Read on Twitter
Prediction: Holarchy with foliated levels will be a dominant aesthetic structure in scientific communication in ~2 years. https://twitter.com/robertghrist/status/1180777892956921856
And here we go: https://twitter.com/3blue1brown/status/1196492747328241664?s=20 With convolution layers and renormalization being actively researched, foliation would be a central visual tool for scientific discourse.
Exhibit 3 — A semantic layout of foliated convolution network layers in an explorable 3D space. https://twitter.com/Reza_Zadeh/status/1209194637715374080
This style of exploring phenomena by breaking it down and making it explorable in multi-dimensional space needs to be more common in scientific communications. Art by Adam Harley: https://scs.ryerson.ca/~aharley/vis/ and @andrey_kurenkov: http://www.andreykurenkov.com/projects/major_projects/KerasJS3D/
Not really a foliation, but highlights the aspect that graphs can be recursively nested.
Source: https://homes.cs.washington.edu/~jrl/papers/pdf/diffusiveSRG.pdf
Source: https://homes.cs.washington.edu/~jrl/papers/pdf/diffusiveSRG.pdf
More foliations in the wild.
1/ Topological Quantum Computations: https://www.ams.org/journals/bull/2018-55-02/S0273-0979-2018-01605-4/S0273-0979-2018-01605-4.pdf
2/ Chiral Crystals: https://www.nature.com/articles/s41586-019-1037-2
3/ Magnetic Topological Insulators: https://physicsworld.com/a/magnetic-topological-insulator-goes-clean/
1/ Topological Quantum Computations: https://www.ams.org/journals/bull/2018-55-02/S0273-0979-2018-01605-4/S0273-0979-2018-01605-4.pdf
2/ Chiral Crystals: https://www.nature.com/articles/s41586-019-1037-2
3/ Magnetic Topological Insulators: https://physicsworld.com/a/magnetic-topological-insulator-goes-clean/
A neat foliation diagram from this deep graph-CNN paper: https://www.cse.ust.hk/~yqsong/papers/2018-WWW-Text-GraphCNN.pdf
Thought I should add the rad work @anvaka is doing with graphs on this thread on foliations: https://twitter.com/anvaka/status/1253572922641313795
