Incubating chicken eggs and objects made by prison inmates are among the artefacts currently on view in a tiny museum in a New York City alleyway (+ slideshow).

Dubbed 4th Season, the unusual show is the latest organised by the Mmuseumm, a cultural institution that stages exhibitions inside a 36-square-foot (three square metre) storefront space that was once a freight elevator. The museum is located in a graffiti-adorned alleyway in the Tribeca neighbourhood.

Founded in 2012, the self-described "modern natural history museum" presents objects and designs that "explore themes of daily human existence, social issues and current events."

Its mission aligns with the "rapid response" collecting movement, in which objects that relate to contemporary issues are quickly acquired by cultural institutions.

London's V&A museum has acquired jeans, a 3D-printed gun and Katy Perry lashes as part of its rapid-response strategy, which was introduced in 2013. It now has a dedicated Rapid Response Collecting display on view until January 2016.

The Mmuseumm exhibition features a range of items organised under 16 themes. Some pieces were selected by the museum, while others were produced or assembled by outside artists.

Incubating Chicken Eggs comprises 12 real eggs sitting within a custom-designed vitrine kept at approximately 90 degrees Fahrenheit (32 degrees Celsius). The eggs are expected to hatch during the exhibition.

Stranger Visions is a collection of 3D-printed human masks produced by artist and "bio-hacker" Heather Dewey-Hagborg. To create the faces, the artist extracted DNA from chewing gum, cigarette butts, and other material discarded by people she had never met.

Through DNA analysis, she was able to create genetic profiles that were then subjected to facial algorithms. "The end result are portraits that speak to today's culture of biological surveillance," said the museum.

The exhibition also includes discontinued promotional items given out by pharmaceutical companies, from an Ambien-branded computer mouse to a wrench advertising Oxycontin.

"Due to government and public pressures to clean up their act, pharmaceutical companies voluntarily halted production on these bizarre gift items that are intended to encourage doctors to prescribe [their products]," said Ryder Ripps, the conceptual artist who assembled the collection.

The Cornflake Index consists of more than 30 individual cornflakes, each slightly different in shape and colour. The collection was produced by UK artist Anne Griffiths.

"I sort through and have categorised these specimens and in the manner of a 19th-century naturalist," stated Griffiths. "I am working to reveal the Cornflakes' morphological patterns and mutations through my indexing system, which categorises by brand, size, colour, texture, geometry, contortion and twinning."

Prison Inmate Inventions features objects from jewellery to a handmade tattoo gun, collected by Stefan Ruiz, who taught art classes at a California jail.

"Inmates would often take the class as a creative outlet but also to learn a practical skill that they could use in order to make money in the prison," Ruiz said. "Some of the items here were considered contraband. But their potential for making money outweighed the consequences."

Other artefacts in the exhibition include plastic coffee cup lids, homemade gas masks, anti-riot police gear, items surgically removed from human bodies and chunks of weathered styrofoam that resemble natural rocks.

In addition to the 4th Season exhibition, the Mmuseumm has opened a new annex called Mmuseumm 2, located just a few metres from the original venue.

In this new storefront space – totalling 20 square feet (two square metres) – the museum has just debuted an installation created with illustrator and designer Maira Kalman, who is the mother of one of the Mmuseumm's co-founders.

The installation is a full-scale replica of a closet that belonged to Kalman's late mother, Sara Berman. All of the contents – clothing, shoes, and other personal items – are shades of white and are meticulously organised.

"In stark contrast to the alley, the uniqueness of the recreation is evident in her entirely white wardrobe and clear pursuit of perfection: starching, ironing, folding, and stacking with loving care – seeking order amidst the chaos of life," stated the museum.

The Mmuseumm was founded three years ago by Alex Kalman, Josh Safdie and Ben Safdie. "Mmuseumm's mission is to allow people to look at the big through the small – to explore the modern world through the curation of modern artefacts," said Kalman.

Past collaborators have included artist Tom Sachs, designer Andy Spade, and the popular American radio show Radiolab.