The Squiggle came to life at the beginning of the years 2000 when designer Damien Newman had the opportunity to design some complex desktop software. And the need to convince the client of the value of the process of design, in less than thirty seconds. It's a few laters when Damien was working at IDEO a colleague surprised him by having found it online (somehow) and using it for the IDEO Intern '06 T-Shirts. One of the books that might have made it even more known is Business Model Generation where the process was displayed.
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The Design Squiggle is one of the images I love to show to people who are new to the design mindset because it translates visually how they'll feel emotionally.
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People often react and say: "How that seems pretty messy at the start", and then you can agree and explain why. And you can show that at the beginning there is a lot of trial and error. You can show that there are moments that feel like back and forth. You can show that design isn't a perfect science with a clear step by step formula. But it's all worth it. To me this drawing is the one that visualizes the nature of the iterative way of working in the best way possible because it doesn't speak to your rational mind, but to your emotions.
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We just need to embrace complexity and mess, then it’s not a scribble anymore. — Roman Lihhavtshuk, Design Manager at F-Secure Corporation

I feel like the end of the squiggle should be a heartbeat pattern. Satisfying customer needs and business goals (via service design) are the heart of a success framework, no? — Brian Sullivan, Principal at Sullivan Designs

I found the image of this process on the official Design Squiggle website created by Damien Newman. There you'll find explanation about the history of the process and a few other fun examples of how the process has been used since then.