Those trees were indeed at Missouri Botanical Gardens. One of the best examples of permeable paving we've seen. Grate sections and other similar products are categorized as "permeable paving", "root protection grid" or "root protection mat"; those at MoBot are for high traffic and heavy wear, they're a concrete grid. For residential use there are plastics like big sections of open honeycomb.
Geogrid was one of the first manufacturers and so its name got attached to many products like Kleenex to facial tissue and Bandaid to adhesive bandages. So if you search for Geogrid or ask at landscape supply firms for it, you'll get a start on what's available.
Recently, in a project at the Detroit Zoo (a project which morphed midstream so this facet of it was left incomplete) we tracked down some grid rated sturdy enough for heavy foot-traffic through a company in Livonia MI. They had the item below, quoting us enough for a 400 sq. ft. area:
This maybe a more cost effective solution for your zoo project.
433 sft with pins would run $932.06 picked up in Livonia, MI
In researching for a client project, we had this site marked:
From an article we included about this in What's Up 168 at our website, some more sites that may be helpful in considering different products:
For more about paving grids. (No endorsement is intended of these specific products.) http://www.invisible...grasspave2.html
and video at
Performance results, University of Washington study of these products used on road shoulders:
Hope this helps. We're posting this exchange here on our Forum so others may comment. If you would like to continue the discussion we hope you'll do that here. We'll reply here.
Janet & Steven