Lissajous Curves

lissajous-curves.rb

# encoding: utf-8

# Screenshots:
# http://joshcheek.deviantart.com/gallery/61181398/Lissajous-Curves

# Videos:
# https://vimeo.com/193155770
# https://vimeo.com/193155808
# https://vimeo.com/193156077
# https://vimeo.com/193156097
# https://vimeo.com/193156142
# https://vimeo.com/193156237
# https://vimeo.com/193156327
# https://vimeo.com/193156506
# https://vimeo.com/193156596
# https://vimeo.com/193159486 (unedited, useful for finding specific values of an animation)

# Inspired by one of the slides (47) at
# https://acko.net/blog/animate-your-way-to-glory/

# Fun Fact!
# Aphex Twin used these to embed images into his music,
# When you look at the sound waves of some of his music
# on an Oscilloscope in Lissajous mode, it makes images!

require 'graphics'

class Lissajous < Graphics::Simulation
  include Math

  def π
    PI
  end

  def initialize
    super 1440, 850, 24
    color.default_proc = -> h, k { k }
  end

  def draw(n)
    return if @pause

    # -----  Various Variables  -----

    # how large the animation is
    x_radius       = w/2-20
    y_radius       = h/2-20

    # speed, frustratingly, this has an impact on the phase shifts & other features >.<
    steps          = 250

    # higher is rounder, varying it across time (eg n/20.0) gives a cool warbly effect
    lines_per_step = 20

    # Pause at the end to look at the final result.
    @pause = true if n == steps # Note that some variations keep going after n==steps


    # -----  The x and y coordinates (how it shifts phases)  -----

    # # these look nice together, but will never get the resolution on video to appreciate it
    # y_numerator, y_denominator = 23, 27
    # x_numerator, x_denominator = 28, 29

    # y_numerator, y_denominator = 12, 17
    # x_numerator, x_denominator = 21, 23

    # y_numerator, y_denominator = 7, 8
    # x_numerator, x_denominator = 2, 9

    y_numerator, y_denominator = 1, 1
    x_numerator, x_denominator = 7, 8


    # -----  Constants  -----
    # There's no point in changing these, they either don't command anything useful,
    # or they're composed of vars above, which let you change them in more meaningful ways.
    y_coefficient  = y_numerator/y_denominator.to_f
    x_coefficient  = x_numerator/x_denominator.to_f
    domain         = 2*π * x_denominator.lcm(y_denominator)
    step_size      = domain / steps

    # -----  Draw Background  -----
    # clear colour(2*π*n/steps) # colour the background over time
    clear :black              # Graphics' default, you'll want to make the lines white or coloured
    # clear :white              # inverted default,

    # -----  Draw the Lines  -----
    0.step(domain*n/steps, by: step_size/lines_per_step).each_cons(2) do |i_prev, i_crnt|
      # -----  Colouring Functions  -----
      # rgb = [0xFF]*3            # uncoloured (white) put it on a coloured background
      # rgb = [0x00]*3            # uncoloured (black)
      rgb = colour(i_prev)      # colour across the line (like yarn)
      # rgb = colour(2*π*n/steps) # colours across time

      # -----  Line Location  -----
      # Makes them migrate over time / show up in nonlocal positions.
      # NOTE this behaves very differently based on number of steps!
      x_prev, y_prev = xy(i_prev, vary(x_radius/2, x_radius, n/domain), y_radius, x_coefficient, y_coefficient)
      x_crnt, y_crnt = xy(i_crnt, x_radius, vary(y_radius/2, y_radius, n/domain), x_coefficient, y_coefficient)

      # # This is the normal lissajuous curve
      # x_prev, y_prev = xy(i_prev, x_radius, y_radius, x_coefficient, y_coefficient)
      # x_crnt, y_crnt = xy(i_crnt, x_radius, y_radius, x_coefficient, y_coefficient)

      # -----  Draw Line  -----
      line x_prev, y_prev, x_crnt, y_crnt, rgb
      # line x_prev+1, y_prev, x_crnt+1, y_crnt, rgb # thicken the line
      # line x_prev, y_prev+1, x_crnt, y_crnt+1, rgb # thicken the line
      # line x_prev-1, y_prev, x_crnt-1, y_crnt, rgb # thicken the line more
      # line x_prev, y_prev-1, x_crnt, y_crnt-1, rgb # thicken the line more
      # circle x_prev, y_prev, 50, rgb, false        # knob on the prev line end
      # circle x_crnt, y_crnt, 50, rgb, false        # knob on the crnt line end
    end
  end

  def xy(ø, x_radius, y_radius, x_coefficient, y_coefficient)
    [ x_radius*sin(x_coefficient*ø) + w/2,
      y_radius*sin(y_coefficient*ø) + h/2,
    ]
  end

  # A relatively nice traversal of colourspace, given an angle
  # (arbitrary quantity, you just don't want it jumping between
  # values that are far apart on 0..2π)
  # It avoids black and white since they're common background colours
  def colour(ø)
    blue    = (Math.cos(ø) * 127.5).to_i + 128
    green   = (Math.sin(ø) *  50.5).to_i + 128
    red     = 255 - blue
    [red, green, blue]
  end

  def vary(min, max, ø)
    ∆ = (max-min)
    min + (1 + sin(2*π*ø))*∆/2
  end
end

Lissajous.new.run