The Samurai followed a Code known as Bunbu Ryodo 文武両道 The Mastery of Sword and Letters.

Most Samurai were trained from a young age in the Neo-Confucian Classics and Shodo, the Way of the Brush.

I did a Series of Articles and Videos exploring this subject in depth for the Magazine Gekkan Hiden called:

The Brush is the Sword of the Mind

Explore the character behind the characters which these Samurai painted: Miyamoto Musashi, Takuan Soho, Matsudaira Katamori, Yoshida Shoin, Sakamoto Ryoma, Nakamura Tempu, Ohishi Kuranosuke, Takeda Shingen, Sen no Rikyu, Oh You Mei, Sanada Ninja, and Yamaoka Tesshu, with additional articles on Ninja and Samurai Calligraphy.

The Entire Series can be viewed in English at: 

http://budojapan.com/samurai-shodo-series/

and in Japanese at: