Decades after their founders connected, Apple and Issey Miyake released a collection of phone pouches that have some people baffled. They hope it will inspire creativity.

It was a meeting of the minds.

In 1981, when Steve Jobs, the founder of Apple, met Issey Miyake, the Japanese designer, the two connected on the power of functional dressing. Mr. Jobs, inspired by the uniforms Mr. Miyake designed for Sony employees, commissioned the designer to create similar attire for his team in Cupertino. The idea got him “booed off,” Mr. Jobs told his biographer Walter Isaacson.

That didn’t stop the men from working together. Mr. Miyake created the black mock turtleneck Mr. Jobs adopted as part of his uniform, which he completed with blue Levi’s 501s and New Balance sneakers. The relaxed outfit shaped what the public came to expect from tech leaders’ style choices.

The two men’s companies never formally collaborated during their lifetimes. But now, four decades later, they have.

In a buzzed-about collaboration that has drawn a range of reactions, Apple and Issey Miyake joined forces to introduce an accessory inspired by Miyake’s “A Piece of Cloth” project, which uses modern technology to create garments that require the person wearing them to think creatively about how it might affect them and their lives. The result: a long fabric pouch for your phone that is called the iPhone Pocket.

The product, which was released on Friday, is a ribbed, vividly hued knit pouch designed to hold a cellphone. As it expands, the mesh paneling underneath the fabric also allows it to hold other accouterments. It can be worn cross-body or attached to a handbag strap, dangling like a charm. Its ribbed texture takes inspiration from Issey Miyake’s popular Pleats Please line.

The partnership came “naturally,” Yoshiyuki Miyamae, the design director of Miyake Design Studio, Issey Miyake’s parent company, said in an interview. It was a result of the brands sharing what they had learned about design over a few years.

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