Ruby script to draw a lorenz attractor with Euler's method.

lorenz_attractor_euler.rb

#! /usr/local/bin/ruby
# *******************************
# Lorenz attractor (Euler method)
# *******************************
#
require 'numo/gnuplot'

class LorenzAttractorEuler
  DT            = 1e-3     # Differential interval
  STEP          = 100000   # Time step count
  X_0, Y_0, Z_0 = 1, 1, 1  # Initial values of x, y, z

  def initialize
    @res = [[], [], []]
  end

  def exec
    xyz = [X_0, Y_0, Z_0]
    STEP.times do
      l = lorenz(xyz)
      3.times do |i|
        xyz[i] += DT * l[i]
        @res[i] << xyz[i]
      end
    end
    plot
  rescue => e
    $stderr.puts "[#{e.class}] #{e.message}"
    e.backtrace.each { |tr| $stderr.puts "\t#{tr}" }
    exit 1
  end

  private

  def lorenz(xyz, p=10, r=28, b=8/3.0)
    return [
      -p * xyz[0] + p * xyz[1],
      -xyz[0] * xyz[2] + r * xyz[0] - xyz[1],
      xyz[0] * xyz[1] - b * xyz[2]
    ]
  rescue => e
    raise
  end

  def plot
    x, y, z = @res

    begin
      Numo.gnuplot do
        set   terminal: "png"
        set   output:   "lorenz_attractor_euler.png"
        set   title:    "Lorenz attractor (Euler method)"
        set   xlabel:   "x"
        set   ylabel:   "y"
        set   zlabel:   "z"
        unset :key
        splot x, y, z, with: :lines, linecolor: {rgb: "blue"}
      end
    rescue => e
      raise
    end
  end
end

exit 0 unless __FILE__ == $0
LorenzAttractorEuler.new.exec