shark.jl

begin
    using Plots, LaTeXStrings; pyplot() 
    # initial condition
    x_0 = 8
    y_0 = -2
    # the "concentration of blood" on the surface of the water
    C(x,y) = ℯ^(-(x^2+2y^2)/(10^4))
    x_range = -10:0.1:10
    y_range = -10:0.1:10
    C_range = [C(x,y) for x in x_range, y in y_range]
    contourf(
        x_range,
        y_range,
        C_range, 
        color=:vikO,
        levels=20,
        dpi=300
    )

    t(x) = (y_0/(x_0)^2)*x^2
    t_range = t.(x_range)
    z_path_range = C.(x_range, t_range)
    plot!(
        x_range,
        t_range,
        color=:gray,
        linewidth = 2,
        label=L"T(x)"
    )
    plot!(
        [x_0],
        [y_0],
        color = :black,
        markersize = 4,
        marker = :circle,
        label = L"P(x_0, y_0)"
    )
    xlims!(-10,10)
    ylims!(-10,10)
end