Static image of Mandelbrot

mandelbrot.rb

# image @ https://twitter.com/josh_cheek/status/846199094519443456
require 'graphics'

# https://www.bowdoin.edu/~dfrancis/askanerd/mandelbrot/
#
# Consider the code:
#   Z = 0
#   C = /* some complex number */
#   loop { Z = Z*Z + C }
#
# The Mandelbrot Set is the set of every C
# where Z doesn't grow beyond the number 2.
#
# This is done by sampling values for C and iterating up to a horizon.
# The colours are applied to the values outside the Mandelbrot Set
# based on how many iterations it took them to grow beyond 2.

class MandelBrot < Graphics::Drawing
  LEFT_CLICK = 1
  def handle_event(event, n)
    if event.kind_of?(SDL::Event::Mouseup) && event.button == LEFT_CLICK
      @target = [h-event.y-1, event.x]
    else
      super
    end
  end
end

def mandelbrot(x, y)
  zx = cx = x
  zy = cy = y
  99.times do |i|
    zx, zy = (zx*zx + cx - zy*zy), (2*zx*zy + cy)
    return i if 2 < zx*zx+zy*zy
  end
  nil
end

w               = 1440
h               = 900
@initial_width  = 5
@initial_height = 2

@target = [w/2, h/2]
@center = [0, 0]

mb                = MandelBrot.new w, h, 24
depth             = 3
mandelbrot_width  = @initial_width  / depth.to_f
mandelbrot_height = @initial_height / depth.to_f

mid_x, mid_y = @center
start_x = mid_x - mandelbrot_width  / 2
start_y = mid_x - mandelbrot_height / 2

end_x   = start_x + 0.04 / depth * 100
end_y   = start_y + 0.03 / depth * 100

∆x = end_x - start_x
∆y = end_y - start_y

colors = [:red, :green, :blue, :cyan, :magenta, :yellow]
x_step = ∆x / w
y_step = ∆y / h

pixel_width  = 1
pixel_height = 1
x_iterations = (w/pixel_width).ceil
y_iterations = (h/pixel_height).ceil

x_iterations.times do |x|
  initial_x = x * ∆x / x_iterations + start_x
  y_iterations.ceil.times do |y|
    initial_y = y * ∆y / y_iterations + start_y
    if depth = mandelbrot(initial_x, initial_y)
      color = :"red#{'%02d'%depth}"
    else
      color = :black
    end
    # mb.rect x*pixel_width, y*pixel_width, pixel_width, pixel_height, color, :fill
    mb.point x*pixel_width, y*pixel_width, color
  end
end

# NOTE ON ZOOMING: It should zoom such that the target is in the same location
# on the screen after the zoom as it was before the zoom
mb.run