fixed_points.jl

function fixed_point(f, x0)
    x, x_old = f(x0), x0
    n = 1
    while x !== x_old
        x, x_old = f(x), x
        n += 1
    end
    (x, n)
end

fixed_point(x -> 0.1 * x, 1.0)
fixed_point(x -> 10.0 * x, 1.0)
fixed_point(x -> exp(x), 1.0)
fixed_point(x -> x + 1.0, 1.0e16)