I had the same experience. Whenever I use t-SNE with noisy data or data grouped densely around some point, they tend to have a very similar visual structure as

I had the same experience. Whenever I use t-SNE with noisy data or data grouped densely around some point, they tend to have a very similar visual structure as the example given in this experiment: a circular shape with some points making small "clusters" but with rather no significant meaning.