Blob equation in $\Bbb{R}^3$

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I'll start by apologizing for the nature of my request. I'm not sure if this kind of post fits exactly what is expected of the forum, but at the same time I can't think of a more suitable place.

I'm looking for a blob around a sphere that looks good in a presentation. The blob should be the image of a smooth function $\phi:S^2\rightarrow \Bbb{R}^3$ such that $\forall p\in S^2~\exists \lambda\in\Bbb{R}_{>1}~\phi(p) = \lambda p$ (purely for aesthetic reasons). A sphere or an ellipse would do, but I'd like something that sounds less biased. Something more like an amoeba.

At the presentation, it will be semi-transparent, so you can see the sphere inside it, and I intend to plot it with the help of Geogebra. It should look something like the image below.

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