The Surrealist writer André Breton once declared that beauty would have to become convulsive, otherwise it would cease to be. As if in late vindication of this injunction, the paintings of Dawn Mellor set off a strange chain reaction of anger and lyricism. She is an artist driven by both sociopolitical protest and ambiguous, personal longings, linking her to Surrealism. Her paintings are at the dual service of Eros and Thanatos, awash equally with alienation and empathy, desire and indignation.

Her vulgarity and iconoclasm are truly prodigious, even within the context of a popular culture that is permeated by brash assaults on traditional values. Her latest show, “A Curse on Your Walls,” has two themes, or perhaps, more appropriately in her case, targets. The first is Dorothy from “The Wizard of Oz,” shown in six mammoth canvases, engaged in bizarre, macabre activities. The second involves a salon-style hang of 71 of Ms. Mellor’s sadistically satirical easel portraits of contemporary and historical celebrities — an ongoing series she titles “Vile Affections” — culled from cultures high and low.

An extremity of attitude comes across in both her paint handling and a visual imagination that is at once vivid and vicious. But through it all is a love of the sheer dynamics of translating mediated images into paint, of handling space, of describing details while keeping up an appearance of frenzy and desperation. She is that rare, wondrous thing: a “bad” painter who really knows how to paint.

At the younger end of the Young British Artist movement lead by Damien Hirst and Tracy Emin, Ms. Mellor came to attention at the same time as Cecily Brown, who could be described as a cooler version of Ms. Mellor’s “bad girl” update of Philip Guston. Closer to her particular fusion of the erotic and the political is American painter Nicole Eisenman, whose imagery, like Ms. Mellor’s, has a love-hate of media constructions of girlhood.

The shifts in scale between the Dorothy paintings and the “Vile Affections” is galvanizing. The Oz pictures are up to 10-by-12-feet; the anti-portraits are generally 2 or 3 feet tall. Both brim with a Gothic humor that is richly disturbing. In her journey through the dark corridors of Ms. Mellor’s imagination, Dorothy survives more than the Wicked Witch of the West would have concocted for her, although certainly the West, in the geopolitical sense, has much to blame for her travails. In “Yellow Bricks Dorothy” (2007-08), for instance, the heroine triplicates into a row of slave workers schlepping bricks in wheelbarrows. In one of these manifestations, Dorothy’s head transmogrifies into a skull of harrowing beauty, another into a brick itself. In “Death Army Dorothy” (2008), she stands amidst a bombed-out city at the head of a group of 10 gold-skinned robots, redolent of the James Bond movie “Goldfinger.” Each of the robots has a white skull for a head, a pretty blue bow in its “hair,” and Renaissance armor on its left shoulder. In “Partisan Dorothy” (2007-08), she has become a terrorist with a bloodcurdling gaze, wielding a submachine gun.

Ms. Mellor’s handling of paint is often at its most subtle and tender when her politicizing is at its most blatant and brutal. “Giant Dorothy” (2007-08) has Dorothy kneeling before a soap-bubble globe containing her longed-for Kansas homestead, floating above a blasted heath. But in a gesture that cripples the innocence of the image, she has spouted an erect penis (in the same blue gingham of her dress) that penetrates the bubble. Her face duplicates as it turns its gaze from the house to the ground, a beautifully handled passage. Around her head is a halo of burning white slogans of militant, anti-religious, anarchic character, burning bright against the dark, ominous sky, that read, “Destroy the Abrahamic Moralist Trilogy of Terror. We will establish a new state. Kill Breeders, Steal Babies.”

Ms. Mellor’s celebrity portraits are at once more extreme and more ambiguous than her Dorothy murals — despite the rape and pillage the latter entail. You are never quite sure what the criteria might be to enter her pantheon, which consists both of personalities toward whom one imagines she is politically antipathetic (Condoleezza Rice, Margaret Thatcher, Shimon Peres, Mother Theresa, and even Cherie Blair come in for rough treatment) and gay icons such as Barbra Streisand, Billie Holliday, Audrey Hepburn, and Madonna. Madonna, in fetish gear and with smoke coming out of her ears, has gaping wounds about her body, a recurring trope in Ms. Mellor’s portraits that perhaps reflects the artist’s past as an S-and-M cabaret performer. Even feminist theorists such as Julia Kristeva and Hélène Cixous come in for some gentle mockery.

Nicole Kidman, who has been the subject of infatuated portraits by Ms. Mellor in the past, has in this series sprouted a beard. There are abstract rays of color intersecting in her left eye. When in the past she was depicted as Judith clutching the bleeding head of Tom Cruise-as-Holofernes, the symbolism was not difficult to decode. The bearded lady, though, could mean anything — and is arguably richer for the ambiguity.

Ms. Mellor manages simultaneously to recall the ferocious politics of Sue Coe and the fey infatuations of Elizabeth Peyton. She seems intent on debunking the whole culture of celebrity while at the same time working through her individual feelings, which run an emotional gamut, toward these individuals. They are given a life in paint with which to counter the disturbingly conflicted meanings projected upon them, whether by the media or by Ms. Mellor herself.

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If Ms. Mellor represents the lesbian artist at her most Dionysian, Danica Phelps’s fusion of the personal and the political could be taken as an Apollonian antidote. Ms. Phelps makes work that documents the artist’s life with a systematic obsession that is at once absurdist and capable of generating its own kind of weird poetry.

Ms. Phelps uses a color-coded system to record her day-to-day activities in monetary terms, in diary cum flow chart form, with red denoting expenditure, green income, and gray debt. A complementary tack presents the ongoing narrative of the artist’s life in graphic illustration.

The present show has a few pieces of Ms. Phelps in accountancy mode, a side of her project that seems to be winding down in favor of other modes of expression. The artist stopped compiling her compulsively accurate daily lists 18 months ago, but even to cope with the backlog needed assistants to handle her $677,000 mortgage, as each dollar has to be denoted by hand. A workstation for assistants to whom this sisyphian task has been delegated is part of the exhibition. Ms. Phelps has made a sculptural piece from letters cut from the last list she made, on January 24, 2007, arranged as concrete poetry.

The main event in this show, however, is a frieze-like set of drawings — running around the walls of the gallery like the Bayeux tapestry, initially in joined-together etchings, then in graphite on paper — that chronicles the artist’s successful in vitro fertilization treatment. She undertook this process in India, where it is a fraction of the cost that it is in America. Moghul architecture and tile work interweave with storyboard episodes in clinics, with her girlfriend in a hotel, visiting various sites, and so on.

As ever, the artist’s clean lines, artful overlaps, and empathic yet gentle touch impart a pleasing neatness to drawing, though her nerdishness nonetheless ensures that no one loses sight of the cool, conceptual attitude that underscores the whole enterprise.

Mellor until August 8 (83 Grand St., between Greene and Wooster streets, 212-279-9219).

Phelps until July 18 (530 W. 24th St., between Tenth and Eleventh avenues, 212-989-7700).