Wolfram Summer School 2018: LatticePlot
Author
Colin Nancarrow
Title
Wolfram Summer School 2018: LatticePlot
Description
Wolfram Summer School 2018: LatticePlot
Category
Essays, Posts & Presentations
Keywords
Wolfram Summer School 2018
URL
http://www.notebookarchive.org/2018-12-53xj8yh/
DOI
https://notebookarchive.org/2018-12-53xj8yh
Date Added
2018-12-11
Date Last Modified
2018-12-11
File Size
1.61 megabytes
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WOLFRAM SUMMER SCHOOL 2018
Last modified on: Monday, July 9, 2018 at 15:03
Author Info
Name:
Colin Nancarrow
Mentor:
Jonathan Gorard
Affiliation:
University of Chicago
Poster Session Content
Title of project:
LatticePlot
Goal of the project:
To code a preliminary framework for visualizing computation on 3D lattices. Problems formulated in 3 dimensions and on nontrivial lattice structures often prove difficult to approach with analytical methods; this is a big problem in Condensed Matter Physics.
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Image:
Summary of Results:
Can plot new cellular automata in three dimensions on the body-centered cubic lattice. Shown above is the evolution of a simple cellular automaton whose rule is basically “grow outward” started from a single point. Then we show the neighborhood structure of an atom on the corner of a lattice cell and an atom in the center of a lattice cell. Finally, the infinite-time evolution of a 3D game of life, which has left 5 “still lifes” of three different types.
Future work:
1. Code can be made vastly more efficient and modular.
2. Two other Bravais lattices of interest, as well as the Pyrochlore lattice.
3. Ising model should be implemented; code too slow to accommodate this currently.
4. TomographyPlot for Bravais lattices: Would produce animations of cross-sections of the lattice along planes specified by Miller indices . This would probably be necessary for seeing deep inside any complicated structures on a large lattice.
2. Two other Bravais lattices of interest, as well as the Pyrochlore lattice.
3. Ising model should be implemented; code too slow to accommodate this currently.
4. TomographyPlot for Bravais lattices: Would produce animations of cross-sections of the lattice along planes specified by Miller indices . This would probably be necessary for seeing deep inside any complicated structures on a large lattice.
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Local Lattice Structure and Simple CA
In[]:=
LatticeData["BodyCenteredCubic","Image"]
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Conway’s Game of Life on Body-Centered Cubic Lattice
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Detailed Project Notes
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Main Results in Detail
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Cite this as: Colin Nancarrow, "Wolfram Summer School 2018: LatticePlot" from the Notebook Archive (2018), https://notebookarchive.org/2018-12-53xj8yh
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