fractals.rb

require 'complex'
require 'matrix'
require 'chunky_png'

module Fractal
  class Mandelbrot
    class << self
      # Returns the mandelbrot value after iterating over c
      def mandelbrot(c, dim=2)
        Array.new(100).inject(0) { |z,i| z ** dim + c }
      end

      # Returns the color of the mandelbrot value acording to its abs
      def mandelbrot_color(c, exp, limit=2)
        abs = mandelbrot(c, exp).abs
        if abs < limit
          intensity = (255 * abs / limit).to_i
          ChunkyPNG::Color.rgba(0, 0, intensity, 255)
        else
          ChunkyPNG::Color::WHITE
        end
      end

      # Returns the mandelbrot set matrix
      def mandelbrot_set(options={})
        resolution = options[:resolution] || 1000
        x1  = options[:x1] || -2.0
        x2  = options[:x2] || 2.0
        y1  = options[:y1] || -2.0
        y2  = options[:y2] || 2.0
        dim = options[:dim] || 2.0
        set = Array.new(resolution) { Array.new(resolution) }

        set.each_with_index do |col, i|
          col.each_with_index do |value, j|
            step_x = (x2 - x1) / resolution
            step_y = (y2 - y1) / resolution
            z = Complex(x1 + i * step_x, y1 + j * step_y)
            set[i][j] = mandelbrot_color(z, dim)
          end
        end
        return set
      end

      # Creates an png image from a mandelbrot set matrix
      def create_image(options)
        image_name = options['image_name'] || 'mandelbrot'
        set = mandelbrot_set(options)
        png = ChunkyPNG::Image.new(set.length, set[0].length, ChunkyPNG::Color::BLACK)

        set.each_with_index do |col, i|
          col.each_with_index do |value, j|
            png[i,j] = value
          end
        end
        png.save("#{image_name}.png")
      end

      # Creates an sequence of png images from a variable exponent mandelbrot set
      def generate_sequence(options={})
        start = options[:start] || 0
        finish = options[:finish] || 10
        step = options[:step] || 0.1
        counter = 0

        (start).step(finish, step) do |dim|
          options[:dim] = dim
          dim_to_s = dim.to_s
          dim_to_s = dim_to_s[0, dim_to_s.index('.') + 2]
          options['image_name'] = "mandelbrot_#{counter}_#{dim_to_s}"
          counter += 1
          create_image(options)
        end
      end
    end
  end
end

## Usage examples
# Fractal::Mandelbrot.mandelbrot_set resolution: 100, x1: -2, x2: 2, y1: -1, y2: 1
# Fractal::Mandelbrot.create_image resolution: 100
# Fractal::Mandelbrot.generate_sequence(resolution: 1000, start: -10, finish: 10)