Is there any meter or rhyme pattern in "A Noiseless Patient Spider" by Walt Whitman and "A Supermarket in California" by Allen Ginsberg?
Nope. Both were written in a form called free verse, which is notable for having neither meter nor rhyme pattern. In Whitman's day, this was a controversial poetic form; Ginsberg, years later, would have found his free verse work much more accepted.
The primary criticism of free verse is that it doesn't rhyme or have meter, therefore it's not really a poem; however, many other poetic elements can be found in most free verse poetry. The language is closer to the natural rhythms of speaking, and the use of imagery, details, and figurative language (metaphor, etc.) is prevalent. Both of these works also use repetition and parallel structure as well, more common poetic elements.
You didn't ask for an explication of these poetry selections, so I will refrain (pun intended).