“Classicists are people who look out with their backs to the world,” the painter Agnes Martin once wrote in a prose poem. Later she added, “You stand with your back to the turmoil.” These words come from a trenchant essay by Lynne Cooke accompanying “Homage to [a] Life, Agnes Martin’s Paintings, 1990–2004,” the fifth and final installment of what has been an ongoing presentation of the artist’s work at Dia: Beacon.

Was Martin (1912–2004), the austere and generally unacknowledged master of late Modernist abstraction, a classical artist? Surely there are as many definitions available as there are critics to utter the word. But, to the extent that her paintings are concerned with order and pointedly not concerned with self-expression, they are classical. They are classical in that Martin abjured emotional exhibitionism: She turned her back on the turmoil. Yet if her paintings are rigorous, ruled, disciplined, cool, and superficially simple, they are also atremble with electric lines, suffused with the subtlest and most joyful colors, alive with affirmation, hot from slow-burning passion, and, to the right eye, about as simple as a twinkling star to a cosmologist.

Consider the manifold variations elaborated in the 23 paintings on view in Beacon. At age 80, around the time of her 1992 retrospective at the Whitney Museum, Martin was working, in acrylic and graphite, on 6-foot-square canvases, as she had for decades. In “Untitled #2” (1992), for example, a thick band of pale, duck-egg blue, a band salmon pink, a thin orange band, and a thin white one, are each defined by horizontal graphite lines that repeat four times.

As with all her paintings, the work has an entirely different visual impact depending on whether one inspects it from close up or gazes upon it from several yards away. Up close, the colors modulate like washes. They pool and eddy, bulk and run; the graphite lines waver like the plucked violin strings. The details, be it a bit of lint stuck in the pigment or the imprecise melding of line and color, are practically infinite. From farther away, the colored bands turn solid and, in part because the graphite lines never reach the edges of the stretcher, seem almost to float free.

This dynamic — to engage equally at the local level of detail and as a structured whole — is essential to great art. In Martin’s work, the interaction of balanced order and trembling energy is, and is meant to be, affirmative: In Ms. Cooke’s words, Martin’s was “an affect based in feelings of happiness, innocence, exaltation, and joy.” Contrary to the opening citation, abstraction was for Martin not a renunciation of the world but an embrace.

When Martin was in her 80s, it became difficult for her to manipulate the 6-foot stretchers and so, shortly after the Whitney retrospective, she switched to 5-foot square stretchers. Advancing age did not, however, sap her spirit, as is evidenced by the titles in the 1999 series “Innocent Love,” such as “Love,” “Contentment,” “Happiness,” and “Innocent Happiness.” For an artist so dedicated to variation within a fairly narrow range of formal options, Martin rarely designated a group of work as a series. So it is particularly exciting that one of the exhibition’s three rooms is given over to eight canvases from “Innocent Love,” all on the smaller stretchers.

What unites these works, aside from the smaller format, is the presence of duck-egg blue. One can see the title piece as two broad planes of the pale blue coursing through a ground of white, or as two extra-wide bands separated by three thinner white bands.

The relentless horizontal drive of those bands ended, along with the decade, in a final creative outburst, which here, like “Innocent Love,” receives its own room. In “Little Children Loving Love” (2001), pale blue-green stripes, each sliced lengthwise by a graphite line, alternate with thinner pale-yellow stripes. A single horizontal graphite line interrupts the vertical stripes, bisecting the canvas.

The most astonishing change occurred in 2002, when, according to Ms. Cooke, Martin “not only abandoned color but forsook luminous washes for impastoed surfaces of viscous acrylic paint.” A single plane of mottled gray runs to the bottom from the top edge of “Untitled #16” (2002). The ground is white, and the gray pigments spill over the wavy graphite lines defining the borders on the side.

Again, far from being evidence of a late renunciation of color, these last works seem to inaugurate a new era of formal experimentation. Shapes appear. In “Untitled #17” (2002), two gray squares hover near the canvas’s lower corners in a large black plane roiling with painterly incident, where lighter and darker areas mass and commingle. A lone gray band defines the plane along the stretcher’s top edge.

Although Martin gave up painting at age 92, after finding she couldn’t move even the 5-foot stretchers on her own, these final, forward-pushing monochrome works feel heroic rather than senescent. She ended as she lived, not so much turning her back on the world as looking out on it.

Until November 26 (3 Beekman St., Beacon, N.Y., 845-440-0100).