# Multiple Plots for Parametric Equations

**URL:** <https://discourse.julialang.org/t/multiple-plots-for-parametric-equations/93131>\
**Category:** General Usage\
**Tags:** plotting\
**Created:** [January 18, 2023, 8:10am UTC](https://discourse.julialang.org/t/multiple-plots-for-parametric-equations/93131 "2023-01-18T08:10:32Z")\
**Posts on this page:** 8\
**Page:** 1

<div class="post-metadata">

**Author:** ![Freya\_the\_Goddess](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/freya_the_goddess/32/36835_2.png) [@Freya\_the\_Goddess](https://discourse.julialang.org/u/Freya_the_Goddess)\
**Post date:** [January 18, 2023, 8:10am UTC](https://discourse.julialang.org/t/multiple-plots-for-parametric-equations/93131/1 "2023-01-18T08:10:32Z")

</div>

Hi all,

I want to do multiple plots with layout for parametric equations. This is my code:

```julia
using Plots, LaTeXStrings
pyplot()

θ1 = 0:0.1:2π
x1 = 3 .*cos.(θ1)
y1 = 3 .*sin.(θ1)

x2 = 3 .*cos.(θ1)
y2 = sin.(θ1)

θ2 = 0:0.1:6π
x3 = θ2.*cos.(θ2)
y3 = θ2.*sin.(θ2)

x4 = cos.(θ1)
y4 = sin.(2θ1)

p1 = (x1, y1, -10,10)
p2 = (x2, y2, -10,10)
p3 = (x3, y3, -10,10)
p4 = (x4, y4, -10,10)

s1 = L"(x,y) = (3 \ \cos \ t, 3 \ \sin \ t)";
s2 = L"(x,y) = (3 \ \cos \ t, \sin \ t)";
s3 = L"(x,y) = (t \ \cos \ t, t \ \sin \ t)";
s4 = L"(x,y) = (\cos \ t, \sin \ 2t)";

plot(p1, p2, p3, p4, layout = (2, 2), xaxis = "x", yaxis = "y", label=[s1 s2 s3 s4], 
title=["a" "b" "c" "d"],
titleloc = :bottom, titlefont = font(8))

```

but there is an error:

```julia
LoadError: Couldn't process recipe args: (Vector{Float64}, Vector{Float64}, Vector{Float64}, Vector{Float64})
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:33
  [2] macro expansion
    @ ~/.julia/packages/RecipesPipeline/XxUHt/src/user_recipe.jl:158 [inlined]
  [3] apply_recipe(::AbstractDict{Symbol, Any}, ::Any, ::Any, ::Any, ::Any)
    @ RecipesPipeline ~/.julia/packages/RecipesBase/eU0hg/src/RecipesBase.jl:300
  [4] _process_userrecipes!(plt::Any, plotattributes::Any, args::Any)
    @ RecipesPipeline ~/.julia/packages/RecipesPipeline/XxUHt/src/user_recipe.jl:38
  [5] recipe_pipeline!(plt::Any, plotattributes::Any, args::Any)
    @ RecipesPipeline ~/.julia/packages/RecipesPipeline/XxUHt/src/RecipesPipeline.jl:72
  [6] _plot!(plt::Plots.Plot, plotattributes::Any, args::Any)
    @ Plots ~/.julia/packages/Plots/M4dfL/src/plot.jl:223
  [7] plot(::Any, ::Vararg{Any}; kw::Base.Pairs{Symbol, V, Tuple{Vararg{Symbol, N}}, NamedTuple{names, T}} where {V, N, names, T<:Tuple{Vararg{Any, N}}})
    @ Plots ~/.julia/packages/Plots/M4dfL/src/plot.jl:102
  [8] top-level scope
    @ ~/LasthrimProjection/Test/plotjulia.jl:28
  [9] include(fname::String)
    @ Base.MainInclude ./client.jl:451
 [10] top-level scope
    @ REPL[1]:1
in expression starting at /home/browni/LasthrimProjection/Test/plotjulia.jl:28

```

---

<div class="post-metadata">

**Author:** ![nilshg](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nilshg/32/2283_2.png) [@nilshg](https://discourse.julialang.org/u/nilshg)\
**Post date:** [January 18, 2023, 8:53am UTC](https://discourse.julialang.org/t/multiple-plots-for-parametric-equations/93131/2 "2023-01-18T08:53:56Z")

</div>

For plotting multiple plots you should pass figures to `plot`, i.e.

```julia
p1 = plot(rand(5))
p2 = plot(rand(5))
plot(p1, p2)

