The highly intricate ink flows that grace archaic clerical scripts and decorative art, the illuminated plates of medieval European manuscripts, may be aesthetically pleasing, but are essentially skillfully beautified elaborations of simplistic lettering.
East Asian ideograms on the other hand, even when reduced to their most skeletal elements, are a complex form of writing that takes years to master.
There are strict rules to follow, some of which may be baffling to Westerners. Why for example, is the order in which strokes are written strictly circumscribed? If the order in which the strokes are written down is incorrect, the kanji character is invalid as pure calligraphy, even if the results are identical to the same character written in the correct order.