Freaky Dot Patterns, based on this video by Numberphile: https://www.youtube.com/watch?v=QAja2jp1VjE

png_dots.rb

# Pics at https://twitter.com/josh_cheek/status/681062928980783104
# Gif at  https://twitter.com/josh_cheek/status/686465757476065280
# Based on https://www.youtube.com/watch?v=QAja2jp1VjE
require 'chunky_png'
require 'matrix'
include Math

def white
  ChunkyPNG::Color.rgb(255, 255, 255)
end

def black
  ChunkyPNG::Color.rgb(  0,   0,   0)
end

def rotate(point, a)
end

def point(x, y)
  z = 0
  Matrix[[x],[y],[z],[1]]
end

def draw(canvas, point)
  x             = point[0, 0].to_i
  y             = point[1, 0].to_i
  radius        = 2
  stroke_colour = black
  fill_colour   = black
  return unless canvas.include_xy? x, y
  canvas.circle x, y, radius, stroke_colour, fill_colour
end


width    = 800
height   = 600
distance = 10

0.step(90, 3).with_index do |degrees, index|
  canvas  = ChunkyPNG::Canvas.new width*2, height*2, white
  radians = degrees*Math::PI/180

  # transformed
  translation1 = Matrix[
    [1,0,0, -width],
    [0,1,0, -height],
    [0,0,1, 0],
    [0,0,1, 1],
  ]
  rotation = Matrix[
    [cos(radians) , -sin(radians) , 0 , 0],
    [sin(radians) , cos(radians)  , 0 , 0],
    [0            , 0             , 1 , 0],
    [0            , 0             , 0 , 1],
  ]
  translation2 = Matrix[
    [1,0,0, width],
    [0,1,0, height],
    [0,0,1, 0],
    [0,0,1, 1],
  ]
  transformation = translation2 * rotation * translation1

  (width*2/distance).times do |x|
    (height*2/distance).times do |y|
      point = point(x*distance, y*distance)
      draw canvas, point
      draw canvas, (transformation*point)
    end
  end

  canvas.save("rotated-#{index}.png")
end

`open .`

svg_dots.rb

require 'erb'

num_cols          = (ARGV[0]||'20').to_i
num_rows          = (ARGV[1]||'20').to_i
radius            = (ARGV[2]||'0.5').to_f
dot_colour        = '#2A211c'
background_colour = '#FFFFFF'

dots_row = num_cols.times.map do |col|
  x = 100.0*col/num_cols
  '<use xlink:href="#dot" x="%0.2f" y="0"/>' % x
end.join("\n")

dots_grid = num_rows.times.map do |row|
  y = 100.0*row/num_rows
  '<use xlink:href="#dotsRow" x="0" y="%0.2f"/>' % y
end.join("\n")

puts ERB.new(DATA.read).result(binding)

__END__
<?xml version="1.0" encoding="utf-8"?>

<svg width               = "800px"
     height              = "800px"
     viewBox             = "0 0 100 100"
     version             = "1.1"
     xmlns               = "http://www.w3.org/2000/svg"
     xmlns:xlink         = "http://www.w3.org/1999/xlink"
     preserveAspectRatio = "xMidYMid"
     baseProfile         = "full"
     >

  <title>Dots</title>
  <desc>Based on https://www.youtube.com/watch?v=QAja2jp1VjE</desc>
  <defs>
    <circle id="dot" cx="0" cy="0" r="<%= radius %>" stroke="black" stroke-width="0%" fill="<%= dot_colour %>" />
    <g id="dotsRow"  cx="0" cy="0"><%= dots_row  %></g>
    <g id="dotsGrid" cx="0" cy="0"><%= dots_grid %></g>
  </defs>

  <g>
    <rect width="100" height="100" fill="<%= background_colour %>" />
    <use xlink:href="#dotsGrid"/>
    <g>
      <use xlink:href="#dotsGrid"></use>
      <animateTransform
        attributeName = "transform"
        type          = "rotate"
        from          = "0 50 50"
        to            = "360 50 50"
        begin         = "0s"
        dur           = "60s"
        repeatCount   = "indefinite"
      />
    </g>
  </g>
</svg>