```

In your example, `p1`, `p2`, etc are just tuples:

```julia
julia> θ1 = 0:0.1:2π;

julia> θ1 = 0:0.1:2π;

julia> y1 = 3 .*sin.(θ1);

julia> x1 = 3 .*cos.(θ1);

julia> p1 = (x1, y1, -10,10)
([3.0, 2.9850124958340776, 2.940199733523725, 2.866009467376818, 2.7631829820086553, 2.6327476856711183, 2.4760068447290347, 2.2945265618534654, 2.0901201280414963, 1.8648299048119932 … 1.6631230085374846, 1.904078627827904, 2.12600932287378, 2.3266976355307505, 2.5041383545174796, 2.656558550823958, 2.782435292232108, 2.880510859951098, 2.949805315327754, 2.9896262910696523], [0.0, 0.29950024994048446, 0.5960079923851836, 0.8865606199840188, 1.1682550269259515, 1.438276615812609, 1.6939274201851064, 1.9326530617130735, 2.1520682726985685, 2.3499807288824504 … -2.4968023266717023, -2.3182934626679614, -2.1166209767111757, -1.8937999136169625, -1.6520566277929127, -1.3938065382412699, -1.121629994490708, -0.8382464945967776, -0.546487512816285, -0.2492682084524892], -10, 10)

```

You probably want to create actual plots in those lines?

---

<div class="post-metadata">

**Author:** ![Freya\_the\_Goddess](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/freya_the_goddess/32/36835_2.png) [@Freya\_the\_Goddess](https://discourse.julialang.org/u/Freya_the_Goddess)\
**Post date:** [January 18, 2023, 8:59am UTC](https://discourse.julialang.org/t/multiple-plots-for-parametric-equations/93131/3 "2023-01-18T08:59:29Z")

</div>

Yes I want to plot it like this, but with layout 2 x 2:

![Capture d’écran_2023-01-18_15-58-57](https://global.discourse-cdn.com/julialang/original/3X/2/c/2cdf01741dad5144077ae2e3ef165740a361d3fd.png)

---

<div class="post-metadata">

**Author:** ![Freya\_the\_Goddess](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/freya_the_goddess/32/36835_2.png) [@Freya\_the\_Goddess](https://discourse.julialang.org/u/Freya_the_Goddess)\
**Post date:** [January 18, 2023, 9:21am UTC](https://discourse.julialang.org/t/multiple-plots-for-parametric-equations/93131/4 "2023-01-18T09:21:30Z")

</div>

I am able to do parametric plot (single plot), here is the code:

```julia
using Plots, LaTeXStrings; gr()

# To plot a spiral centered at (0, 0) 
θ = 0:0.1:10.1π
x = θ.*cos.(θ)
y = θ.*sin.(θ)
plot(x, y, xlims=(-50,50), ylims=(-50,50),
	label=L"(x,y) = (t \ \cos \ t , t \ \sin \ t)",
	framestyle=:zerolines, aspect_ratio=:equal)

```

How to make multiple plots for parametric equations? What do I need to do to fix p1,p2,p3,p4 ?

---

<div class="post-metadata">

**Author:** ![nilshg](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nilshg/32/2283_2.png) [@nilshg](https://discourse.julialang.org/u/nilshg)\
**Post date:** [January 18, 2023, 9:22am UTC](https://discourse.julialang.org/t/multiple-plots-for-parametric-equations/93131/5 "2023-01-18T09:22:47Z")

</div>

Yes that’s what I thought and that’s my point above - `p1` needs to be the actual plot you want to have in the [1, 1] position.

So you need:

```julia
p1 = plot(x, y, xlims=(-50,50), ylims=(-50,50),
	label=L"(x,y) = (t \ \cos \ t , t \ \sin \ t)",
	framestyle=:zerolines, aspect_ratio=:equal)

```

then something equivalent for `p2` etc and _then_ you do

```julia
plot(p1, p2, p3, p4, layout = (2, 2))

```

---

<div class="post-metadata">

**Author:** ![Freya\_the\_Goddess](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/freya_the_goddess/32/36835_2.png) [@Freya\_the\_Goddess](https://discourse.julialang.org/u/Freya_the_Goddess)\
**Post date:** [January 18, 2023, 9:28am UTC](https://discourse.julialang.org/t/multiple-plots-for-parametric-equations/93131/6 "2023-01-18T09:28:18Z")

