CRITIC’S NOTEBOOK

How’s your weekend looking? Can you set aside a couple of hours for a visit to a pair of deceptively modest-looking exhibitions downtown?

The shows -- which are in walking distance of each other, one at REDCAT and the other at the Central Library -- offer very different takes on the urban and architectural history of Los Angeles.

Each one closes Sunday. And each one is worth seeking out for the subtle intelligence it displays about the city’s built landscapes and hardest-to-shake stereotypes.

In REDCAT’s “Small Case Study House,” the architects Yoshiharu Tsukamoto and Momoyo Kaijima, who call their influential Tokyo firm Atelier Bow-Wow, have installed three structures loosely based on the landmark postwar Case Study houses. While in residence last year at UCLA, the architects, both born in the 1960s, led a seminar on the Case Study program, visiting 10 of the houses.

The first thing you notice about the structures, though, is that they can’t be called houses at all: Each one is open to the elements, better suited to hold a backyard gathering than shelter a family, and rather loosely hammered together from salvaged timber. They’re probably best thought of as outdoor installations, hovering somewhere between residential design and landscape architecture. Designed at a small scale for a single activity, they suggest a spin on Japanese teahouse design.

That’s a departure from the Case Study houses, of course, which were designed by architects including Richard Neutra and Pierre Koenig and squeezed all the activities of an American family into a clean-lined, crisply designed, open-plan space. But it’s in line with the character of the firm’s other work, which relies on a concept called “pet architecture”: small structures that toy with notions of cuteness, ownership and portability.

The installation closest to the entrance of the REDCAT Gallery, called “BBQ House,” takes the form of an amphitheater, with three rows of seating wrapped tightly around three barrel barbecues. Next to it is a satellite dish-shaped piece entitled “Sunset House.” Tilted a bit toward the sky, it’s filled with pillows and positioned to offer a view of sunset scenes from around the city projected onto the gallery wall. At the back, finally, is “Hammock House,” a piece that has the look of a medieval catapult but is in fact designed as a double-hammock: It’s not possible to lie down and relax on one side of this structure unless someone is doing the same on the other side. It’s part outdoor recliner, part seesaw.

Happily, Tsukamoto and Kaijima have resisted the temptation to turn this show into a vanity project showing their recent architectural work, or even displaying their take on what it would mean to update the Case Study program in a literal, purely architectural way. Instead, they behave here more like artists, raising far more questions than they answer and being entirely content, even eager, to position these new works somewhere in the slippery middle ground between art and architecture or, more precisely, between concept and function. At the same time, the show is very clearly dedicated to a straightforward idea about construction, about nailing boards together in an honest and less-than-polished way.

The show offers a critique of American excess without wanting to give up on an admiration for the resiliency of our culture and, in particular, the loose, informal appeal of the best Los Angeles architecture. The installations don’t just suggest but require togetherness -- and even, in the case of the hammocks, reject the very idea of reclining alone in favor of an odd sort of teamwork.

If the “Sunset” piece argues that the end is near for American hegemony, the others have a rough-edged optimism, even a sweetness, about L.A. culture. They create open-air places to gather, relax and even celebrate in hard times, with all the contradictions that combination implies.

At the Central Library’s Getty Gallery, meanwhile, a similar attempt is underway to discover something about the city’s present by digging into its past. “L.A. Unfolded: Maps From the Los Angeles Public Library” displays a number of historic and recent maps of Los Angeles alongside quotes from scholars, mapmakers and others about how technology is changing the very idea of navigation through -- and knowledge of -- cities.

Curated by Gloria Gerace and Glen Creason, the exhibition is a gold mine for map fanatics, of whom every city has plenty. But it is most valuable for the questions it raises about the way Angelenos have related to the urban landscape -- and how that relationship is changing.

No U.S. city needs maps, or has exploited them, more than Los Angeles: Star maps, tourist maps and real-estate maps have all helped sell the notion of the city as a sunny oasis. Los Angeles is laid out in a manner that has nothing to do with the reliable grids of Manhattan and other urban centers. Its most famous architectural icons -- including many from the same Case Study program explored in the REDCAT exhibition -- are scattered across the landscape, generally hidden from view by fences or lush landscape and impossible to find without a guide.

Indeed, we have learned to navigate the city in a series of point-A-to-point-B transactions. Instead of walking through a neighborhood and understanding it from the ground up, we tend to move directly from house to office or house to restaurant, barely slowing to acknowledge the landscape in between.

At least that’s how it has long been. Growth, density, traffic and new demographics are changing that equation. Lives and architecture are more exposed and connected in Los Angeles than they have been since the city’s earliest days. A new focus on neighborhoods is promoting the idea that it is possible to make your way in the city without a map, or at least with some combination of iPhone or Google Maps navigation and your own eyesight and sense of adventure. Infill construction means we spend more time now in the parts of the city that used to be interstitial territory on the map -- the L.A. version of “fly-over country.”

That transition from the city as an arrangement of a la carte pleasures to a denser, more collective one -- a change as much psychological as conceptual or physical -- is among the richest subjects explored in this surprisingly rewarding show.

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christopher.hawthorne @latimes.com

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‘Small Case Study House’

Where: Gallery at REDCAT, Walt Disney Concert Hall, 631 W. 2nd St., Los Angeles

When: Noon to 6 p.m. daily. Ends Sunday.

Price: Free

‘L.A. Unfolded:

Maps From the Los Angeles Public Library’

Where: Getty Gallery, Central Library, 630 W. 5th St., Los Angeles

When: 10 a.m. to 6 p.m. today and Saturday, 1 to 5 p.m. Sunday. Ends Sunday.

Price: Free