These creations are made in the Chaoscope software.
From what I understand, you can create a "point cloud" from the software, but massaging it into a more physical form, like an STL file (which we could print on the Ultimaker), is hard to do. However, there has got to be a way around that. Apparently Geomagic is the software that people use to do that sort of thing professionally. It's hugely expensive, but you can download a free 30 day trial.
Peter Jansen also did other sculpture,
beside the strange attractors


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