Circular typography design

I just ran across this, and I'm curious about whether it can be replicated in TeX... Ideally one would have the spiral getting tighter and tighter as one got to the centre, as in I know TikZ has ...

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Rounded fonts are commonly used in creative designs to add a bit of elegance and style to titles and headings. They are also a great choice for paragraph text as they improve readability. You can use rounded fonts with almost every type of design. Including for crafting logos, poster title...

I'm having problems adding text using the type path tool in illustrator within a round vector. Every time I go to type on a path though the background colour disappears. Here's an example: If any...