複素関数論 マンデルブロ集合

index.haml

!!!html5
%html
  %body
    %form{:action => '.', :method => 'get'}
      width
      %input{:name => 'width', :value => @params['width']}
      height
      %input{:name => 'height', :value => @params['height']}
      fineness
      %input{:name => 'fineness', :value => @params['fineness']}
      center_x
      %input{:name => 'center_x', :value => @params['center_x']}
      center_y
      %input{:name => 'center_y', :value => @params['center_y']}
      %input{:type => 'submit', :value => '描画'}
    %img{src: @result_path}

mandelbrot.c

#include <math.h>
#include <complex.h>

const int MAX_ITERATION = 20;
const double THRESHOLD = 3.5f;

int calc
(
  const unsigned w, const unsigned h, const double cx, const double cy,
  const double step,
  const unsigned x, const unsigned y
)
{
  double real = step * (x - w/2.0) + cx;
  double imag = step * (h/2.0 - y) + cy;
  double complex c = real + I * imag;
  double complex z = c;
  for(int i = 0; i < MAX_ITERATION; ++i) {
    if(cabs(z) > THRESHOLD) {
      return 255 - i * 10;
    }
    z = z * z + c;
  }
  return 0;
}

mandelbrot.rb

# coding: UTF-8
require 'ffi'
require 'zlib'
require 'sinatra'

module Mandelbrot
   extend FFI::Library
   ffi_lib "libmandelbrot.so"
   attach_function :calc, [:uint, :uint, :double, :double, :double, :uint, :uint], :int
end

# チャンクのバイト列生成関数
def chunk(type, data)
  [data.bytesize, type, data, Zlib.crc32(type + data)].pack('NA4A*N')
end

def data2png width, height, data
   # ファイルシグニチャ
   res = "\x89PNG\r\n\x1a\n".force_encoding(Encoding::BINARY)
   # ヘッダ
   res += chunk('IHDR', [width, height, 8, 2, 0, 0, 0].pack('NNCCCCC'))
   # 画像データ
   img_data = data.map {|l| ([0] + l.flatten).pack('C*') }.join
   res += chunk('IDAT', Zlib::Deflate.deflate(img_data))
   # 終端
   res + chunk('IEND', '')
end

get '/' do
   defaults = {
      'width' => '500',
      'height' => '500',
      'fineness' => '0.006',
      'center_x' => '-0.7',
      'center_y' => '0.0',
   }
   @params = params
   defaults.keys.each do |s|
      @params[s] ||= defaults[s]
      @params[s] = @params[s].to_f
   end
   @params['width'] = @params['width'].to_i
   @params['height'] = @params['height'].to_i
   raw_data = (0...@params['height']).map do |y|
      (0...@params['width']).map do |x|
         res = Mandelbrot.calc @params['width'], @params['height'], @params['center_x'], @params['center_y'], @params['fineness'], x, y
         [res, res, res]
      end
   end
   png = data2png @params['width'], @params['height'], raw_data
   @result_path = rand(999999).to_s + '.png'
   File.binwrite('./public/' + @result_path, png)
   haml :index
end