By the look of the renderings officially unveiled on Wednesday morning, New York’s next significant landmark may be the city’s biggest Rorschach test, too.

Big, bold and basket-shaped, the structure, “Vessel,” stands 15 stories, weighs 600 tons and is filled with 2,500 climbable steps. Long under wraps, it is the creation of Thomas Heatherwick, 46, an acclaimed and controversial British designer, and will rise in the mammoth Far West Side development Hudson Yards, anchoring a five-acre plaza and garden that will not open until 2018. Some may see a jungle gym, others a honeycomb.

But Stephen M. Ross, the billionaire founder and chairman of Related Companies, which is developing Hudson Yards with Oxford Properties Group, has his own nickname for “Vessel”: “the social climber.” And the steep price tag Mr. Ross’s privately held company is paying for Mr. Heatherwick’s installation? More than $150 million.

The back story of the stair-filled “Vessel” involves two men who are in step in more ways than one: a designer known for dreaming big, and a deep-pocketed developer who will spend whatever it takes to make a statement.