This pattern, originally among the 35 designs in the 2009 Dishcloth Calendar, has now been released as a free pattern on the Mason-Dixon Knitting blog.
This dishcloth was inspired by the geometric patterns of linoleum floors, which were popular through the 50s and beyond. I searched through stitch dictionaries for a pattern reminiscent of linoleum tiles, and found this interlocking diamond motif in several sources.
A bonus: this is a slip-stitch pattern, so it results in a scrubby cloth with an attractive woven appearance on the wrong side. It’s quite simple to follow the row-by-row instructions, but once you get going, it’s a pleasant challenge to work this pattern from memory, following the diamonds as they expand and contract.