Unicorns in the bible... how exciting. Although I'm not sure I understand the made fat with fatness part. Isaiah 34:7 And the unicorns will come down with them, and the bullocks with the bulls; and their land shall be soaked with blood, and their dust be made fat with fatness.
The picture looks like the medevial imagination of a unicorn and what we normally think of today. This Answers in Genesis article discusses possibilities for the animal refered to in its Biblical references. :)