1_application.js

$(document).ready(function () {

   $('form').submit(function (e) {
      e.preventDefault();

      $.post('/', function(response) {
        source = response + '.png';        
        $('#die_pic').attr('src', source);
      });
    });

});

1_index.rb

get '/' do
  erb :index
end

post '/' do
  value = params[:value] ? params[:value].to_i : nil
  @roll = value ? Roll.create({ value: value }) : Roll.create
  @roll.value.to_s
end

2_index.erb

<div class="container">
  <h1>Simplest Possible AJAX</h1>
  <p>This contrived app will simulate a roll of a 6-sided die.</p>

  <form method="post" action="/">
    <input type="submit" value="Roll the Die">
  </form>

  <div id="die">
      <img id = "die_pic">
  </div>

</div>

database.rb

# The below was the only line that I changed in this file.
require_relative 'environment'

# Log queries to STDOUT in development
if Sinatra::Application.development?
  ActiveRecord::Base.logger = Logger.new(STDOUT)
end

# Automatically load every file in APP_ROOT/app/models/*.rb, e.g.,
#   autoload "Person", 'app/models/person.rb'
#
# See http://www.rubyinside.com/ruby-techniques-revealed-autoload-1652.html
#
Dir[APP_ROOT.join('app', 'models', '*.rb')].each do |model_file|
  filename = File.basename(model_file).gsub('.rb', '')
  autoload ActiveSupport::Inflector.camelize(filename), model_file
end

# We have to do this in case we have models that inherit from each other.
# If model Student inherits from model Person and app/models/student.rb is
# required first, it will throw an error saying "Person" is undefined.
#
# With this lazy-loading technique, Ruby will try to load app/models/person.rb
# the first time it sees "Person" and will only throw an exception if
# that file doesn't define the Person class.

# Heroku controls what database we connect to by setting the DATABASE_URL environment variable
# We need to respect that if we want our Sinatra apps to run on Heroku without modification
db = URI.parse(ENV['DATABASE_URL'] || "postgres://localhost/#{APP_NAME}_#{Sinatra::Application.environment}")

DB_NAME = db.path[1..-1]

# Note:
#   Sinatra::Application.environment is set to the value of ENV['RACK_ENV']
#   if ENV['RACK_ENV'] is set.  If ENV['RACK_ENV'] is not set, it defaults
#   to :development

ActiveRecord::Base.establish_connection(
  :adapter  => db.scheme == 'postgres' ? 'postgresql' : db.scheme,
  :host     => db.host,
  :port     => db.port,
  :username => db.user,
  :password => db.password,
  :database => DB_NAME,
  :encoding => 'utf8'
)

roll.rb

# Below is the only line that I changed in this file.
require_relative '../../config/environment'

class Roll < ActiveRecord::Base
  attr_accessible :value

  validates :value, :inclusion => { :in => (1..6), :message => "must be between 1 and 6" }

  after_initialize :roll_if_value_is_nil

  private
  # If the user passes-in a "value", let's use it. Otherwise, we'll generate a random one.
  def roll_if_value_is_nil
    self.value = (rand(6) + 1) if not self.value
  end

end