I had an amazing 50 responses to this request for help.  For those of you who are interested, I've attempted to summarize the answers to my query re "term or label for image made up of multiples of small images like letters, words, etc."  I hope I didn't overlook any.  Many thanks for being so helpful.
 
Arcimboldo / Arcimboldo effect
I was aware of Arcimboldo's paintings, but it wasn't what I was looking for.  I was looking for a relatively contemporary image composed of many small identical or similar components, something graphic, in black and white, that I may have seen in commercial art or perhaps advertising.  In Arcimboldo's paintings, the fruit, vegetables, etc. are too unlike in size and shape. 

Image mosaic / Photomosaic

I was not looking for images with photographic components that make up a larger image.  However, these images were new to me and there's a lot out there about them. Photomosaic images are really interesting, the technique or the software is copyrighted by Robert Silver (or perhaps just the term?).  Apparently there is other, free, downloadable software to create the images as well.

Photo montages / Photo tiled pictures / Photo tapestries / Composite photo montages
These are other terms suggested for photomosaics

Pixel art (a version of pointillism) or Composite images
Chuck Close's portraits were mentioned as an example of pixel art.  Also the work of Graham Kelman, Chris Jordan
http://gk3dlab.wordpress.com/tag/pixel-art/
http://www.chrisjordan.com/

Micrography / Microcalligraphy / Calligrams
I was not aware of this either; historically, it began with the prohibition on images in Jewish texts and Islamic culture; apparently words in patterns that result in images circumvent the prohibition.

I was probably looking for a contemporary, secular descendant of this.
http://www.jtsa.edu/prebuilt/exhib/microg/index.shtml
 
Typographic portraits / Typographic images / Pictures made of text /
Check these out - these sites have some amazing examples of the typographer's art:
http://abduzeedo.com/45-amazing-type-faces-typographic-portraits
 http://www.artext.co.uk/gallery/typography_kingdom.html
 http://weburbanist.com/2009/05/10/the-art-of-words-15-creative-typography-artworks/
 
<http://tinyurl.com/yedtybp>
http://blog.creativityden.com/the-beauty-of-typographic-portraits/ 

Text portraits
.    A symbiosis out of text and photo, biography and portrait. A text portrait is a version of lettering and photo of a usual portrait, with the difference, that the text (e.g. biography) and the photo (e.g. passport picture) create an inseparable symbiosis. The fusion of two visually different components to a readable portrait? the text portrait.

More amazing typography:
Source: <http://yatzer.com/1835_text-portraits_by_ralph_ueltzhoeffer>
 
The Serif Fairy by Rene Siegfried (2007).  (children's book)
The poor, little serif fairy, composed entirely of Garamond type, has lost a wing and travels through a typographic landscape to find it again. 
On Amazon:
http://www.amazon.com/Serif-Fairy-Rene-Siegfried/dp/0979048621
 

Word portraits

Portraits, e.g. of Barack Obama, created with script; See John Sokol 

Text drawing

Drawings created with script, not typography.  See Ayakoh Furukawa 

Pushpin portraits
See work of Eric Daigh 

Images made with toy soldiers
See work of Vik Muniz 

Images made of a child's handprint
the controversial work of Marcus Harvey

Collage / Photo collage / Montage / Computer created montage
In light of all the other terms that are more specific, I don't think these are as applicable as the others. 

Type drawing software / ASCII Art

e.g., Michelangelo's David, or cows created by text files
(similar images used to be done with typewriter before computers)

Non-western art
Indian composite paintings;  in Islamic art, Arabic calligraphy to create animals

Semiomorphism
a new, made-up word suggested as an answer

 

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