Halsey Rodman's "It's Not Getting Bigger You're Getting Closer" at Laurel Gitlen.

Happy birthday, abstract painting! One of the prides and joys of Western modernism is in the vicinity of its first centennial. It’s hard to be much more exact, since its invention was a scattered effort extending over years if not decades. Fans of Frantisek Kupka should have celebrated last year; Kandinsky’s crowd can uncork the Champagne in 2012. Devotees of Mondrian or Malevich will have to wait a year or two longer.

Of course one can make too much of this anniversary. Beyond the narrow precincts of Western painting and sculpture, abstraction has been a free radical in visual culture for a lot longer than a century, a vital component in ceramics and textiles worldwide, for example, since time immemorial, or in Chinese painting for most of a millennium. Still, within a global history of abstraction, the Western variety has its own substantial chapter, one that is still being written.

Since its inception, abstract painting in the West has given as good as it has gotten. It has spawned styles, schools and opposing camps, not to mention volumes of criticism. It has repeatedly cross-fertilized with representational painting; absorbed found materials and aspects of popular culture; adopted the strategies of postmodern irony and appropriation.

In addition the principles of abstraction have spread to photography and sculpture and beyond — even to the mind-set behind Conceptual Art, with its penchant for systems, categories and repetition that isolate and reorganize, and thereby abstract, aspects of reality. It is worth remembering, when considering the ever-expanding definition of abstract art, that the term refers to the act of abstracting from reality. For whatever reason, such art — in paint and other mediums — is unusually visible in Manhattan galleries this summer. The shows in question don’t always set out to focus on abstraction per se, but that doesn’t stop them from providing a lively account of some of its movements.

Miguel Abreu Gallery

The camera — as a tool for creating not so much abstraction but the aura of it — is at the center of “False/Divide: representations of abstraction in a few photographic works,” a slightly esoteric but completely intriguing show at Miguel Abreu (36 Orchard Street, Lower East Side). Basically, the works here use different elements of photography to make the world less legible, forcing us to sort through what we’re seeing, what we think we’re seeing, and what we’re thinking.

Liz Deschene’s silver-toned photogram is blank, a ghostly modernist monochrome whose main visual incident, in its lower left corner, is a shadow on or crease in the paper; you can’t tell which. Eileen Quinlan’s silver gelatin print, an angular abstract, seemingly made with light, shadow and perhaps a shard of mirror, is only slightly more substantial. And Zoe Leonard presents two photographs of what appear to be the same tangled bush with berries — one large and in color, the other smaller and black and white — to mind-bending effect. Puzzling out whether they are from the same negative dissolves the images into masses of details.

Sam Lewitt achieves a similar mystery by taking the letters and forms from hot-type printing, photographing them individually, then enlarging and combining the images on a computer. The final assemblagelike composition of perpendicular elements of wood and metal is completely ambiguous in terms of its actual size, weight, function, orientation and vintage, although it resembles one of Irving Penn’s elegant, white-ground images.

Moyra Davey’s 1990 color photograph “Copperhead #1” features an especially startling enlargement: the head on a Lincoln penny blown up to a height of two feet to resemble a relief. The magnified nicks and dents come across as sculptured texture, introducing the abstracting illusion of an artistic process that never happened.

This piece resonates unexpectedly with Matthew Buckingham’s “The Six Grandfathers, Paha Sapa, in the Year 502,002 C.E.,” a 2002 work that uses an illuminating timeline and a manipulated W.P.A. photograph to follow the mountain range that includes Mount Rushmore for nearly 70 million years, from its geological past, through its role in American history and into its distant future, when the presidential portraits have worn away like soap, becoming abstract. After reading the timeline detailing the troubled history of this particular stretch of rock, which the Sioux call Paha Sapa, the erosion seems just.

Lisa Cooley Fine Art

At Lisa Cooley (34 Orchard Street, Lower East Side), the equally exceptional “No Barrier Fun” lives up to its nearly nonsensical title (borrowed from a new song by Liars, the ostentatiously dour post-punk band). The show’s one photograph — an especially blurry body-print earthwork by Ana Mendieta — provides an uncanny link to the Abreu show (right next door). But otherwise much serious play transpires in mostly abstract paintings, and at every turn we encounter the freedoms (fun) of ignoring or accentuating edges and boundaries (barriers) of all kinds, whether literal, stylistic, bodily or psychic.

Ballast is provided by two older artists: Jo Baer, who reconfigures her signature two-toned Minimalist borders as quasi-legible letters, and Dan Walsh, who is represented by a field of concentric green lines that effectively mines the terrain of Frank Stella’s Black Paintings. But most of the work is by refreshingly unfamiliar names.

Using grout, Molly Zuckerman Hartung gives a small green abstract canvas a protective border of tiny stones and bits of glass to poetic effect. Heather Guertin surgically separates stretcher, frame, canvas and image into three separate occasions for painting. Francesca Fuchs makes small, wonderfully wan renditions of even smaller snapshots and drawings, including mats, frames and those frames’ shadows, that seem to be fading into the mist, toward abstraction.

In Scott Calhoun’s “Emperor Gum,” an enormous pale bubble jostles the canvas’s edges while ambiguous shapes and forms percolate within its translucent, skinlike expanse. Michael Bauer adds tilelike black-and-white borders to a painterly tangle that evokes the liquidity of Wols and the precision of early Dalí. And Alex Olson’s “Weaver” echoes much of all this with admirably relaxed simplicity: thicker white over thinner black on white, finished with some languid scratched lines, looping back and forth.

