interactive_lorenz.jl

## setup differential equation
using DifferentialEquations,
      ParameterizedFunctions

lorenz = @ode_def Lorenz begin           # define the system
 dx = σ * (y - x)
 dy = x * (ρ - z) - y
 dz = x * y - β*z
    end σ ρ β

u0 = [1.0,0.0,0.0]                       # initial conditions
tspan0 = (0.0,100.0)                      # initial timespan
p0 = [10.0,28.0,8/3]                      # initial parameters
prob = ODEProblem(lorenz, u0, tspan0, p0)  # define the problem

using Makie
using AbstractPlotting: textslider
## setup sliders and plotting

"The order of magnitude to range between."
OME = 8

sσ, oσ = textslider(exp10.(-OME:0.001:OME), "σ", start = p0[1]);

sρ, oρ = textslider(exp10.(-OME:0.001:OME), "ρ", start = p0[2]);

sβ, oβ = textslider(exp10.(-OME:0.001:OME), "β", start = p0[3]);

st, ot = textslider(exp10.(-OME:0.001:OME), "tₘₐₓ", start = tspan0[end]);

sr, or = textslider(100:10000, "resolution", start = 2000);

trange = lift(ot, or) do tmax, resolution

            LinRange(0.0, tmax, resolution)

        end

data = lift(oσ, oρ, oβ, trange) do σ, ρ, β, ts

            Point3f0.(
                solve(
                    remake(
                        prob;
                        p = [σ, ρ, β],
                        tspan = (ts[1], ts[end])
                        )
                    )(ts).u
                )  # change to fit the dimensionality - maybe even return 2 arrays, or a set of `Point2`s...
    end

three = lines(data)

vbox(hbox(sσ, sρ, sβ, st, sr), three)