So I was looking to plot the phase diagram for simple ode systems using Makie. Now in the past I have used the `Streamplot`

to display simple phase diagrams where I had an analytic solution for the ODE, as in this example.

However, in most cases ODEs are solved numerically. So I wanted to see if I can use a Makie streamplot to plot the phase diagram for the numerical solutions to an ODE. I found this example of doing the process manually, using regular plots.

```
# Simple Pendulum Problem
using DifferentialEquations, Plots
# Constants
const g = 9.81
const L = 1.0
#Initial Conditions
u₀ = [0,π/2]
tspan = (0.0,6.3)
#Define the problem
function simplependulum(du,u,p,t)
θ = u[1]
dθ = u[2]
du[1] = dθ
du[2] = -(g/L)*sin(θ)
end
#Pass to solvers
prob = ODEProblem(simplependulum,u₀, tspan)
sol = solve(prob,Tsit5())
#Plot
plot(sol,linewidth=2,
title ="Simple Pendulum Problem",
xaxis = "Time",
yaxis = "Height",
label = ["Theta","dTheta"])
p = plot(sol, vars = (1,2), xlims = (-9,9),
title = "Phase Space Plot",
xaxis = "Velocity",
yaxis = "Position",
leg=false)
function phase_plot(prob, u0, p, tspan=2pi)
_prob = ODEProblem(prob.f,u0,(0.0,tspan))
sol = solve(_prob, Vern9()) # Use Vern9 solver for higher accuracy
plot!(p, sol, vars = (1,2), xlims = nothing, ylims = nothing)
end
for i in -4pi:pi/2:4π
for j in -4pi:pi/2:4π
phase_plot(prob, [j,i], p)
end
end
plot(p,xlims = (-9,9))
```

Now in this example, the authors just discretize some range of initial conditions, solve for the trajectory of a timespan, and then plot the output.

In the case of the Makie `Streamplot`

, I can provide a range of initial conditions, but I don’t have a way to feed the solver like a timespan or such. For the Streamplot, it seems like I need to provide a value as `Point2f()`

or `Point3f()`

, but of course the solved numerical solution of the ODE is an array. So would I just return values of the second timestep in the solution array as a `Point2f`

? I say the second timestep, because the first timestep is undoubtedly the initial value.

If anyone know a good recipe or example for this, please share the knowledge.