The show’s finishing touch is a continuing work by Peter Coffin in which members of the gallery staff draw circles in colored chalk on the floor around visitors, recording a linear afterimage.

Mitchell-Innes & Nash

Some of the works in “Item” at Mitchell-Innes & Nash (534 West 26th Street, Chelsea) are abstract, others reflect an abstracting state of mind. Organized by Mamie Tinkler, a gallery staff member, it focuses, in the words of the news release, on “lists, arrangements, collections and patterns” — reorganizing reality into things less real.

Mel Bochner’s painting “Die” covers a pink surface with synonyms and colloquialisms for the word, in bright cheerful colors. Next to it, Wayne Gonzales’s more traditionally abstract painting layers concentric hourglass shapes of white into a hazy reformulation of Op Art. To the other side Roger White’s nonrepeating pattern of blue shapes on white suggests a lifetime’s accumulation of abstract tchotchkes; next to it, the bottles and vases in a drawing by Giorgio Morandi seem only slightly more specific.

More abstraction of everyday life is seen in Stephen Shore’s 1972 photograph of a New York City shop window: a sign in the form of a pointing hand makes the row of five small potted cactuses in front of it look like a chorus line of mittens. Erica Baum reveals the random abstracting powers of the book index — “Nude Figures, Shells, Triumphs” — while reminding us that poetry is but another form of abstraction. Carol Bove makes a paintinglike surface from scores of peacock feathers (eyes only). And the performance artist Michael Smith poses at the center of a group portrait of his students at the University of Texas. It is as if the shapes in Mr. Gonzales’s painting have suddenly come into focus.

Anton Kern Gallery

At Anton Kern (532 West 20th Street, Chelsea), Shio Kusaka, a young Los Angeles artist, is making an exciting New York debut with works that deliberately relocate some of abstract art’s staples — grids, parallel lines, repeating marks — to ceramics, a medium that has yet to receive its due from modernist art history. Pots, bowls and vases cover the surfaces of two long tables, balancing subtly but insistently between function and nonfunction, sculpture and drawing.

Ms. Kusaka approaches her medium with a Process artist’s deliberation, combining and recombining abstract motifs, marking techniques, pale glazes, clay bodies and vessel shapes with a consistent sparseness. Every difference is carefully exploited, as in the contrast, for example, between black clay left plain and matte or glazed shiny black. If the Minimalist painter Agnes Martin had been a potter, she might have made vessels like these. Around Town

There is plenty more abstraction around town. In Chelsea, D’Amelio Terras (525 West 22nd Street) is presenting “Spray!” a punchy survey of the use of spray-paint by artists like David Smith, Keltie Ferris, Sterling Ruby and Rosy Keyser, with the star turn being a literally loopy spray painting from 1968 by Dan Christensen. At Tracy Williams Ltd. (521 West 23rd Street), a show called “Daniel Hesidence Curates” presents the work of seven women selected by Mr. Hesidence, a painter, including Kinke Kooi, Carrie Moyer and the newcomer Ji yeon Park. Circles, spheres, ellipses and various orifices abound, but the work is so diverse and strong you don’t initially see this formal through line. In a single gesture Mr. Hesidence seems to validate feminist essentialism and kiss it goodbye.

In SoHo you can see more of Ms. Kusaka’s ceramics in “Not Extractions, but Abstractions (Part 2),” at Clifton Benevento, a newly opened gallery at 515 Broadway. Jonas Wood contributes meditations on shades of orange in jaunty arrangements of triangles that evoke Christmas trees. Also outstanding are Polly Apfelbaum’s small riotously bright floor pieces in polystyrene clay (which can also be seen at D’Amelio Terras).

Back on the Lower East Side “In Here” at Laurel Gitlen (261 Broome Street) begins with another riot: Halsey Rodman’s “It’s Not Getting Bigger You’re Getting Closer,” a biomorphic aggregate of aluminum tubing, aluminum foil and wire that sends up 1960s abstract public sculpture from a base painted shades of fluorescent pink and orange. Behind it, three studies silhouette the sculpture on its side against bright colors, in successively bigger versions.

The main focus in “You Were There” at the Rachel Uffner Gallery (47 Orchard Street) is artistic growth. The show juxtaposes one work from 2010 and one from 2005 by each of seven artists of largely abstract inclination. Many developments are for the better. Joe Bradley, for instance, has returned to mucking around aggressively with paint and canvas with terrific results. And Justin Adian has gone from perfectly respectable abstract paintings to bulging painted reliefs that are weirder and more his own.

An energizing place to finish is Markus Linnenbrink’s “NOMATTERWHEREYOUGOTHEREYOUARE,” a site-specific painting in the tiny storefront gallery Number 35 (39 Essex Street). Mr. Linnenbrink has covered the walls, ceiling and floor with narrow bands of vibrant color that all seem to rush toward a vanishing point in one corner that they never quite reach, at least not in unison. The colors on the floor are often shaded: green to orange, gray to violet. The colors on the walls drip and splatter over one another. It’s a great space to stand in and think about abstraction as an infinitely renewal energy source.