Lorentz system

A Lorenz system by Henri Menke:

% !TEX lualatex
\documentclass[tikz]{standalone}
\usepackage{luacode,pgfplots}
\begin{luacode*}
-- Differential equation of Lorenz attractor
function f(x,y,z)
    local sigma = 3
    local rho = 26.5
    local beta = 1
    return {sigma*(y-x),-x*z + rho*x - y,x*y - beta*z}
end

-- Code to write PGFplots data as coordinates
function print_LorAttrWithEulerMethod(h,npoints,option)
    -- The initial point (x0,y0,z0)
    local x0 = 0.0
    local y0 = 1.0
    local z0 = 0.0
    -- add random number between -0.25 and 0.25
    local x = x0 + (math.random()-0.5)/2
    local y = y0 + (math.random()-0.5)/2
    local z = z0 + (math.random()-0.5)/2
    if option ~= [[]] then
        tex.sprint("\\addplot3[" .. option .. "] coordinates{")
    else
        tex.sprint("\\addplot3 coordinates{")
    end
    -- dismiss the first 100 points
    -- to go into the attractor
    for i=1, 100 do
        m = f(x,y,z)
        x = x + h * m[1]
        y = y + h * m[2]
        z = z + h * m[3]
    end
    for i=1, npoints do
        m = f(x,y,z)
        x = x + h * m[1]
        y = y + h * m[2]
        z = z + h * m[3]
        tex.sprint("("..x..","..y..","..z..")")
    end
    tex.sprint("}")
end
\end{luacode*}
\newcommand\addLUADEDplot[3][]{%
  \directlua{print_LorAttrWithEulerMethod(#2,#3,[[#1]])}%
}
\pgfplotsset{width=.9\hsize}
\begin{document}
\begin{tikzpicture}
  \begin{axis}
    % SYNTAX: Solution of the Lorenz system
    % with step h=0.02 sampled at 1000 points.
    \addLUADEDplot[color=red,smooth]{0.02}{1000};
    \addLUADEDplot[color=green,smooth]{0.02}{1000};
    \addLUADEDplot[color=blue,smooth]{0.02}{1000};
    \addLUADEDplot[color=cyan,smooth]{0.02}{1000};
    \addLUADEDplot[color=magenta,smooth]{0.02}{1000};
    \addLUADEDplot[color=yellow,smooth]{0.02}{1000};
  \end{axis}
\end{tikzpicture}
\end{document}