Raul wrote:
"Using < is an excellent way to visualize this process"

In this case <^:2 is even better:

   (1 1 1 0,:1 0 1 1)<^:2;. 1 i. 4 4
+---------+-----------+-------------+
|+-------+|+-------+  |+-----------+|
||0 1 2 3|||4 5 6 7|  || 8  9 10 11||
|+-------+|+-------+  ||12 13 14 15||
|         |           |+-----------+|
+---------+-----------+-------------+
|+-------+|+---------+|+-----------+|
||0 1 2 3|||8 9 10 11|||12 13 14 15||
||4 5 6 7||+---------+|+-----------+|
|+-------+|           |             |
+---------+-----------+-------------+
----------------------------------------------------------------------
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