Dugan (@duganhammock) 's Twitter Profile
Dugan

@duganhammock

Is it maths? ...or is it art?

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calendar_today13-03-2019 23:04:46

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These are 3D slices of a 4D hypershape known as the dodecacontachoron (120-cell) which is a tessellation of the hypersphere by 120 dodecahedrons.

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Progressive 3D slices of the 4-dimensional hypertorus. Notice the discrete critical points as the slice changes topology from a sphere, to a torus, then a genus-2 surface, with the equatorial slice being two separate tori.

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Slicing the 4D hypertorus again. This time the slice hyperplane is tilted and the locations of the 8 critical points are shifted, altering their sequencing. As a result, the equatorial slice is not a pair of disjoint tori, but instead is a surface of genus 3.

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Penrose tilings made using de Bruijn's multigrid method. These have a nice effect when zoomed out. Made using @Wolfram language. Notebook available here: community.wolfram.com/groups/-/m/t/2…

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Rhombic tiling using de Bruijn's multi-grid method. This tiling uses a 49-grid pattern. Perturbations in the tiling are contrained so as to preserve 7-fold rotational periodicity.

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Alex Kontorovich will be in Austin next week. Would be awesome if we had an opportunity to engage with him. x.com/AlexKontorovic…

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Excited to accompany Stephen Wolfram at the augmentation lab Human Augmentation Summit hosted by the MIT Media Lab MIT Media Lab. Looking forward to present my work and to see what awesome projects have been created! ekkolapto Curt Jaimungal Daniel Van Zant