Here's the steps on how to achieve this in Blender.

1. Cell Fracture (any setting as you please).
2. Remove Doubles (adjust the merge of vertices, this help to clean things for Skin Modifier)
3. Skin Modifier
4. Smooth Modifier

No matter which version of Blender you are using, this process should be quite self-evident, and well within the grasp of any intermediate Blender user.  I believe the object in your photo was created using Grasshopper for Rhino, or some other Nurbs-based mathematical modeling software, but it's entirely possible in Blender using polygons, with the right combination of addons and modifiers. The results may not be exact, depending on how you decide to fracture the object, but you should be able to come quite close.

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