</div>

This works:

```julia
using Plots, LaTeXStrings
pyplot()

θ1 = 0:0.1:2π
x1 = 3 .*cos.(θ1)
y1 = 3 .*sin.(θ1)

x2 = 3 .*cos.(θ1)
y2 = sin.(θ1)

θ2 = 0:0.1:6π
x3 = θ2.*cos.(θ2)
y3 = θ2.*sin.(θ2)

x4 = cos.(θ1)
y4 = sin.(2θ1)

p1 = plot(x1, y1, xlims=(-50,50), ylims=(-50,50),
	framestyle=:zerolines)
p2 = plot(x2, y2, xlims=(-50,50), ylims=(-50,50),
	framestyle=:zerolines)
p3 = plot(x3, y3, xlims=(-50,50), ylims=(-50,50),
	framestyle=:zerolines)
p4 = plot(x4, y4, xlims=(-50,50), ylims=(-50,50),
	framestyle=:zerolines)

s1 = L"(x,y) = (3 \ \cos \ t, 3 \ \sin \ t)";
s2 = L"(x,y) = (3 \ \cos \ t, \sin \ t)";
s3 = L"(x,y) = (t \ \cos \ t, t \ \sin \ t)";
s4 = L"(x,y) = (\cos \ t, \sin \ 2t)";

plot(p1, p2, p3, p4, layout = (2, 2), xaxis = "x", yaxis = "y", label=[s1 s2 s3 s4], 
title=["a" "b" "c" "d"],
titleloc = :bottom, titlefont = font(8))

```

but it is so weird, I think `p1 = (x1, y1, -10,10)` is enough to plot… or I just lack of experience…

---

<div class="post-metadata">

**Author:** ![nilshg](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nilshg/32/2283_2.png) [@nilshg](https://discourse.julialang.org/u/nilshg)\
**Post date:** [January 18, 2023, 10:53am UTC](https://discourse.julialang.org/t/multiple-plots-for-parametric-equations/93131/7 "2023-01-18T10:53:59Z")

</div>

This suggests that you have some deep misunderstanding about how Julia works which would probably be useful to address to make your future coding easier. Have you considered reading the Julia manual to get a better understanding of how the language works at the most basic level (e.g. what is a function call, what is a variable, what are the basic data structures etc)?

The section on tuples is here:

[https://docs.julialang.org/en/v1/manual/functions/#Tuples](https://docs.julialang.org/en/v1/manual/functions/#Tuples)

But the wider function section of the manual is probably relevant for you. The key here is that parentheses `()` are used for different things in Julia, in the main:

- Grouping statements to change the order of evaluation:

```julia
julia> 1 == 2 | 3 == 3
false

julia> (1 == 2) | (3 == 3)
true

```

This is similar to what you do in maths notation, 2 + 3 \times 4 \neq (2 + 3) \times 4

- Constructing tuples (see the link above)

```julia
julia> typeof((1, 2))
Tuple{Int64, Int64}

julia> typeof((1, ))
Tuple{Int64}

```

- Calling functions:

```julia
julia> f(x, y) = 2x + 3y
f (generic function with 2 methods)

julia> f(1, 2)
8

```

Now the key here is that to call a function, the parens need to directly follow the identifier of the function:

```julia
julia> f (1, 2)
ERROR: syntax: space before "(" not allowed in "f (" at REPL[20]:1

```

That’s because - as we’ve seen in the second bullet point above - just writing `(1, 2)` just creates a tuple with the elements 1 and 2.

So when you say

> [@Freya\_the\_Goddess](#):
>
> I think `p1 = (x1, y1, -10,10)` is enough to plot

you are conflating the function call with the tuple syntax. There is no way for Julia to know that when you write

```julia
(x1, y1, -10, 10)

```

you **actually** meant

```julia
plot(x1, y1, -10, 10)

```

because `(x1, y1, -10, 10)` is perfectly valid syntax which means “please create a tuple with four elements, the first element being the vector `x1`, the second element being the vector `y1`, the third element being -10 and the fourth element being 10”.

I hope that thinking about why `(x1, y1, -10, 10)` cannot be the same as `plot(x1, y1, -10, 10)` will help you get a better understanding of how the language works - if somehow it isn’t clear do ask further questions.

---

<div class="post-metadata">

**Author:** ![Freya\_the\_Goddess](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/freya_the_goddess/32/36835_2.png) [@Freya\_the\_Goddess](https://discourse.julialang.org/u/Freya_the_Goddess)\
**Post date:** [January 18, 2023, 12:00pm UTC](https://discourse.julialang.org/t/multiple-plots-for-parametric-equations/93131/8 "2023-01-18T12:00:00Z")

</div>

Yes I misunderstand it, because I am trying to make it work fast, guess I should have be more slower and read the Julia’ manual more.