinpath(@OUTPUT,"roses.gif"), fps=2)